Dynamics Analysis of the Steady and Transient States of a Nonlinear Piezoelectric Beam by a Finite Element Method

This paper presents a finite element formulation for the dynamics analysis of the steady and transient states of a nonlinear piezoelectric beam. A piezoelectric beam with damping is studied under harmonic excitation. A numerical method is used for this analysis. In the paper, the central difference formula of four order is used and compared with the central difference formula of two order in the time response of the structure. The NPBDA program is developed with Matlab software. In this program, the Newmark technique for dynamic analysis is used, the Newton-Raphson iterative and Simpson methods are used for the nonlinear solution. To verify the NPBDA results, the experimental results of Malatkar are used for the nonlinear vibration analysis of a beam without piezoelectric properties. Then, the piezoelectric effect on the frequency mode values and the time response are obtained. Afterwards, the modulation frequency in the nonlinear beam and the piezoelectric effect in this parameter are verified.