Electric potential response analysis of a piezoelectric shell under random micro-vibrationexcitations

Abstract

The response characteristics of a spherically symmetric piezoelectric shell under randomboundary micro-vibration excitations are analyzed and calculated. The equation for electricpotential is integrated radially to obtain the electric potential as a function ofdisplacement, so that the differential equations for the piezoelectric shell with electrical andmechanical coupling are converted into an equation only for the displacement. Thedisplacement transformation is constructed to convert the random boundary conditionsinto homogeneous ones, and the transformed displacement is expanded in space to furtherconvert the partial differential equation for the displacement into ordinary differentialequations using the Galerkin method. The equations represent a multi-degree-of-freedomdynamic system with an asymmetric stiffness matrix under random micro-vibrationexcitations. The frequency-response function matrix, power spectral density matrix andcorrelation function matrix of the system response are derived from these equations basedon the theory of random vibration. The expressions of mean-square displacement,stress and electric potential of the piezoelectric shell are finally obtained andillustrated by numerical results for random micro-vibration excitations. The randomelectrical and mechanical coupling properties, in particular the relations betweenboundary electric potential responses and micro-displacement excitations, areexplored.