{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:52:25Z","timestamp":1760057545282,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,9]],"date-time":"2025-02-09T00:00:00Z","timestamp":1739059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study aimed to investigate the structure-borne sound suppression of a strongly\/weakly excited curved panel. Quadratic nonlinear resonance can induce anti-symmetric modal responses to replace symmetric modal responses, even though the physical panel dimensions and excitation distribution are symmetric. Unlike cubic nonlinear resonance, quadratic nonlinear resonance can be induced regardless of whether the panel vibration amplitude is small or large. As the sound radiation efficiency of anti-symmetric responses is much lower than that of symmetric responses, this quadratic nonlinear resonance effect is thus used for sound suppression. A set of multimode formulations was developed from the nonlinear structural governing equation and sound radiation efficiency equation. The quadratic nonlinear resonant responses and some other nonlinear responses were computed from the multimode formulations. Modal convergence studies and parametric studies were performed to understand the effects of various parameters on the quadratic nonlinear responses and sound suppression. The results showed that when the panel was strongly excited, the difference between the peak sound levels in the linear and nonlinear cases was up to 12 dB, and when the panel was weakly excited, the difference was up to 6 dB.<\/jats:p>","DOI":"10.3390\/axioms14020125","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T03:39:47Z","timestamp":1739158787000},"page":"125","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Structure-Borne Sound Suppression of a Strongly\/Weakly Excited Curved Panel Using a Quadratic Nonlinear Resonance Effect"],"prefix":"10.3390","volume":"14","author":[{"given":"Yiu-Yin","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon 852, Hong Kong"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Shi, G.M., Wu, X.X., Jiang, R.J., and Li, S.D. (2023). A particle reinforced gradient honeycomb sandwich panel for broadband sound insulation. Mathematics, 11.","DOI":"10.3390\/math11030502"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2574","DOI":"10.21595\/jve.2016.16603","article-title":"Sound insulation performance optimization of lightweight sandwich panels","volume":"18","author":"Xu","year":"2016","journal-title":"J. Vibro Eng."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Mo, J., Peng, Z.R., and Wang, X. (2022). Achieving enhanced sound insulation through micromembranes-type acoustic metamaterials. Appl. Sci., 12.","DOI":"10.3390\/app12041950"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Urb\u00e1n, D., Roozen, N.B., Muellner, H., Zat\u2019ko, P., Niemczanowski, A., Rycht\u00e1rikov\u00e1, M., and Glorieux, C. (2018). Vibrometry assessment of the external thermal composite insulation systems influence on the facade airborne sound insulation. Appl. Sci., 8.","DOI":"10.3390\/app8050703"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ou, D.Y. (2018). An optimization method for maximizing the low frequency sound insulation of plate structures. Shock. Vib., 7849327.","DOI":"10.1155\/2018\/7849327"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"025116","DOI":"10.1063\/1.4942513","article-title":"A lightweight low-frequency sound insulation membrane-type acoustic metamaterial","volume":"6","author":"Lu","year":"2016","journal-title":"AIP Adv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"055121","DOI":"10.1063\/1.5095710","article-title":"Sound insulation properties of a spherical structure of subwavelength size","volume":"9","author":"Han","year":"2019","journal-title":"AIP Adv."},{"key":"ref_8","first-page":"479","article-title":"Analysis of the Influencing Factors of the Acoustic Performance of the Muffler Considering Acoustic-structural Coupling","volume":"47","author":"Zhao","year":"2022","journal-title":"Arch. Acoust."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1142\/S0218396X04002407","article-title":"A finite element structural-acoustic model of coupled membranes","volume":"12","author":"Givoli","year":"2004","journal-title":"J. Comput. Acoust."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s42417-019-00122-3","article-title":"Structural-acoustic modeling and analysis for a flexible partition panel in three-dimensional acoustic cavity","volume":"7","author":"Zhang","year":"2019","journal-title":"J. Vib. Eng. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1177\/14613484231157514","article-title":"A time-domain method for free vibration responses of an equivalent viscous damped system based on a complex damping model","volume":"42","author":"Wang","year":"2023","journal-title":"J. Low Freq. Noise Vib. Act. Control."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"110011","DOI":"10.1016\/j.apacoust.2024.110011","article-title":"Improvement of broadband low-frequency sound absorption and energy absorbing of arched curve Helmholtz resonator with negative Poisson\u2019s ratio","volume":"221","author":"Kong","year":"2024","journal-title":"Appl. Acoust."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1006\/jsvi.1998.1748","article-title":"Sound insertion loss of stiffened enclosure plates using the finite element method and the classical approach","volume":"217","author":"Lee","year":"1998","journal-title":"J. Sound Vib."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1006\/jsvi.2002.5096","article-title":"Insertion loss of a cavity-backed semi-cylindrical enclosure panel","volume":"259","author":"Lee","year":"2003","journal-title":"J. Sound Vib."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.cja.2024.05.031","article-title":"Identification of aircraft longitudinal aerodynamic parameters using an online corrective test for wind tunnel virtual flight","volume":"37","author":"Tai","year":"2024","journal-title":"Chin. J. Aeronaut."},{"key":"ref_16","first-page":"5001713","article-title":"Dynamic-Wave Interference Suppression Based on Angular Increment Assistance for Underwater Imaging Polarization Sensor","volume":"74","author":"Li","year":"2025","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"110344","DOI":"10.1016\/j.apacoust.2024.110344","article-title":"Omnidirectional sound wave absorption based on the multi-oriented acoustic meta-materials","volume":"228","author":"Bai","year":"2025","journal-title":"Appl. Acoust."