Vibration Analysis of Piezoelectric Kirchhoff-Love Shells based on Catmull-Clark Subdivision Surfaces

TL;DR

This paper introduces an isogeometric Galerkin method using Catmull-Clark subdivision surfaces for analyzing free vibrations of piezoelectric shells, enabling accurate modeling of complex geometries with piezoelectric effects.

Contribution

It develops a novel isogeometric approach combining subdivision surfaces with Kirchhoff-Love shell theory for piezoelectric vibration analysis, handling complex geometries and anisotropic materials.

Findings

Verified formulation with spherical shell benchmark

Analyzed vibration modes of a curved piezoelectric plate

Demonstrated applicability to complex CAD models of speaker shells

Abstract

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.