{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T17:45:15Z","timestamp":1782841515408,"version":"3.54.5"},"reference-count":197,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2020,12,19]],"date-time":"2020-12-19T00:00:00Z","timestamp":1608336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Nantong Science and Technology Plan Project","award":["No. MS22019016"],"award-info":[{"award-number":["No. MS22019016"]}]},{"name":"Transportation Science Research Project of Jiangsu Province","award":["No. 2019Z02"],"award-info":[{"award-number":["No. 2019Z02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In recent decades, nonlinear damping identification (NDI) in structural dynamics has attracted wide research interests and intensive studies. Different NDI strategies, from conventional to more advanced, have been developed for a variety of structural types. With apparent advantages over classical linear methods, these strategies are able to quantify the nonlinear damping characteristics, providing powerful tools for the analysis and design of complex engineering structures. Since the current trend in many applications tends to more advanced and sophisticated applications, it is of great necessity to work on developing these methods to keep pace with this progress. Moreover, NDI can provide an effective and promising tool for structural damage detection purposes, where the changes in the dynamic features of structures can be correlated with damage levels. This review paper provides an overview of NDI methods by explaining the fundamental challenges and potentials of these methods based on the available literature. Furthermore, this research offers a comprehensive survey of different applications and future research trends of NDI. For potential development and application work for nonlinear damping methods, the anticipated results and recommendations of the current paper can assist researchers and developers worldwide to find out the gaps and unsolved issues in the field of NDI.<\/jats:p>","DOI":"10.3390\/s20247303","type":"journal-article","created":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T01:01:08Z","timestamp":1608512468000},"page":"7303","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":66,"title":["A Critical Review of Nonlinear Damping Identification in Structural Dynamics: Methods, Applications, and Challenges"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5992-8055","authenticated-orcid":false,"given":"Tareq","family":"Al-hababi","sequence":"first","affiliation":[{"name":"Department of Engineering Mechanics, Hohai University, Nanjing 210098, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maosen","family":"Cao","sequence":"additional","affiliation":[{"name":"Jiangxi Provincial Key Laboratory of Environmental Geotechnical Engineering and Disaster Control, Jiangxi University of Science and Technology, Ganzhou 341000, China"},{"name":"Nantong Ocean and Coastal Engineering Research Institute, Hohai University, Nantong 226000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5239-2673","authenticated-orcid":false,"given":"Bassiouny","family":"Saleh","sequence":"additional","affiliation":[{"name":"College of Mechanics and Materials, Hohai University, Nanjing 211100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6598-8713","authenticated-orcid":false,"given":"Nizar Faisal","family":"Alkayem","sequence":"additional","affiliation":[{"name":"College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Xu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.ymssp.2005.04.008","article-title":"Past, present and future of nonlinear system identification in structural dynamics","volume":"20","author":"Kerschen","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"043001","DOI":"10.1088\/1361-665X\/aa550a","article-title":"Structural damage identification using damping: A compendium of uses and features","volume":"26","author":"Cao","year":"2017","journal-title":"Smart Mater. Struct."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1155\/2007\/260183","article-title":"The evaluation of the damping characteristics of a hard coating on titanium","volume":"14","author":"Blackwell","year":"2007","journal-title":"Shock Vib."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1038\/nnano.2011.71","article-title":"Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene","volume":"6","author":"Eichler","year":"2011","journal-title":"Nat. Nanotechnol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1115\/1.1640356","article-title":"Identifying Coulomb and viscous friction in forced dual-damped oscillators","volume":"126","author":"Liang","year":"2004","journal-title":"J. Vib. Acoust. Trans. ASME"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.proeng.2016.05.013","article-title":"Experimental Determination of Structural Damping of Different Materials","volume":"144","author":"Mevada","year":"2016","journal-title":"Proc. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.jweia.2011.12.005","article-title":"Frequency modulated empirical mode decomposition method for the identification of instantaneous modal parameters of aeroelastic systems","volume":"101","author":"Zhang","year":"2012","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7061","DOI":"10.1016\/j.matpr.2017.11.370","article-title":"Study of damping in composite beams","volume":"5","author":"Kulkarni","year":"2018","journal-title":"Mater. Today Proc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"103518","DOI":"10.1016\/j.ijnonlinmec.2020.103518","article-title":"Identification and parameter estimation of cubic nonlinear damping using harmonic probing and volterra series","volume":"125","author":"Chatterjee","year":"2020","journal-title":"Int. J. Non. Linear. Mech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"103750","DOI":"10.1016\/j.mechmachtheory.2019.103750","article-title":"On discontinuous dynamics of a class of friction-influenced oscillators with nonlinear damping under bilateral rigid constraints","volume":"147","author":"Dou","year":"2020","journal-title":"Mech. Mach. