Małe Punktowo-Symetryczne Drgania Ośrodka Sprężystego Odkształcającego się z Upływem Czasu

Abstract

A small motion is superimposed on the finite motion of a sphere with the radius increasing uniformly with time. The fundamental deformation determined, a small time-dependent displacement field is imposed on this motion. The equations to be satisfied by these small displacements are found, their trivial solutions being derived. After expanding the additional displacements into a Fourier series of spherical functions the case is considered when the solution is a product of a function of time and a function of the remaining variables. It is shown that the only possible vibrations are, in this case, radial vibrations of the sphere.
A plane wave propagating in the sphere undergoing the finite deformation is considered.