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"014307","DOI":"10.7498\/aps.66.014307","article-title":"A broadband low-frequency sound insulation structure based on two-dimensionally inbuilt Helmholtz resonator","volume":"66","author":"Gao","year":"2017","journal-title":"Acta Phys. Sin."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1515\/aoa-2017-0068","article-title":"Prediction of sound insulation of sandwich partition panels by means of artificial neural networks","volume":"42","author":"Garg","year":"2017","journal-title":"Arch. Acoust."},{"key":"ref_20","first-page":"63","article-title":"Improvement of sound insulation through double-panel structure by using hybrid local resonator array","volume":"48","author":"Ri","year":"2023","journal-title":"Arch. Acoust."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"63","DOI":"10.37763\/wr.1336-4561\/65.1.063074","article-title":"Calculation of sound insulation of softwood samples at normal incidence and comparison with experimental data","volume":"65","author":"Ju","year":"2020","journal-title":"Wood Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1177\/14613484231220187","article-title":"Research on acoustic-structural coupling model and tire parameters of tire acoustic cavity resonance noise","volume":"43","author":"Bao","year":"2024","journal-title":"J. Low Freq. Noise Vib. Act. Control."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0895-7177(96)00002-7","article-title":"Parameter estimation in a structural acoustic system with fully nonlinear coupling conditions","volume":"23","author":"Banks","year":"1996","journal-title":"Math. Comput. Model."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1002\/mma.737","article-title":"Uniform stabilization of a nonlinear structural acoustic model with a Timoshenko beam interface","volume":"29","author":"Dalsen","year":"2006","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1038\/s41378-020-00230-1","article-title":"Strong internal resonance in a nonlinear, asymmetric microbeam resonator","volume":"7","author":"Asadi","year":"2021","journal-title":"Microsyst. Nanoeng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"114619","DOI":"10.1016\/j.sna.2023.114619","article-title":"Exploiting and tailoring 1:2 internal resonance in a stepped beam micromechanical resonator for frequency stabilization","volume":"362","author":"Yu","year":"2023","journal-title":"Sens. Actuators A\u2014Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1515\/IJNSNS.2008.9.3.221","article-title":"Nonlinear multi-modal structural\/acoustic interaction between a composite plate vibration and the induced pressure","volume":"9","author":"Lee","year":"2008","journal-title":"Int. J. Nonlinear Sci. Numer. Simul."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s11071-011-0249-2","article-title":"The jump phenomenon effect on the sound absorption of a nonlinear panel absorber and sound transmission loss of a nonlinear panel backed by a cavity","volume":"69","author":"Lee","year":"2012","journal-title":"Nonlinear Dyn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s40430-023-04594-z","article-title":"Nonlinear vibro-acoustic analysis of a double-panel structure with an enclosure cavity","volume":"46","author":"Anvariyeh","year":"2024","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1016\/j.jsv.2009.02.042","article-title":"The effect of modal energy transfer on the sound radiation and vibration of a curved panel: Theory and experiment","volume":"32","author":"Lee","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"118086","DOI":"10.1016\/j.jsv.2023.118086","article-title":"Nonlinear aeroelastic fluid-structure-acoustic interaction analysis of a coupled composite panel with an acoustic cavity in supersonic flow","volume":"569","author":"Liu","year":"2024","journal-title":"J. Sound Vib."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1007\/s11071-013-1039-9","article-title":"Nonlinear harmonic vibration analysis of a plate-cavity system","volume":"7","author":"Sadri","year":"2013","journal-title":"Nonlinear Dyn."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1007\/s40430-019-1565-6","article-title":"Nonlinear vibration analysis of a circular plate-cavity system","volume":"41","author":"Anvariyeh","year":"2019","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.2514\/1.J051657","article-title":"Nonlinear bifurcation structure of panels subject to periodic acoustic fluid-structure interaction","volume":"50","author":"Aginsky","year":"2012","journal-title":"AIAA J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"015007","DOI":"10.1088\/1361-6439\/ad0de8","article-title":"One-to-two internal resonance in a micro-mechanical resonator with strong Duffing nonlinearity","volume":"34","author":"Yu","year":"2024","journal-title":"J. Micromech. Microeng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"014011","DOI":"10.1103\/PhysRevApplied.13.014011","article-title":"Ultrabroadband microresonators with geometrically nonlinear stiffness and dissipation","volume":"13","author":"Potekin","year":"2020","journal-title":"Phys. Rev. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"5574","DOI":"10.1016\/j.apm.2012.01.006","article-title":"Sound absorption of a quadratic and cubic nonlinearly vibrating curved panel absorber","volume":"36","author":"Lee","year":"2012","journal-title":"Appl. Math. Model."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.ast.2018.03.010","article-title":"The effect of nature of porous material on diffuse field acoustic transmission of the sandwich aerospace composite doubly curved shell","volume":"78","author":"Talebitooti","year":"2018","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1121\/1.1912942","article-title":"Radiation resistance of a baffled beam","volume":"51","author":"Wallace","year":"1972","journal-title":"J. Acoust. Soc. Am."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/125\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:29:55Z","timestamp":1760027395000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/125"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,9]]},"references-count":39,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["axioms14020125"],"URL":"https:\/\/doi.org\/10.3390\/axioms14020125","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,2,9]]}}}