A method for resolving a thermoelasticity problem with inhomogeneous boundary conditions is presented. Boundary conditions represent uneven surface heating of the layer. An asymptotic procedure for separation of variables based on introduction of additional dimensional scales is used. With an additional assumption that the unevenness of the heating is small enough this procedure makes it possible to obtain the solution. The method is shown for periodic heating case. After the separation of variables the solution is obtained using Fourier series.
A method for solving time-dependent bound problems of propagation of electromagnetoelastic waves is used. The linearized problem formulation relative to initial static electromagnetic field for homogeneous isotropous medium with the absence of piezoelectric effects taking into consideration Lorentz force is presented. The solution method is described for one-dimensional problem for a spherical layer. To obtain the solution the Laplace transform of time and resolution in series, in terms of a small parameter have been used. The latter characterizes the degree of coherence between elastic properties and electromagnetic field. The example of the calculation has been introduced.
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 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.
