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Technical Briefs

Closed Form Expression for the Vibration Problem of a Transversely Isotropic Magneto-Electro-Elastic Plate

[+] Author and Article Information
Mei-Feng Liu

Department of Applied Mathematics, I-Shou University, Dashu Township, Kaohsiung County 840, Taiwan, R.O.C.

Tai-Ping Chang

Department of Construction Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung 811, Taiwan, R.O.C.

J. Appl. Mech 77(2), 024502 (Dec 09, 2009) (8 pages) doi:10.1115/1.3176996 History: Received November 06, 2008; Revised June 03, 2009; Published December 09, 2009; Online December 09, 2009

A closed form expression for the transverse vibration of a magnetoelectroelastic (MEE) thin plate is derived, and the exact solution for the free vibration of a two-layered BaTiO3CoFe2O4 composite is obtained. Based on the Kirchhoff thin plate theory, the bending problem of a transversely isotropic MEE rectangular plate is investigated, and the governing equation in terms of the transverse displacement is then presented in a rather compact form. The material coefficients for such MEE plate are expressed uniquely by the volume fraction (vf) of the two-layered BaTiO3CoFe2O4 composite, which indicates a transversely isotropic MEE medium. The natural frequencies of such MEE plate are evaluated analytically, and the effects of different volume fractions on the natural frequency are further discussed.

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Figures

Grahic Jump Location
Figure 1

Natural frequencies versus volume fractions of a MEE thin plate with various mode number (m=1)

Grahic Jump Location
Figure 2

Natural frequencies versus mode numbers for a MEE thin plate with various volume fractions (n=1)

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