Nonlinear Statics/Dynamics Analysis Of Piezoelastic Laminated Microbeam

In this dissertation, considering piezoelectric laminated microbeam under electric field conditions as the subjects investigated, taking into account the impact of external DC and AC, geometric nonlinearity, piezoelectric effect, squeeze film damping, edge effects and other factors, the static and dynamic behavior of laminated piezoelectric micro-beam structure are studied, which reveals the essential characteristics of the mechanical behavior of the structures. The results of this research is not only the more important academic value, but also has strong significance in engineering. The main research work are as follows.Nonlinear static mechanical behavior of the laminated piezoelectric beam under micro-power excitation is investigated. Considerring two kinds of external incentives DC and AC loads, control voltage of the piezoelectric layer and geometric nonlinearity, the Nonlinear Dynamicsamics equations of the micro laminated piezoelectric cantilever are established. Numerical solutions of nonlinear dynamic response of the micro-laminated piezoelectric beams with different physical parameters are gotten. The impact of the geometric nonlinearity of the collapse threshold voltage is studied.Axial and lateral load in the cycle, the role of, the incremental harmonic balance method is utilized to study the nonlinear dynamics staibility of the axial movable clamped laminated piezoelectric micro-beam under periodic axial loads and DC electric field. Impact of the parameters on its main nonlinear dynamic instability areas is discussed. Considering the axial x static load and lateral AC and DC field effects, when the mixed electric load are with the same phase, a nonlinear differential-integral Mathieu equation is developed. Using the maximum Lyapunov index as the criterion, the influence of the DC and AC load amplitude and the axial static load on the elastic stability of the micro-beam is discussed. When the mixed electrical load are with antiphase, the differential-integral Duffing equation is yielded. It is found that with the increase in amplitude of the AC load, chaotic vibrations of the laminated piezoelectric micro-beam occur through period doubling bifurcation.Based on Euler-Bernoulli beam theory, considerring the geometric nonlinearity, electric field edge effects and materials, as well as squeeze film damping effect, dynamics of the laminated piezoelectric micro-beam under two-way electrical loads are studied. The bifurcation and chaos under different parameters are discussed in detail. Meanwhile the cycle rate is adopted to verify the accuracy.