Non-stationary axisymmetric waves in electromagnetoelastic space with a spherical cavity

We consider the associated non-stationary problem of propagation of axisymmetric disturbances from a spherical cavity in electromagnetoelastic space. It is assumed that the medium is a homogeneous isotropic conductor. Linear equations of motion of an elastic medium are used taking into account the linearized Lorentz forces, as well as Maxwell's equations, together with the linearized generalized law. The initial conditions are zero, at the boundary of the cavity defined displacement and the tangential component of the electric field. The desired functions are arranged in series of Legendre and Gegenbauer polynomials, as well as in series according to a small parameter characterizing the connection of mechanical and electromagnetic fields. Apart from that the applicable Laplace transform in time is used. The result is a recurrence of the small parameter sequence of boundary value problems, the solution of which is represented in the integral form with kernels in the form of volume and surface Green's functions. Images of Green's functions are found in an explicit manner. Their "elastic" part due to the relation between the modified Bessel functions and elementary functions is reduced to the sum of products of rational functions of the parameter of the Laplace transform to the exponent that lets you find exactly the originals using the corresponding theorems of operational calculus. The “Electromagnetic” part of the Green's function is being constructed in a quasi-static approximation. As a result, in the space of the original resolution of the system is became possible to build recurrence equations which allows finding and moving all the components of the electromagnetic field. In calculating its constituent integrals quadrature formulas are used. The examples of computations are provided. The numerical study of the convergence of series in the small parameter is presented.