Nonlinear dynamics of thin plates excited by a high-power ultrasonic transducer
Strong superharmonic and high-order subharmonic vibrations of thin metal plates are observed in the experiments when a high-power ultrasonic transducer is used to excite plate vibrations. A finite element model and a lumped-mass discrete parameter model are established, respectively, and numerical simulations are carried out to study the mechanism of nonlinear vibrations. The plate vibrations are characterized by time series, power spectra, phase portraits, Poincaré maps and bifurcation diagram. It can be seen that the contact force waveform distortion is the reason for generating superharmonic vibration, while the intermittent contact between the thin plates and the ultrasonic transducer is the cause of subharmonic vibrations in the plates. The FEM simulation results are in agreement with the numerical results obtained from the discrete model, which have implications for the predication and control of nonlinear vibrations in ultrasonic assisted manufacturing and testing.
KeywordsNonlinear dynamics Vibro-impact Plate vibration Ultrasonic transducer Superharmonic and subharmonics
This work was supported by the National Natural Science Foundation of China under Grant Nos. 11304286, 11274279 and 11174255, and the Fund of the State Key Laboratory of Acoustics, Chinese Academy of Sciences under Grant No. SKLA201404. The author gratefully acknowledges these supports.
- 3.Ribeiro, P.: Non-linear free periodic vibrations of variable stiffness composite laminated plates. Nonlinear Dyn. 70, 1535–1548 (2012)Google Scholar
- 4.Sathyamoorthy, M.: Nonlinear vibration analysis of plates: a review and survey of current developments. Appl. Mech. Rev. 40, 1553–1561 (1987)Google Scholar
- 17.Hallquist, J.: LS-DYNA Theory Manual. Livermore Software Technology Corporation, Livermore (2006)Google Scholar