Forced vibrations of orthotropic shells when there is viscous resistance

Forced vibrations of orthotropic shells when there is viscous resistance are considered, when two versions of the spatial boundary conditions are given on the upper face of the shell, and the displacement vector is given on the lower face. The solution of the corresponding dynamic equations of the three-dimensional problem of elasticity theory is obtained by an asymptotic method. The amplitudes of the forced vibrations are determined and it is established that the viscous resistance causes the amplitudes of the forced vibrations to increase in the range of values of natural vibrations, but they remain finite. Boundary-layer type functions are obtained, and characteristic equations for determining the rate of decay of boundary vibrations in the direction from the side surface into the shell are established.