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

Liu Z, McBride A, Saxena P, Heltai L, Qu Y, Steinmann P (2022)

Publication Type: Journal article

Publication year: 2022

Journal

International Journal for Numerical Methods in Engineering Wiley

DOI: 10.1002/nme.7010

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 (Formula presented.) -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.

Additional Organisation(s)

Graduiertenkolleg 2495/2 Energiekonvertierungssysteme: von Materialien zu Bauteilen (Energy Conversion Systems: From Materials to Devices)

Involved external institutions

Scuola Internazionale Superiore di Studi Avanzati (SISSA) IT Italy (IT) Xi’an Jiaotong-Liverpool University (XJTLU) CN China (CN) University of Glasgow GB United Kingdom (GB) Hohai University CN China (CN)

How to cite

APA:

Liu, Z., McBride, A., Saxena, P., Heltai, L., Qu, Y., & Steinmann, P. (2022). Vibration analysis of piezoelectric Kirchhoff–Love shells based on Catmull–Clark subdivision surfaces. International Journal for Numerical Methods in Engineering. https://dx.doi.org/10.1002/nme.7010

MLA:

Liu, Zhaowei, et al. "Vibration analysis of piezoelectric Kirchhoff–Love shells based on Catmull–Clark subdivision surfaces." International Journal for Numerical Methods in Engineering (2022).

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