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Vibration of beams with piezoelectric inclusions

Vibration of beams with piezoelectric inclusions
Vibration of beams with piezoelectric inclusions
A mathematical model for the vibration of beams with piezoelectric inclusions is presented. The piezoelectric inclusion in a non-piezoelectric matrix (host beam) is analyzed as two inhomogeneous inclusion problems, elastic and dielectric, by using Eshelby’s equivalent inclusion method. The natural frequency of the beam is determined from the variational principle in Rayleigh quotient form, which is expressed as functions of the elastic strain energy and dielectric energy of the piezoelectric inclusion. The Euler–Bernoulli beam theory and Rayleigh–Ritz approximation technique are used in the present analysis. In addition, a parametric study is conducted to investigate the influence of the energies due to piezoelectric coupling on the natural frequency of the beam.
vibration, beam, piezoelectric inclusions, natural frequency, eshelby’s equivalent inclusion method
0020-7683
2509-2522
Della, Christian N.
218552a1-70df-411c-9197-a24a243b1002
Shu, Dongwei
c54c2744-7263-43e5-8eda-7d329d44c4d8
Della, Christian N.
218552a1-70df-411c-9197-a24a243b1002
Shu, Dongwei
c54c2744-7263-43e5-8eda-7d329d44c4d8

Della, Christian N. and Shu, Dongwei (2007) Vibration of beams with piezoelectric inclusions. International Journal of Solids and Structures, 44 (7-8), 2509-2522. (doi:10.1016/j.ijsolstr.2006.08.002).

Record type: Article

Abstract

A mathematical model for the vibration of beams with piezoelectric inclusions is presented. The piezoelectric inclusion in a non-piezoelectric matrix (host beam) is analyzed as two inhomogeneous inclusion problems, elastic and dielectric, by using Eshelby’s equivalent inclusion method. The natural frequency of the beam is determined from the variational principle in Rayleigh quotient form, which is expressed as functions of the elastic strain energy and dielectric energy of the piezoelectric inclusion. The Euler–Bernoulli beam theory and Rayleigh–Ritz approximation technique are used in the present analysis. In addition, a parametric study is conducted to investigate the influence of the energies due to piezoelectric coupling on the natural frequency of the beam.

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More information

Submitted date: 16 September 2005
Published date: April 2007
Keywords: vibration, beam, piezoelectric inclusions, natural frequency, eshelby’s equivalent inclusion method
Organisations: Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 50326
URI: http://eprints.soton.ac.uk/id/eprint/50326
ISSN: 0020-7683
PURE UUID: bbbc2670-794b-40b6-a92d-1ea2cc73ee75

Catalogue record

Date deposited: 15 Feb 2008
Last modified: 08 Jan 2022 16:00

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Contributors

Author: Christian N. Della
Author: Dongwei Shu

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