| Summary: | 碩士 === 國立臺灣大學 === 應用力學研究所 === 104 === A study of nonlinear vibration of MEMs cantilevered piezoelectric oscillator subjected to intense excitations is presented. Several nonlinear sources within the oscillator will be considered and discussed for the effect to the dynamic response of the system. First, the material nonlinearity in the PZT layer of cantilever beam is considered, the geometrical nonlinearity and inertia nonlinearity which caused by the large deformation of cantilever beam are taken into account in this thesis as well. The derivation of governing equations is based on Hamilton variational principle, together with several assumptions including Euler-Bernoulli beam theory and inextensible beam condition. Reduced-order models by Rayleigh-Ritz approximation are also developed to focus on the first vibration mode of the system.
For further understanding of the system, the approximation analytic solution of the system can be obtained by the method of multiple scale analysis. The effective nonlinear parameter Neff defined in the frequency-response equation is found to be a key parameter for the dynamic response of the system. By substituting the real system dimensions into the simulation, the shape function with point load exerted on the end tip of the beam is found to be a choice to become a standard for the effective coefficients of the governing equations.
The damping and material nonlinearity coefficients in the governing equations are estimated by the curve fitting via experimental data. A good qualitative agreement is obtained between experimental and numerical results.
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