Asymptotic analysis of the forced oscillations of double-layered plates with viscous resistance (Q2656451)

In this paper, the asymptotic solution of the three-dimensional dynamic problem of forced oscillations is determined for an orthotropic double-layered plate accounting for the influence of friction in the layers. It is assumed that the friction is proportional to the velocity of points. The general asymptotic solution of the problem is found. It is shown that it is possible to discover the general solution of the interior problem, and to obtain the solution of the formulated interior problem after the boundary conditions, and the contact conditions are satisfied. It is shown that due to the presence of resistance the oscillation amplitudes are always limited. While in the absence of viscous resistance, there are frequencies (resonance), at which the amplitudes become infinite. The first root of the corresponding transcendental equation is calculated. The first layer of the packet is fiberglass orthogonally reinforced at a ratio of two to one. The second layer is rubber.