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1016\/j.engstruct.2019.03.058","article-title":"Identification of an equivalent viscous damping function depending on engineering demand parameters","volume":"188","author":"Heitz","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.ast.2014.10.011","article-title":"Analytically driven experimental characterisation of damping in viscoelastic materials","volume":"40","author":"Ghiringhelli","year":"2015","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.jmps.2018.06.004","article-title":"Nonlinear damping in nonlinear vibrations of rectangular plates: Derivation from viscoelasticity and experimental validation","volume":"118","author":"Amabili","year":"2018","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1016\/j.jsv.2019.07.005","article-title":"Experimental identification of distributed nonlinearities in the modal domain","volume":"458","author":"Anastasio","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4709","DOI":"10.1016\/j.jsv.2013.03.029","article-title":"Experimental dynamic modelling of peripheral milling with process damping, structural and cutting force nonlinearities","volume":"332","author":"Moradi","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.ymssp.2017.04.037","article-title":"Coupled oscillators in identification of nonlinear damping of a real parametric pendulum","volume":"98","author":"Olejnik","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1088\/0957-0233\/19\/12\/122001","article-title":"Structural health monitoring for a wind turbine system: A review of damage detection methods","volume":"19","author":"Ciang","year":"2008","journal-title":"Meas. Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1016\/j.jsv.2017.02.001","article-title":"Seismic damage diagnosis of a masonry building using short-term damping measurements","volume":"394","author":"Kouris","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2751","DOI":"10.1016\/j.jsv.2010.01.012","article-title":"Two-mode vibration control of a beam using nonlinear synchronized switching damping based on the maximization of converted energy","volume":"329","author":"Ji","year":"2010","journal-title":"J. Sound Vib."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"112345","DOI":"10.1016\/j.compstruct.2020.112345","article-title":"Nonlinear impact and damping investigations of viscoporoelastic functionally graded plates with in-plane diffusion and partial supports","volume":"245","author":"Shariyat","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_21","unstructured":"Peters, R.D. (2003). Nonlinear Damping of the \u2018Linear\u2019 Pendulum. arXiv."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1007\/s11071-011-0031-5","article-title":"Nonlinear damping in a micromechanical oscillator","volume":"67","author":"Zaitsev","year":"2012","journal-title":"Nonlinear Dyn."},{"key":"ref_23","unstructured":"No\u00ebl, J.P., and Kerschen, G. (2016, January 19\u201321). 10 years of advances in nonlinear system identification in structural dynamics: A review. Proceedings of the ISMA 2016-International Conference on Noise and Vibration Engineering, Leuven, Belgium."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"106872","DOI":"10.1016\/j.ymssp.2020.106872","article-title":"A frequency domain nonparametric identification method for nonlinear structures: Describing surface method","volume":"144","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1016\/j.ymssp.2004.01.004","article-title":"Enhancements to the continuous wavelet transform for damping identifications on short signals","volume":"18","year":"2004","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.jsv.2019.03.010","article-title":"System identification of lumped parameter models for weakly nonlinear systems","volume":"450","author":"Heaney","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1119\/1.4935358","article-title":"Forced oscillations with linear and nonlinear damping","volume":"84","author":"Li","year":"2016","journal-title":"Am. J. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.jsv.2018.09.004","article-title":"Experimental results on the vibratory energy exchanges between a linear system and a chain of nonlinear oscillators","volume":"437","author":"Lamarque","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.ijsolstr.2015.08.017","article-title":"The modelling of nonlinear rheological behaviour and Mullins effect in High Damping Rubber","volume":"75\u201376","author":"Nguyen","year":"2015","journal-title":"Int. J. Solids Struct."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Haghdoust, P., Conte, A.L., Cinquemani, S., and Lecis, N. (2018). A numerical method to model non-linear damping behaviour of martensitic shape memory alloys. Materials, 11.","DOI":"10.3390\/ma11112178"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1177\/1077546309356463","article-title":"Dynamic modeling and analysis of an elastic mechanism with a nonlinear damping model","volume":"19","author":"Yuan","year":"2013","journal-title":"JVC\/J. Vib. Control"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.jsv.2006.12.031","article-title":"Viscous damping identification in linear vibration","volume":"303","author":"Phani","year":"2007","journal-title":"J. Sound Vib."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1016\/j.jsv.2009.01.022","article-title":"An assessment of damping identification methods","volume":"323","author":"Prandina","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.compositesb.2005.04.003","article-title":"Damping behavior of continuous fiber\/metal composite materials by the free vibration method","volume":"37","author":"Botelho","year":"2005","journal-title":"Compos. Part B Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.compstruct.2007.10.024","article-title":"Damping analysis of composite materials and structures","volume":"85","author":"Berthelot","year":"2008","journal-title":"Compos. Struct."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.jsv.2014.10.040","article-title":"Damping identification in frequency domain using integral method","volume":"338","author":"Guo","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"8547","DOI":"10.1021\/nn402479d","article-title":"Modeling and measurement of geometrically nonlinear damping in a microcantilever-nanotube system","volume":"7","author":"Jeong","year":"2013","journal-title":"ACS Nano"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"A23","DOI":"10.1051\/0004-6361\/201321175","article-title":"Nonlinear damped standing slow waves in hot coronal magnetic loops","volume":"553","author":"Ruderman","year":"2013","journal-title":"Astron. Astrophys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2588","DOI":"10.1016\/j.jsv.2014.01.024","article-title":"Complex dynamics of a nonlinear aerospace structure: Experimental identification and modal interactions","volume":"333","author":"Renson","year":"2014","journal-title":"J. Sound Vib."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.jsv.2017.01.006","article-title":"Analytical investigation of machining chatter by considering the nonlinearity of process damping","volume":"393","author":"Ahmadi","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_41","first-page":"55","article-title":"Numerical studies on vibration propagation and damping test V1","volume":"51","author":"Saarenheimo","year":"2018","journal-title":"Raken. Mek."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"106158","DOI":"10.1016\/j.aml.2019.106158","article-title":"Efficient schemes for the damped nonlinear Schr\u00f6dinger equation in high dimensions","volume":"102","author":"Cai","year":"2020","journal-title":"Appl. Math. