Free Vibration of the System of Two Timoshenko Beams Coupled by a Viscoelastic Interlayer - Cabańska-Płaczkiewicz, K. (Engineering Transactions, 1999)
In this paper the uniform analytical method [3] has been used for solving a problem of free vibrations of continuous sandwich beam with damping. External layers are modelled as Timoshenko beams, while the internal layer possesses the characteristics of a viscoelastic, one-directional Winkler foundation. The phenomenon of free vibration has been described using a homogenous system of coupled partial differential equations. After separation of variables in the system of differential equations, the boundary problem has been solved and four complex sequences have been obtained: the sequences of frequencies, and the sequences of free vibration modes. Then, the property of orthogonality of complex free vibration modes has been demonstrated. The free vibration problem has been solved for arbitrarily assumed initial conditions.