Vibration analysis of piezoelectric Kirchhoff-Love shells based on Catmull-Clark subdivision surfaces

Liu, Z. , McBride, A. , Saxena, P. , Heltai, L., Qu, Y. and Steinmann, P. (2022) Vibration analysis of piezoelectric Kirchhoff-Love shells based on Catmull-Clark subdivision surfaces. International Journal for Numerical Methods in Engineering, 123(18), pp. 4296-4322. (doi: 10.1002/nme.7010)

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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. This 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 shell formulation is verified using a one dimensional piezoelectric beam. 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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:McBride, Professor Andrew and Liu, Dr Zhaowei and Saxena, Dr Prashant and Steinmann, Professor Paul
Authors: Liu, Z., McBride, A., Saxena, P., Heltai, L., Qu, Y., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:International Journal for Numerical Methods in Engineering
ISSN (Online):1097-0207
Published Online:10 May 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in International Journal for Numerical Methods in Engineering 123(18): 4296-4322
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300129Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational MechanicsChristopher PearceEngineering and Physical Sciences Research Council (EPSRC)EP/R008531/1ENG - Infrastructure & Environment