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Structural Engineering and Mechanics Volume 23, Number 5, July30 2006 , pages 525-542 DOI: https://doi.org/10.12989/sem.2006.23.5.525 |
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Spherically symmetric transient responses of functionally graded magneto-electro-elastic hollow sphere |
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H. M. Wang and H. J. Ding
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| Abstract | ||
| On the basis of equilibrium equations for static electric and magnetic fields, two unknown functions related to electric and magnetic fields were firstly introduced to rewrite the governing equations, boundary conditions and initial conditions for mechanical field. Then by introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is obtained. By using the separation of variables technique as well as the electric and magnetic boundary conditions, the dynamic problem of a functionally graded magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two unknown functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula for solving the integral equations is derived. Transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented and discussed. | ||
| Key Words | ||
| hollow sphere; magneto-electro-elastic; functionally graded materials; transient response. | ||
| Address | ||
| H. M. Wang; Department of Mechanics, Zhejiang University, Hangzhou 310027, P. R. China H. J. Ding; Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P. R. China | ||