  An isogeometric Galerkin approach for analysing the free vibrations of
piezoelectric shells is presented. The shell kinematics is specialised to
infinitesimal deformations and follow the Kirchhoff-Love hypothesis. Both the
geometry and physical fields are discretised using Catmull-Clark subdivision
bases. It provides the required C1 continuous discretisation for the
Kirchhoff-Love theory. The crystalline structure of piezoelectric materials is
described using an anisotropic constitutive relation. Hamilton's variational
principle is applied to the dynamic analysis to derive the weak form of the
governing equations. The coupled eigenvalue problem is formulated by
considering the problem of harmonic vibration in the absence of external load.
The formulation for the purely elastic case is verified using a spherical thin
shell benchmark. Thereafter, the piezoelectric effect and vibration modes of a
transverse isotropic curved plate are analysed and evaluated for the
Scordelis-Lo roof problem. Finally, the eigenvalue analysis of a CAD model of a
piezoelectric speaker shell structure showcases the ability of the proposed
method to handle complex geometries.