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"107038","DOI":"10.1016\/j.ymssp.2020.107038","article-title":"Direct identification of nonlinear damping: Application to a magnetic damped system","volume":"146","author":"Lisitano","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1016\/j.jsv.2008.06.022","article-title":"Experimental identification of viscous damping in linear vibration","volume":"319","author":"Woodhouse","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"245407","DOI":"10.1103\/PhysRevB.93.245407","article-title":"Negative nonlinear damping of a multilayer graphene mechanical resonator","volume":"93","author":"Singh","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1007\/s11071-015-2257-0","article-title":"Model-free nonlinear restoring force identification for SMA dampers with double Chebyshev polynomials: Approach and validation","volume":"82","author":"Xu","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.ymssp.2018.02.014","article-title":"Superior nonlinear passive damping characteristics of the bio-inspired limb-like or X-shaped structure","volume":"125","author":"Bian","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"115184","DOI":"10.1016\/j.jsv.2020.115184","article-title":"Theoretical modeling and experimental analysis of nonlinear electromagnetic shunt damping","volume":"471","author":"Yan","year":"2020","journal-title":"J. Sound Vib."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"106504","DOI":"10.1016\/j.ymssp.2019.106504","article-title":"A bistable vibration isolator with nonlinear electromagnetic shunt damping","volume":"136","author":"Yan","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1115\/1.3424568","article-title":"A nonparametric identification technique for nonlinear dynamic problems","volume":"46","author":"Masri","year":"1979","journal-title":"J. Appl. Mech. Trans. ASME"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.jsv.2018.08.055","article-title":"Experimental direct spatial damping identification by the Stabilised Layers Method","volume":"437","author":"Lisitano","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"3205","DOI":"10.1016\/j.ymssp.2010.05.014","article-title":"Identification and quantification of nonlinear stiffness and nonlinear damping in resonant circuits","volume":"24","author":"Lumori","year":"2010","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1546","DOI":"10.2514\/1.26706","article-title":"Flutter-boundary identification for time-domain computational aeroelasticity","volume":"45","author":"McNamara","year":"2007","journal-title":"AIAA J."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1006\/mssp.2000.1308","article-title":"Application of the time domain Fourier filter output (TDFFO) method to the identification of a lightly damped non-linear system with an odd-spring characteristic","volume":"15","author":"Sainsbury","year":"2001","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.jsv.2019.01.025","article-title":"Nonlinear system identification of soft materials based on Hilbert transform","volume":"447","author":"Boz","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.paerosci.2015.05.006","article-title":"Damping measurements of laminated composite materials and aluminum using the hysteresis loop method","volume":"78","author":"Abramovich","year":"2015","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.ymssp.2018.08.012","article-title":"Multiple analytical mode decompositions (M-AMD) for high accuracy parameter identification of nonlinear oscillators from free vibration","volume":"117","author":"Qu","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1006\/mssp.1996.0078","article-title":"Natural frequencies and dampings identification using wavelet transform: Application to real data","volume":"11","author":"Ruzzene","year":"1997","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s11071-005-1914-0","article-title":"Nonlinear system identification of systems with periodic limit-cycle response","volume":"39","author":"Thothadri","year":"2005","journal-title":"Nonlinear Dyn."},{"key":"ref_60","first-page":"89","article-title":"Damping measurement in composite materials using combined finite element and frequency response method","volume":"2","author":"Ben","year":"2013","journal-title":"Int. J. Eng. Sci. Invent."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.jsv.2015.05.010","article-title":"Identification of the dynamic characteristics of a viscoelastic, nonlinear adhesive joint","volume":"352","author":"Naraghi","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.jsv.2005.09.021","article-title":"Identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform","volume":"293","author":"Ta","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1563","DOI":"10.1177\/1077546308097270","article-title":"Experimental identification of nonlinearities under free and forced vibration using the Hilbert transform","volume":"15","author":"Feldman","year":"2009","journal-title":"JVC\/J. Vib. Control"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.engstruct.2018.10.021","article-title":"Damage identification in underground tunnel structures with wavelet based residual force vector","volume":"178","author":"Wang","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Ebrahimi, Z., Asemani, M.H., and Safavi, A.A. (2020). Observer-based controller design for uncertain disturbed Takagi-Sugeno fuzzy systems: A fuzzy wavelet neural network approach. Int. J. Adapt. Control Signal Process.","DOI":"10.1002\/acs.3195"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"106008","DOI":"10.1016\/j.ijmecsci.2020.106008","article-title":"Nonlinear process damping identification using finite amplitude stability and the influence analysis on five-axis milling stability","volume":"190","author":"Tang","year":"2020","journal-title":"Int. J. Mech. Sci."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1006\/mssp.1995.0016","article-title":"Finite element model updating using frequency response function data\u2014II. case study on a medium-size finite element model","volume":"9","author":"Imregun","year":"1995","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"5733","DOI":"10.1023\/A:1012999616049","article-title":"Review: Materials for vibration damping","volume":"36","author":"Chung","year":"2001","journal-title":"J. Mater. Sci."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"2054","DOI":"10.1016\/j.jsv.2013.11.021","article-title":"Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification","volume":"333","author":"Kurt","year":"2014","journal-title":"J. Sound Vib."},{"key":"ref_70","first-page":"1949","article-title":"Aerodynamic damping properties of transmission tower estimated by combining several identification methods","volume":"74","author":"Fujimura","year":"2010","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1109\/9.61008","article-title":"The Spectral Density of the Nonlinear Damping Model: Single DOF Case","volume":"35","author":"Zhang","year":"1990","journal-title":"IEEE Trans. Automat. Contr."