In work questions of distribution of waves in a viscoelastic wedge with any corner of top is considered. The elastic cylinder with a radial crack is a wedge 180 ϕ <  corner. The regional task for system of the differential equations in private derivatives is decided by means of a method of straight lines that allows using a method of orthogonal prorace.

On the basis of the method of orthogonal sweep and the Mueller method, the solution of the problem of intrinsic oscillation of a Toroidal shell with a flowing liquid is discussed. The problem of determining the frequencies and forms of intrinsic bending vibrations in the plane of curvature of curvilinear sections of thin-walled Toroidal shells of large diameter with a flowing liquid, with different conditions for fixing the end sections is solved. The behavior of complex Eigen frequencies as a function of the curvature of the shell axis is studied.

We investigated the natural oscillations of dissipative inhomogeneous plate mechanical systems with point connections. Based on the principle of virtual displacements, we equate to zero the sum of all active work force, including the force of inertia which obtain equations vibrations of mechanical systems. Frequency equation is solved numerically by the method of Muller. According to the result of numerical analysis we established nonmonotonic dependence damping coefficients of the system parameters.

In this paper we consider of natural oscillations cylindrical bodies with external friction. Complex rates changes from friction parameters are shown. Rate equations are solved numerically-by method of Muller.

The paper considers the seismic resistance of subterranean hydro constructions of various shapes under the influence of seismic waves. The review is dedicated to the abovementioned issues. Recommendations on increasing seismic resistance of underground hydraulic structures under the action of seismic waves are suggested.