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TECHNICAL PAPERS

# Electromagnetoelastic Dynamic Response of Transversely Isotropic Piezoelectric Hollow Spheres in a Uniform Magnetic Field

[+] Author and Article Information
H. L. Dai1

Department of Engineering Mechanics, Hunan University, Changsha 410082, Hunan Province, P. R. C.hldai520@sina.com

Y. M. Fu, T. X. Liu

Department of Engineering Mechanics, Hunan University, Changsha 410082, Hunan Province, P. R. C.

1

To whom correspondence should be addressed.

J. Appl. Mech 74(1), 65-73 (Oct 18, 2005) (9 pages) doi:10.1115/1.2178361 History: Received May 13, 2005; Revised October 18, 2005

## Abstract

An analytical method is presented to solve the problem of electromagnetoelastic dynamic response of transversely isotropic piezoelectric hollow spheres in a uniform magnetic field, subjected to arbitrary mechanical load and electric excitation. Exact expressions for the dynamic responses of stresses, perturbation of magnetic field vector, electric displacement, and electric potential in piezoelectric hollow spheres are obtained by means of Hankel transform, Laplace transform and their inverse transforms. An interpolation method is applied to solve the Volterra integral equation of the second kind involved in the exact expression, which is caused by interaction between electric-elastic field and electric-magnetic field. Thus, an analytical solution for the problem of dynamic response of a transversely isotropic piezoelectric hollow sphere in a uniform magnetic field is obtained. Finally, some numerical examples are carried out, and may be used as a reference to solve other dynamic coupled problems of electromagneto-elasticity.

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## Figures

Figure 1

A geometric graph of the piezoelectric hollow sphere placed in a uniform magnetic field, subjected to mechanical load and electric excitation

Figure 2

Response histories of the dynamic radial stresses σr*, where R=(r−a)∕(b−a), τ=CLt∕(b−a), pa(t)=p0, and σr*=σr∕p0. (a) R=0 and R=0.1; (b) R=0.5 and R=1.

Figure 3

Response histories of the dynamic hoop stresses σθ* at R=0, R=0.5, and R=1, where R=(r−a)∕(b−a), τ=CLt∕(b−a), pa(t)=p0, and σθ*=σθ∕p0

Figure 6

Distributions of the dynamic electric potentials ϕ* at R=0, R=0.5, and R=1, where R=(r−a)∕(b−a), τ=CLt∕(b−a), pa(t)=p0, and ϕ*=ϕ∕p0

Figure 9

Response histories of perturbation of magnetic field vector hu* at R=0, R=0.5, and R=1, where R=(r−a)∕(b−a), τ=CLt∕(b−a), ϕb(t)=ϕ0, and hu*=hu∕(Huϕ0)

Figure 5

Response histories of the dynamic electric displacements Dr at R=0, R=0.5, and R=1, where R=(r−a)∕(b−a), τ=CLt∕(b−a), pa(t)=p0, and Dr*=Dr∕p0

Figure 4

Response histories of perturbation of magnetic field vector hu* at R=0, R=0.5, and R=1, where R=(r−a)∕(b−a), τ=CLt∕(b−a), pa(t)=p0, and hu*=hu∕(Hup0)

Figure 14

(a) Response histories of dynamic radial stress σr at R=0.5; (b) response histories of dynamic hoop stress σθ at R=0

Figure 13

Response histories of the dynamic hoop stresses σθ* at R=0.5, where R=(r−a)∕(b−a), τ=CLt∕(b−a), pa(t)=p0, and σθ*=σθ∕p0

Figure 12

Response histories of the dynamic radial stresses σr* at R=0.5, where R=(r−a)∕(b−a), τ=CLt∕(b−a), pa(t)=p0, and σr*=σr∕p0

Figure 11

Distributions of the dynamic electric potentials ϕ* at τ=0.1, τ=0.5, and τ=1, where R=(r−a)∕(b−a), τ=CLt∕(b−a), ϕb(t)=ϕ0, and ϕ*=ϕ∕ϕ0

Figure 10

Response histories of the dynamic electric displacements Dr at R=0, R=0.5, and R=1, where R=(r−a)∕(b−a), τ=CLt∕(b−a), ϕb(t)=ϕ0, and Dr*=Dr∕ϕ0

Figure 8

Response histories of the dynamic hoop stresses σθ* at R=0, R=0.5, and R=1, where R=(r−a)∕(b−a), τ=CLt∕(b−a), ϕb(t)=ϕ0, and σθ*=σθ∕ϕ0

Figure 7

Response histories of the dynamic radial stresses σr* at R=0, R=0.1,R=0.5, and R=1, where R=(r−a)∕(b−a), τ=CLt∕(b−a), ϕb(t)=ϕ0, and σr*=σr∕ϕ0

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