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1006\/jsvi.1996.0864","article-title":"Identification of Damping in Mdof Systems Using Time-Scale Decomposition","volume":"203","author":"StaszewskI","year":"1997","journal-title":"J. Sound Vib."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"5393","DOI":"10.1016\/j.jsv.2012.06.023","article-title":"Passive damping enhancement of a two-degree-of-freedom system through a strongly nonlinear two-degree-of-freedom attachment","volume":"331","author":"Wierschem","year":"2012","journal-title":"J. Sound Vib."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"110791","DOI":"10.1016\/j.engstruct.2020.110791","article-title":"Identification of nonlinear aerodynamic damping from stochastic crosswind response of tall buildings using unscented Kalman filter technique","volume":"220","author":"Wu","year":"2020","journal-title":"Eng. Struct."},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Elliott, S.J., Tehrani, M.G., and Langley, R.S. (2015). Nonlinear damping and quasi-linear modelling. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., 373.","DOI":"10.1098\/rsta.2014.0402"},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Hieu, D.V., Hai, N.Q., and Hung, D.T. (2018). The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators. J. Appl. Math., 2018.","DOI":"10.1155\/2018\/7487851"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1177\/1077546313507098","article-title":"Damping analysis of a free aluminum plate","volume":"21","author":"Zoghaib","year":"2015","journal-title":"JVC\/J. Vib. Control"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"1584","DOI":"10.1016\/j.compstruc.2005.02.004","article-title":"Damped response analysis of nonlinear cushion systems by a linearization method","volume":"83","author":"Wang","year":"2005","journal-title":"Comput. Struct."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.ymssp.2017.11.042","article-title":"Estimation of hysteretic damping of structures by stochastic subspace identification","volume":"105","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_80","unstructured":"Gao, G.-Z., Zhu, L.-D., and Ding, Q.-S. (2013, January 10\u201314). Identification of nonlinear damping and stiffness of spring-suspended sectional model. Proceedings of the Eighth Asia-Pacific Conference on Wind Engineering, Chennai, India."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.jsv.2015.05.033","article-title":"Nonlinearity of mechanical damping and stiffness of a spring-suspended sectional model system for wind tunnel tests","volume":"355","author":"Gao","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_82","doi-asserted-by":"crossref","unstructured":"Chen, Z., and Tse, K.T. (2019). Identification of physical nonlinearities of a hybrid aeroelastic\u2013pressure balance. Nonlinear Dyn.","DOI":"10.1007\/s11071-019-05173-5"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.jsv.2019.04.021","article-title":"Comparison of nonlinear system identification methods for free decay measurements with application to jointed structures","volume":"453","author":"Jin","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.compstruc.2013.02.008","article-title":"A method for simultaneous identification of the full nonlinear damping and the phase shift and amplitude of the external harmonic excitation in a forced nonlinear oscillator","volume":"120","author":"Jang","year":"2013","journal-title":"Comput. Struct."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.jfluidstructs.2019.03.011","article-title":"Evaluation of time-domain damping identification methods for flutter-constrained optimization","volume":"87","author":"Jacobson","year":"2019","journal-title":"J. Fluids Struct."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1016\/j.jsv.2007.08.002","article-title":"A practical approach to parameter identification for a lightly damped, weakly nonlinear system","volume":"310","author":"Eret","year":"2008","journal-title":"J. Sound Vib."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1016\/j.jsv.2006.02.005","article-title":"A decrement method for quantifying nonlinear and linear damping parameters","volume":"296","author":"Meskell","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_88","unstructured":"Frizzarin, M., Feng, M.Q., Franchetti, P., Soyoz, S., and Modena, C. (2010). Damage detection based on damping analysis of ambient vibration data. Struct. Control Health Monit., 742\u2013760."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.jsv.2007.02.026","article-title":"Identification of nonlinear viscous damping and Coulomb friction from the free response data","volume":"304","author":"Wu","year":"2007","journal-title":"J. Sound Vib."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"1596","DOI":"10.1016\/j.jsv.2013.10.015","article-title":"External damping losses in measuring the vibration damping properties in lightly damped specimens using transient time-domain methods","volume":"333","author":"Vanwalleghem","year":"2014","journal-title":"J. Sound Vib."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.proeng.2014.11.121","article-title":"Nonlinear damped vibrations of a hybrid laminated composite plate subjected to blast load","volume":"88","author":"Uyanik","year":"2014","journal-title":"Procedia Eng."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.ymssp.2016.03.015","article-title":"Nonlinear vibrating system identification via Hilbert decomposition","volume":"84","author":"Feldman","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.jsv.2018.03.017","article-title":"Evaluation of damping loss factor of flat laminates by sound transmission","volume":"424","author":"Parrinello","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MCS.2019.2938121","article-title":"Nonlinear System Identification: A User-Oriented Roadmap","volume":"39","author":"Schoukens","year":"2019","journal-title":"IEEE Control Syst."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.sigpro.2015.10.009","article-title":"The damping iterative parameter identification method for dynamical systems based on the sine signal measurement","volume":"120","author":"Xu","year":"2016","journal-title":"Signal Process."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.jsv.2019.02.033","article-title":"Design and experiment of nonlinear absorber for equal-peak and de-nonlinearity","volume":"449","author":"Sun","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.jsv.2019.04.022","article-title":"Identification of frequency-dependent viscoelastic damped structures using an adjoint method","volume":"453","author":"Hamdaoui","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s11071-017-3889-z","article-title":"Nonlinear damping in large-amplitude vibrations: Modelling and experiments","volume":"93","author":"Amabili","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_99","first-page":"770","article-title":"Damping identification for the nonlinear stiffness structure","volume":"16","author":"Sun","year":"2014","journal-title":"J. Vibroeng."