Vibration analysis of piezoelectric Kirchhoff–Love shells based on Catmull–Clark subdivision surfaces
Zhaowei Liu, Andrew McBride, Prashant Saxena, Luca Heltai, Yilin Qu, Paul Steinmann
Abstract
Abstract An isogeometric Galerkin approach for analysing the free vibrations of piezoelectric shells is presented. The shell kinematics is specialized to infinitesimal deformations and follow the Kirchhoff–Love hypothesis. Both the geometry and physical fields are discretized using Catmull–Clark subdivision bases. This provides the required ‐continuous discretization 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 shell formulation is verified using a one dimensional piezoelectric beam. The piezoelectric effect and vibration modes of a transverse isotropic curved plate are analyzed 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.