{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T02:55:39Z","timestamp":1777604139648,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2009,5,20]],"date-time":"2009-05-20T00:00:00Z","timestamp":1242777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincar\u00e9 maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale.<\/jats:p>","DOI":"10.3390\/s90503854","type":"journal-article","created":{"date-parts":[[2009,5,20]],"date-time":"2009-05-20T11:56:26Z","timestamp":1242820586000},"page":"3854-3874","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects"],"prefix":"10.3390","volume":"9","author":[{"given":"Wen-Ming","family":"Zhang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guang","family":"Meng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian-Bin","family":"Zhou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie-Yu","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2009,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3497","DOI":"10.3390\/s8053497","article-title":"Measurement of mechanical properties of cantilever shaped materials","volume":"8","author":"Finot","year":"2008","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1016\/j.mechatronics.2004.04.005","article-title":"A review of atomic force microscopy imaging systems: application to molecular metrology and biological sciences","volume":"14","author":"Jalili","year":"2004","journal-title":"Mechatronics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1122","DOI":"10.1002\/smll.200600272","article-title":"Monitoring and analyzing nonlinear dynamics in atomic force microscopy","volume":"2","author":"Hersam","year":"2006","journal-title":"Small"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4368","DOI":"10.1088\/0022-3727\/40\/14\/036","article-title":"Growth of liquid bridge in AFM","volume":"40","author":"Wei","year":"2008","journal-title":"J. Phys. D: Appl. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"103001","DOI":"10.1088\/0022-3727\/41\/10\/103001","article-title":"Aspects of scanning force microscope probes and their effects on dimensional measurement","volume":"41","author":"Yacoot","year":"2008","journal-title":"J. Phys. D: Appl. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"115409","DOI":"10.1103\/PhysRevB.66.115409","article-title":"Nonlinear dynamics of microcantilevers in tapping mode atomic force microscopy: a comparison between theory and experiment","volume":"66","author":"Lee","year":"2002","journal-title":"Phys. Rev. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1115\/1.2162864","article-title":"Characterization of intermittent contact in tapping-mode atomic force microscopy","volume":"1","author":"Zhao","year":"2006","journal-title":"ASME J. Comput. Nonlin. Dyn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"245419","DOI":"10.1103\/PhysRevB.70.245419","article-title":"Nonlinear dynamics of vibrating microcantilevers in tapping-mode atomic force microscopy","volume":"70","author":"Yagasaki","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1925","DOI":"10.1098\/rspa.2002.1115","article-title":"Nonlinear dynamics of atomic-force-microscope probes driven in Lennard-Jones potentials","volume":"459","author":"Rutzel","year":"2003","journal-title":"Proc. R. Soc. Lond. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"093512","DOI":"10.1063\/1.2913054","article-title":"The nonlinear dynamics of tapping mode atomic force microscopy with capillary force interactions","volume":"103","author":"Hashemi","year":"2008","journal-title":"J. Appl. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1023\/A:1008342408448","article-title":"Melnikov-based dynamical analysis of microcantilevers in scanning probe microscopy","volume":"20","author":"Ashhab","year":"1999","journal-title":"Nonlin. Dyn."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1115\/1.482465","article-title":"Complex dynamics in a harmonically excited Lennard-Jones oscillator: microcantilever\u2013sample interaction in scanning probe microscopes","volume":"122","author":"Basso","year":"2000","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"193411","DOI":"10.1103\/PhysRevB.64.193411","article-title":"Tip-surface forces, amplitude, and energy dissipation in amplitude-modulation (tapping mode) force microscopy","volume":"64","author":"Paulo","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2551","DOI":"10.1063\/1.125074","article-title":"Phase imaging: Deep or superficial?","volume":"75","author":"Behrend","year":"1999","journal-title":"Appl. Phys. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"155436","DOI":"10.1103\/PhysRevB.66.155436","article-title":"Capillary forces in tapping mode atomic force microscopy","volume":"66","author":"Zitzler","year":"2002","journal-title":"Phys. Rev. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2726","DOI":"10.1063\/1.1564274","article-title":"Noncontacta tomic force microscopy: Stability criterion and dynamical responses of the shift of frequency and damping signal","volume":"74","author":"Couturier","year":"2003","journal-title":"Rev. Sci. Instr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.sna.2004.09.025","article-title":"Nonlinear dynamical system of micro-cantilever under combined parametric and forcing excitations in MEMS","volume":"119","author":"Zhang","year":"2005","journal-title":"Sens. Actuat. A: Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1109\/JSEN.2006.890158","article-title":"Nonlinear dynamic analysis of electrostatically actuated resonant MEMS sensors under parametric excitation","volume":"7","author":"Zhang","year":"2007","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5927","DOI":"10.3390\/s8095927","article-title":"Influence of fluid cell design on the frequency response of AFM microcantilevers in liquid media","volume":"8","author":"Motamedi","year":"2008","journal-title":"Sensors"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"114906","DOI":"10.1063\/1.2202232","article-title":"Hydrodynamic loading of microcantilevers vibrating in viscous fluids","volume":"99","author":"Basak","year":"2006","journal-title":"J. Appl. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1063\/1.368002","article-title":"Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope","volume":"84","author":"Sader","year":"1998","journal-title":"J. Appl. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3967","DOI":"10.1063\/1.1150021","article-title":"Calibration of rectangular atomic force microscope cantilevers","volume":"70","author":"Sader","year":"1999","journal-title":"Rev. Sci. Instr."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"023706","DOI":"10.1063\/1.2839913","article-title":"Simultaneous normal and shear measurements of nanoconfined liquids in a fiber-based atomic force microscope","volume":"79","author":"Matei","year":"2008","journal-title":"Rev. Sci. Instr."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.sna.2007.01.008","article-title":"Squeeze film damping in MEMS","volume":"136","author":"Bao","year":"2007","journal-title":"Sens. Actuat. A: Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/S0924-4247(97)01732-9","article-title":"The influence of gas-surface interaction on gas film damping in a silicon accelerometer","volume":"66","author":"Veijola","year":"1998","journal-title":"Sens. Actuat. A: Phys."},{"key":"ref_26","first-page":"225012","article-title":"Atomic force microscopy dynamic modes: modeling and applications","volume":"20","author":"Song","year":"2008","journal-title":"J. Phys.: Condens. Matter."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/0924-4247(93)80144-6","article-title":"comparison of squeeze-film theory with measurements on a microstructure","volume":"36","author":"Andrews","year":"1993","journal-title":"Sens. Actuat. A: Phys."},{"key":"ref_28","unstructured":"Ostergaard, D. Available online: http:\/\/www.ansys.com\/assets\/tech-papers\/mems-thermal-analogy-fsi-damping.pdf."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/9\/5\/3854\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:10:26Z","timestamp":1760220626000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/9\/5\/3854"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,20]]},"references-count":28,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2009,5]]}},"alternative-id":["s90503854"],"URL":"https:\/\/doi.org\/10.3390\/s90503854","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5,20]]}}}