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1023\/A:1024489210804","article-title":"Nonlinear system identification of multi-degree-of-freedom systems","volume":"32","author":"Thothadri","year":"2003","journal-title":"Nonlinear Dyn."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.ymssp.2018.03.061","article-title":"Identification of the viscoelastic response and nonlinear damping of a rubber plate in nonlinear vibration regime","volume":"111","author":"Balasubramanian","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"105010","DOI":"10.1088\/0964-1726\/22\/10\/105010","article-title":"Vibration isolation using nonlinear damping implemented by a feedback-controlled MR damper","volume":"22","author":"Ho","year":"2013","journal-title":"Smart Mater. Struct."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.jsv.2016.06.005","article-title":"Identification of the effect of debonding on the linear and nonlinear effective damping of an adhesive joint","volume":"380","author":"Pazand","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.jsv.2015.06.042","article-title":"Damping loss factor estimation of two-dimensional orthotropic structures from a displacement field measurement","volume":"356","author":"Cherif","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.jsv.2019.03.017","article-title":"Experiments and nonlinear simulations of a rubber isolator subjected to harmonic and random vibrations","volume":"451","author":"Roncen","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"103056","DOI":"10.1016\/j.jfluidstructs.2020.103056","article-title":"Very large amplitude vibrations of flexible structures: Experimental identification and validation of a quadratic drag damping model","volume":"97","author":"Colin","year":"2020","journal-title":"J. Fluids Struct."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1177\/1475921708089830","article-title":"Time-frequency method for nonlinear system identification and damage detection","volume":"7","author":"Pai","year":"2008","journal-title":"Struct. Health Monit."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.ijnonlinmec.2018.09.004","article-title":"Strong geometric softening\u2013hardening nonlinearities in an oscillator composed of linear stiffness and damping elements","volume":"107","author":"Mojahed","year":"2018","journal-title":"Int. J. Non. Linear. Mech."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/j.ymssp.2016.05.005","article-title":"Synchrosqueezed wavelet transform for damping identification","volume":"80","author":"Mihalec","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1098\/rsta.2006.1936","article-title":"Time-frequency and time-scale analyses for structural health monitoring","volume":"365","author":"Staszewski","year":"2007","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1006\/jsvi.2000.3407","article-title":"Identification of coupled non-linear modes from free vibration using time-frequency representations","volume":"243","author":"Bellizzi","year":"2001","journal-title":"J. Sound Vib."},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"1679","DOI":"10.1007\/s11071-016-2786-1","article-title":"Nonlinear time-varying vibration system identification using parametric time\u2013frequency transform with spline kernel","volume":"85","author":"Yang","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"107000","DOI":"10.1016\/j.tws.2020.107000","article-title":"Nonlinear vibration analysis of fiber reinforced composite cylindrical shells with partial constrained layer damping treatment","volume":"157","author":"Li","year":"2020","journal-title":"Thin-Walled Struct."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.oceaneng.2015.09.019","article-title":"Identification of the nonlinear roll damping and restoring moment of a FPSO using Hilbert transform","volume":"109","author":"Kim","year":"2015","journal-title":"Ocean Eng."},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1111\/j.1467-8667.2009.00612.x","article-title":"Nonlinear Damping Identification in Precast Prestressed Reinforced Concrete Beams","volume":"24","author":"Franchetti","year":"2009","journal-title":"Comput. Civ. Infrastruct. Eng."},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.jsv.2015.12.040","article-title":"Experimental characterization of a nonlinear vibration absorber using free vibration","volume":"367","author":"Tang","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.mechmachtheory.2016.02.007","article-title":"Nonlinear damping identification in rotors using wavelet transform","volume":"100","author":"Chandra","year":"2016","journal-title":"Mech. Mach. Theory"},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"1262","DOI":"10.1016\/j.ijmecsci.2005.04.010","article-title":"A wavelet-based approach for the identification of damping in non-linear oscillators","volume":"47","author":"Joseph","year":"2005","journal-title":"Int. J. Mech. Sci."},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"3497","DOI":"10.1016\/j.engstruct.2008.05.024","article-title":"Damage detection by means of structural damping identification","volume":"30","author":"Curadelli","year":"2008","journal-title":"Eng. Struct."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.jsv.2009.06.008","article-title":"Experimental identification of nonlinear dynamic properties of built-up structures","volume":"327","author":"Heller","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1016\/j.engstruct.2018.01.015","article-title":"Analysis of tuned liquid column damper nonlinearities","volume":"171","author":"Dziedziech","year":"2018","journal-title":"Eng. Struct."},{"key":"ref_122","first-page":"324","article-title":"Damping identification using the wavelet-based demodulation method: Application to Gearbox signals","volume":"3","author":"Dien","year":"2007","journal-title":"Tech. Mech."},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1016\/j.jsv.2006.01.037","article-title":"Identification of modal parameters of a mdof system by modified L-P wavelet packets","volume":"295","author":"Chakraborty","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_124","unstructured":"Kerschen, G., Worden, K., Vakakis, A.F., and Golinval, J.C. (2007, January 19\u201322). Nonlinear system identification in structural dynamics: Current status and future directions. Proceedings of the 25th International Modal Analysis Conference, Orlando, FL, USA."},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"103308","DOI":"10.1016\/j.ijnonlinmec.2019.103308","article-title":"Multimodal vibration damping of nonlinear structures using multiple nonlinear absorbers","volume":"119","author":"Raze","year":"2020","journal-title":"Int. J. Non. Linear. Mech."