Finite Element Modeling of Nonlinear Vibration Behavior of Piezo-Beam

Nonlinear vibration behavior of piezoceramics at strong electric field is a well-known phenomenon. In recent experimental studies when the piezoceramics were excited close to their natural frequencies, at weak electric field also nonlinear vibration behavior was observed. This nonlinear vibration behavior was observed in the form of dependence of resonance frequency on the vibration amplitude and nonlinear relationship between excitation voltage and vibration amplitude. This book aims to provide a thorough understanding of nonlinear vibration behavior of piezo beam system subjected to weak electric field. A finite element model is presented to describe the nonlinear behavior observed during experiments. The equations of motion for the finite element model is derived by introducing nonlinear constitutive relations of piezoceramics in Hamilton's principle. Modal reduction is used to reduce the equations of motion. Thus obtained reduced equation of motion is solved by harmonic balance method and numerical integration. Experimental validation of finite element model is carried out by comparing the results obtained by exciting the piezo-beam system close to its natural frequencies.