Let us consider the problem of forcedsymmetric vibrations of a thin hemisphere of radius R with a mass of M, rigidly fixed along the equator, under the action of a normal load of constant surface density P. The front of the load wave propagates at a constant velocity v. ...

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 is considered.

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