Free vibration of a system composed of two beams separated by an elastic layer

The problem of transverse free vibration of a system of two axially loaded beams which are separated by an elastic layer is considered. The solution of the problem for different types of boundary conditions is performed. The frequency equation is obtained in the case when the first beam of the system is compressed under the force P_1 while the second one under goes action of tensile force P_2=P_1. Influence of the stiffness modulus of the elastic layer on vibration frequencies of the compound system is investigated.