},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.ymssp.2019.05.066","article-title":"Characteristic nonlinear system identification: A data-driven approach for local nonlinear attachments","volume":"131","author":"Moore","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1016\/j.crme.2017.03.004","article-title":"Identification of nonlinear anti-vibration isolator properties","volume":"345","author":"Mezghani","year":"2017","journal-title":"Comptes Rendus Mec."},{"key":"ref_128","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1115\/1.1687395","article-title":"Identification of multi-degree of freedom systems with nonproportional damping using the resonant decay method","volume":"126","author":"Naylor","year":"2004","journal-title":"J. Vib. Acoust. Trans. ASME"},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.jsv.2015.03.015","article-title":"Identification of backbone curves of nonlinear systems from resonance decay responses","volume":"348","author":"Neild","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_130","doi-asserted-by":"crossref","first-page":"6798","DOI":"10.1016\/j.jsv.2013.08.009","article-title":"A method for nonlinear modal analysis and synthesis: Application to harmonically forced and self-excited mechanical systems","volume":"332","author":"Krack","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.compstruc.2015.03.008","article-title":"Nonlinear modal analysis of nonconservative systems: Extension of the periodic motion concept","volume":"154","author":"Krack","year":"2015","journal-title":"Comput. Struct."},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1016\/j.ymssp.2018.11.009","article-title":"A method for numerical and experimental nonlinear modal analysis of nonsmooth systems","volume":"120","author":"Peter","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_133","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.jsv.2018.07.010","article-title":"A phase resonance approach for modal testing of structures with nonlinear dissipation","volume":"435","author":"Scheel","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_134","doi-asserted-by":"crossref","first-page":"115580","DOI":"10.1016\/j.jsv.2020.115580","article-title":"Challenging an experimental nonlinear modal analysis method with a new strongly friction-damped structure","volume":"485","author":"Scheel","year":"2020","journal-title":"J. Sound Vib."},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"107023","DOI":"10.1016\/j.ymssp.2020.107023","article-title":"Experimental modal analysis of nonlinear systems by using response-controlled stepped-sine testing","volume":"146","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_136","first-page":"1","article-title":"Nonlinear Black-Box Models in System Identifiaction","volume":"30","author":"Juditsky","year":"1995","journal-title":"Neural Netw."},{"key":"ref_137","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S1367-5788(03)00009-9","article-title":"Neuro-fuzzy methods for nonlinear system identification","volume":"27","author":"Verbruggen","year":"2003","journal-title":"Annu. Rev. Control"},{"key":"ref_138","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.ymssp.2009.03.013","article-title":"Black-box model identification for a continuously variable, electro-hydraulic semi-active damper","volume":"24","author":"Witters","year":"2010","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_139","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.sna.2011.02.048","article-title":"Nonlinear black-box models and force-sensorless damping control for damping systems using magneto-rheological fluid dampers","volume":"167","author":"Truong","year":"2011","journal-title":"Sensors Actuators A Phys."},{"key":"ref_140","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1111\/mice.12005","article-title":"Nonlinear identification of a magneto-rheological damper based on dynamic neural networks","volume":"29","author":"Khalid","year":"2014","journal-title":"Comput. Civ. Infrastruct. Eng."},{"key":"ref_141","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1016\/j.neucom.2016.07.021","article-title":"Identification of nonlinear aeroelastic system using fuzzy wavelet neural network","volume":"214","author":"Dou","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_142","doi-asserted-by":"crossref","first-page":"2200","DOI":"10.1016\/j.ymssp.2006.05.008","article-title":"Model updating of damped structures using FRF data","volume":"20","author":"Lin","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_143","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.jsv.2012.09.024","article-title":"Soft hollow particle damping identification in honeycomb structures","volume":"332","author":"Michon","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_144","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.ymssp.2012.07.002","article-title":"A method for damping matrix identification using frequency response data","volume":"33","author":"Pradhan","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_145","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1111\/mice.12012","article-title":"A two-step model updating algorithm for parameter identification of linear elastic damped structures","volume":"28","year":"2013","journal-title":"Comput. Civ. Infrastruct. Eng."},{"key":"ref_146","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1016\/j.jsv.2012.10.021","article-title":"Model updating using antiresonant frequencies identified from transmissibility functions","volume":"332","author":"Meruane","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_147","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.jsv.2008.08.014","article-title":"Damped model updating using complex updating parameters","volume":"320","author":"Arora","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_148","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1016\/j.jsv.2009.02.048","article-title":"Finite element model updating with damping identification","volume":"324","author":"Arora","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_149","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.jsv.2014.08.040","article-title":"Direct structural damping identification method using complex FRFs","volume":"339","author":"Arora","year":"2014","journal-title":"J. Sound Vib."},{"key":"ref_150","first-page":"V04AT05A039","article-title":"Identification of non-linear damping of nuclear reactor components in case of one-to-one internal resonance","volume":"50541","author":"Delannoy","year":"2016","journal-title":"Am. Soc. Mech. Eng."},{"key":"ref_151","doi-asserted-by":"crossref","first-page":"108376","DOI":"10.1016\/j.compositesb.2020.108376","article-title":"30 Years of functionally graded materials: An overview of manufacturing methods, Applications and Future Challenges","volume":"201","author":"Saleh","year":"2020","journal-title":"Compos Part B Eng."