A time-dependent problem of two-dimensional waves propagating from the boundary of a semi-infinite medium is described. Linear equations of coherent electromagnetoelasticity for isotropic conductors are used to formulate the problem. To obtain the solution, a small parameter method is used, where the small parameter is the quotient that characterizes the relation between mechanic and electromagnetic fields. The resolving system is formulated as a system of recurrent relations in terms of small parameter series' quotients. The null approximation is actually the solution for a purely mechanic problem. It is shown that in order to obtain higher order approximation one should first construct solutions for mechanical problems with specific time-dependent volumetric disturbances that depend on area's geometry. Solutions for half-plane and infinite medium with spherical cavity are used as examples of this approach.
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