Abstract
A new method for construction of an explicit solution of the initial value problem for the partial differential equations of magneto-electro-elasticity is suggested. This method consists of the reduction of the time-dependent equations of magneto-electro-elasticity to a symmetric hyperbolic system of the first-order partial differential equations. The explicit formula for the solution is found by application of the theory and methods of symmetric hyperbolic systems. This formula can be applied for modelling wave propagation in magneto-electro-elastic materials as well as in artificial magneto-electro-elastic materials obtained from laminated heterostructure composed of materials by asymptotic homogenization method.
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