},{"key":"ref_152","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.jsv.2017.07.015","article-title":"A novel air spring dynamic model with pneumatic thermodynamics, effective friction and viscoelastic damping","volume":"408","author":"Zhu","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_153","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.ymssp.2007.11.031","article-title":"Nonlinear system identification of automotive dampers: A time and frequency-domain analysis","volume":"23","author":"Worden","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_154","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1016\/j.ymssp.2009.09.005","article-title":"The experimental identification of magnetorheological dampers and evaluation of their controllers","volume":"24","author":"Metered","year":"2010","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_155","doi-asserted-by":"crossref","unstructured":"Salton, A.T., Eckhard, D., Flores, J.V., Fernandes, G., and Azevedo, G. (2016, January 19\u201322). Disturbance observer and nonlinear damping control for fast tracking quadrotor vehicles. Proceedings of the 2016 IEEE Conference on Control Applications (CCA), Buenos Aires, Argentina.","DOI":"10.1109\/CCA.2016.7587901"},{"key":"ref_156","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.ymssp.2018.06.013","article-title":"Damping identification and localisation via Layer Method: Experimental application to a vehicle chassis focused on shock absorbers effects","volume":"116","author":"Bonisoli","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_157","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.jsv.2019.04.006","article-title":"Analysis of a rotordynamic system with anisotropy and nonlinearity using the Floquet theory and the method of normal forms","volume":"453","author":"Maldonado","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_158","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1016\/j.apm.2019.08.030","article-title":"A model order reduction technique for systems with nonlinear frequency dependent damping","volume":"77","author":"Jith","year":"2020","journal-title":"Appl. Math. Model."},{"key":"ref_159","doi-asserted-by":"crossref","unstructured":"Gary, K., and Ertas, B. (2020). Experimental Rotordynamic Force Coefficients for a Diffusion Bonded Compliant Hybrid Journal Gas Bearing Utilizing Fluid-Filled Hermetic Dampers. J. Eng. Gas Turbines Power, 142.","DOI":"10.1115\/1.4044643"},{"key":"ref_160","first-page":"961","article-title":"Identification and correction of rotor instability in an oil-free gas turbine","volume":"5","author":"Lubell","year":"2008","journal-title":"Proc. ASME Turbo Expo"},{"key":"ref_161","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.2514\/3.11074","article-title":"Nonlinear damping estimation from rotor stability data using time and frequency domain techniques","volume":"30","author":"Tasker","year":"1992","journal-title":"AIAA J."},{"key":"ref_162","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1006\/jsvi.1996.0014","article-title":"A frequency domain parametric identification method for studying the non-linear performance of squeeze-film dampers","volume":"189","author":"Zhang","year":"1996","journal-title":"J. Sound Vib."},{"key":"ref_163","first-page":"2473","article-title":"Linear and nonlinear damping identification in helicopter rotor systems","volume":"4","author":"Smith","year":"1998","journal-title":"Collect. Tech. Pap. AIAA\/ASME\/ASCE\/AHS\/ASC Struct. Struct. Dyn. Mater. Conf."},{"key":"ref_164","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.2514\/2.644","article-title":"Nonlinear damping identification from transient data","volume":"37","author":"Smith","year":"1999","journal-title":"AIAA J."},{"key":"ref_165","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1007\/s11071-014-1526-7","article-title":"Effects of nonlinear damping suspension on nonperiodic motions of a flexible rotor in journal bearings","volume":"78","author":"Yan","year":"2014","journal-title":"Nonlinear Dyn."},{"key":"ref_166","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.jsv.2016.07.002","article-title":"A quasi-modal parameter based system identification procedure with non-proportional hysteretic damping","volume":"382","author":"Yu","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_167","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1115\/1.4037151","article-title":"Numerical and Experimental Analyses of the Dynamic Characteristics of Journal Bearings with Square Dimples","volume":"140","author":"Yamada","year":"2018","journal-title":"J. Tribol."},{"key":"ref_168","doi-asserted-by":"crossref","unstructured":"Delgado, A., and Ertas, B. (2019). Dynamic Characterization of a Novel Externally Pressurized Compliantly Damped Gas-Lubricated Bearing with Hermetically Sealed Squeeze Film Damper Modules. J. Eng. Gas Turbines Power, 141.","DOI":"10.1115\/1.4041311"},{"key":"ref_169","doi-asserted-by":"crossref","first-page":"104064","DOI":"10.1016\/j.jweia.2019.104064","article-title":"Modelling nonlinear aerodynamic damping during transverse aerodynamic instabilities for slender rectangular prisms with typical side ratios","volume":"197","author":"Gao","year":"2020","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_170","doi-asserted-by":"crossref","first-page":"109575","DOI":"10.1016\/j.engstruct.2019.109575","article-title":"Nonlinear damping and nonlinear responses of recycled aggregate concrete frames under earthquake loading","volume":"201","author":"Wang","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_171","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s13349-013-0067-y","article-title":"Field tests and verification of damping calculation methods for operating highway bridges","volume":"4","author":"Zarafshan","year":"2014","journal-title":"J. Civ. Struct. Health Monit."},{"key":"ref_172","unstructured":"Dammika, A.J., Yamaguchi, H., Kawarai, K., Yoshioka, T., and Matsumoto, Y. (2013, January 11\u201313). Energy-based damping estimation of steel bridges and its applicability to damage detection. Proceedings of the The Thirteenth East Asia-Pacific Conference on Structural Engineering and Construction (EASEC-13), Sapporo, Japan."},{"key":"ref_173","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1061\/(ASCE)BE.1943-5592.0000691","article-title":"Analytical damping evaluation complementary to experimental structural health monitoring of bridges","volume":"20","author":"Dammika","year":"2015","journal-title":"J. Bridg. Eng."},{"key":"ref_174","first-page":"139","article-title":"Nonlinear damping in floor vibrations serviceability: Verification on a laboratory structure","volume":"2 Part F2","author":"Avci","year":"2017","journal-title":"Conf. Proc. Soc. Exp. Mech. Ser."