Nonlinear Behavior of Piezo-Beam-Systems Subjected to Weak Electric Field

Abstract

Abstract Experimental studies of piezo-beam systems subjected to weak harmonic electric fields have revealed typical nonlinear effects, e.g. dependence of the resonance frequency on the amplitude, superharmonics in spectra and a nonlinear relationship between excitation voltage and vibration amplitude. In contrast to the well-known nonlinear effects for piezoceramics in presence of strong electric fields, these effects have not been widely described in the literature. In this paper we attempt a description of these phenomena by nonlinear constitutive relations, in particular by a non-constant elastic modulus Ec and piezoelectric factor d31. The equations of motion for the system under consideration are derived via the Ritz-method using Hamilton’s principle. The ‘nonlinear’ parameters are determined and the numerical results are compared to those obtained experimentally. The effects described herein may have a significant influence whenever structures are excited close to resonance frequencies via piezo-electric elements.