Non-symmetric dynamic characteristics of spherically symmetric piezoelectric shell

Abstract

Piezoelectric structures are applied broadly in engineering and their accurate analysis is necessary. Piezoelectric shell structures have better electrical-mechanical coupling properties, but they have non-symmetric dynamic characteristics. This paper studies on the non-symmetric characteristics of spherically symmetric piezoelectric shells. The basic equations of piezoelectric spherical shell are given and converted into ordinary differential equations by using the Galerkin method. The description in spherical coordinates with electrical-mechanical coupling induces the non-symmetric generalized stiffness matrix. The asymmetric system eigenvalues differ from the corresponding singular values and the symmetrized system eigenvalues. The left and right eigenvectors of the asymmetric system have the cross-orthogonality relations which differ from the conventional symmetric system relations. Numerical results illustrate the non-symmetric system eigenvalues and singular values, and their relative differences for different piezoelectric constants. Then the non-symmetry of piezoelectric shells needs to be considered in the dynamic analysis.