},{"key":"ref_175","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s11340-010-9360-4","article-title":"Non-linear Damping and Frequency Identification in a Progressively Damaged, R.C. Element","volume":"51","author":"Demarie","year":"2011","journal-title":"Exp. Mech."},{"key":"ref_176","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1023\/A:1008335522973","article-title":"Damping identification using perturbation techniques and higher-order spectra","volume":"23","author":"Hajj","year":"2000","journal-title":"Nonlinear Dyn."},{"key":"ref_177","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.1016\/j.ymssp.2009.02.011","article-title":"Damping estimation using free decays and ambient vibration tests","volume":"24","author":"Cunha","year":"2010","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_178","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/j.jsv.2015.07.020","article-title":"An enhanced nonlinear damping approach accounting for system constraints in active mass dampers","volume":"357","author":"Venanzi","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_179","first-page":"132","article-title":"Damage Localization in Reinforced Concrete Structures by using Damping Measurements","volume":"168","author":"Publications","year":"1999","journal-title":"Key Eng. Mater. Vols. 167-168"},{"key":"ref_180","doi-asserted-by":"crossref","first-page":"318","DOI":"10.4028\/www.scientific.net\/KEM.693.318","article-title":"Energy balancing method to identify nonlinear damping of bolted-joint interface","volume":"693","author":"Liao","year":"2016","journal-title":"Key Eng. Mater."},{"key":"ref_181","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1061\/(ASCE)0733-9399(2004)130:8(877)","article-title":"Element level system identification with unknown input with Rayleigh damping","volume":"130","author":"Ling","year":"2004","journal-title":"J. Eng. Mech."},{"key":"ref_182","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0167-6105(96)00004-9","article-title":"Damping in structures: Its evaluation and treatment of uncertainty","volume":"59","author":"Kareem","year":"1996","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_183","first-page":"1","article-title":"Envelope Random Decrement Technique for Identification of Nonlinear Damping of Tall Buildings","volume":"142","author":"Huang","year":"2016","journal-title":"J. Struct. Eng. (United States)"},{"key":"ref_184","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1115\/1.3423835","article-title":"Identification of viscous damping in structures from modal information","volume":"43","year":"1976","journal-title":"J. Appl. Mech. Trans. ASME"},{"key":"ref_185","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.proeng.2017.04.470","article-title":"Automatic Estimation of Natural Frequencies and Damping Ratios of Building Structures","volume":"188","author":"Mimura","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_186","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.apor.2015.11.007","article-title":"Parameter identification of nonlinear roll motion equation for floating structures in irregular waves","volume":"55","author":"Hou","year":"2016","journal-title":"Appl. Ocean Res."},{"key":"ref_187","doi-asserted-by":"crossref","first-page":"106298","DOI":"10.1016\/j.oceaneng.2019.106298","article-title":"Parametric roll prediction of the KCS containership in head waves with emphasis on the roll damping and nonlinear restoring moment","volume":"188","author":"Yu","year":"2019","journal-title":"Ocean Eng."},{"key":"ref_188","doi-asserted-by":"crossref","unstructured":"Han, S.L., and Kinoshita, T. (2012). Stochastic inverse identification of nonlinear roll damping moment of a ship moving at nonzero-forward speeds. Math. Probl. Eng., 2012.","DOI":"10.1155\/2012\/769385"},{"key":"ref_189","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1016\/j.ijnonlinmec.2009.05.001","article-title":"A new method for detecting non-linear damping and restoring forces in non-linear oscillation systems from transient data","volume":"44","author":"Jang","year":"2009","journal-title":"Int. J. Non. Linear. Mech."},{"key":"ref_190","doi-asserted-by":"crossref","first-page":"102014","DOI":"10.1016\/j.apor.2019.102014","article-title":"Most often instantaneous rotation center (MOIRC) for roll damping assessment in the free decay test of a FPSO","volume":"95","author":"Asgari","year":"2020","journal-title":"Appl. Ocean Res."},{"key":"ref_191","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1109\/TCSI.2002.801239","article-title":"A modified Volterra series approach for nonlinear dynamic systems modeling","volume":"49","author":"Mirri","year":"2002","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"ref_192","doi-asserted-by":"crossref","first-page":"332","DOI":"10.3182\/20060329-3-AU-2901.00048","article-title":"Identification of Nonlinear Viscous Damping for Marine Vessels","volume":"39","author":"Golding","year":"2006","journal-title":"IFAC Proc. Vol."},{"key":"ref_193","doi-asserted-by":"crossref","first-page":"100","DOI":"10.2174\/1874835X01003010100","article-title":"A Numerical Investigation on Nonparametric Identification of Nonlinear Roll Damping Moment of a Ship from Transient Response","volume":"3","author":"Jang","year":"2010","journal-title":"Open Ocean Eng. J."},{"key":"ref_194","doi-asserted-by":"crossref","first-page":"1337","DOI":"10.1016\/j.oceaneng.2010.06.012","article-title":"Recovering the functional form of the nonlinear roll damping of ships from a free-roll decay experiment: An inverse formulism","volume":"37","author":"Jang","year":"2010","journal-title":"Ocean Eng."},{"key":"ref_195","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1016\/j.ymssp.2010.11.002","article-title":"Non-parametric simultaneous identification of both the nonlinear damping and restoring characteristics of nonlinear systems whose dampings depend on velocity alone","volume":"25","author":"Jang","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_196","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/574291","article-title":"Nonlinear damping identification in nonlinear dynamic system based on stochastic inverse approach","volume":"2012","author":"Han","year":"2012","journal-title":"Math. Probl. Eng."},{"key":"ref_197","first-page":"138","article-title":"Parameter identification for nonlinear damping coefficient from large-amplitude ship roll motion using wavelets","volume":"6","author":"Sathyaseelan","year":"2017","journal-title":"Beni-Suef Univ. J. Basic Appl. Sci."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7303\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:47:17Z","timestamp":1760179637000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,19]]},"references-count":197,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20247303"],"URL":"https:\/\/doi.org\/10.3390\/s20247303","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,19]]}}}