Free Vibration of the Axially Loaded System of Two Beams Connected by a Two-Directional Viscoelastic Interlayer

In this paper, the analytical method has been used for solving a problem of free vibration with clamping of an axially loaded sandwich beam. The sandwich beam consists of two external layers connected by a viscoelastic two-directional Winkler interlayer. The upper external layer is described by the Bernoulli–Euler model, which is loaded by a constant axial force. The lower external layer is modeled as the Timoshenko model. The phenomenon of free vibration has been described using a homogenous system of conjugate partial differential equations. After separation of variables in the system of differential equations, the boundary problem has been solved and three complex equations for the definition of frequency and modes of free vibration have been obtained. The free-vibration problem for arbitrarily assumed initial conditions and various axial forces has been considered.