A Galerkin approach for analysing coupling effects in the piezoelectric semiconducting beams

Liu, Z. , Bian, P.-L., Qu, Y., Huang, W., Chen, L., Chen, J., Saxena, P. and Yu, T. (2024) A Galerkin approach for analysing coupling effects in the piezoelectric semiconducting beams. European Journal of Mechanics - A/Solids, 103, 105145. (doi: 10.1016/j.euromechsol.2023.105145)

Abstract

The piezoelectric semiconductor combines the characteristics of both piezoelectric and semiconducting materials, making it highly promising for a variety of engineering applications. The present work adopts a Galerkin approach to derive a general weak form of the coupled governing equations for the analysis of piezoelectric semiconductors. The coupling effect between the strain, the electric field, and the gradients of the concentrations of holes and electrons has been considered. Piezoelectric semiconductors are often deployed in the shape of rods and beams and therefore commonly experience axial and transverse load. Thus, the Euler–Bernoulli beam theory is employed to formulate a numerical approach to analyse the coupling behaviour of such piezoelectric semiconductor beams. In order to satisfy the C1 continuity requirement of Euler–Bernoulli beam theory without introducing additional degrees of freedom, a discretisation with B-Splines is used. Non-mechanical variables, including electrical potential, holes and electrons concentrations, are decomposed into constant, linear and quadratic terms through series expansion along the thickness, which ensures compatibility with beam formulation. To validate the proposed method, an N-type piezoelectric semiconducting beam under a sinusoidal distributed load, for which an analytical solution is available, is initially examined. Subsequently, complex examples including a cantilever beam with generalised loading conditions and a beam with PN-junction are analysed to demonstrate the capabilities of the proposed method in handling more challenging scenarios.

• Item Type: Articles
• Keywords: Piezoelectric semiconductor, Galerkin method, semiconducting material, PN-junction, B-Splines discretisation.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Saxena, Dr Prashant and Liu, Dr Zhaowei
• Authors: Liu, Z., Bian, P.-L., Qu, Y., Huang, W., Chen, L., Chen, J., Saxena, P., and Yu, T.
• College/School: College of Science and Engineering > School of Engineering; College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: European Journal of Mechanics - A/Solids
• Publisher: Elsevier
• ISSN: 0997-7538
• ISSN (Online): 1873-7285
• First Published: First published in European Journal of Mechanics - A/Solids 103: 105145
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
311183		Extreme deformations of magneto- and electro-active membranes: A framework to model instabilities due to large multi-physics loads in thin structures	Prashant Saxena	Engineering and Physical Sciences Research Council (EPSRC)	EP/V030833/1	ENG - Infrastructure & Environment