Let us consider the problem of forced symmetrical oscillations of a thin hemisphere of radius R with a mass of M, rigidly fixed along the equator, under the influence of a normal load of constant surface density R. The front of the load wave propagates at a constant velocity ѵ...

Consider the problem of calculating the natural frequencies of axisymmetric oscillations of a thin hemisphere of radius R with mass M, rigidly fixed at the equator. The system of equations in displacements describing the oscillations of the shell element has the form...

Calculation of the integral from the square of the Lejandre function...