Boundary- value problems correspond to forced vibration of the pre-stressed plate-strip resting on a rigid foundation

In this study, boundary-value problems correspond to forced vibration of initially stressed plate-strip with finite length resting on a rigid foundation both for one layered and for bi-layered cases are investigated. The mathematical modeling of the considered problems is made by the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies.First, boundary-value problem for a pre-stressed plate-strip resting on a rigid foundation is considered and the mathematical modeling of the considered problem is made. The numerical solution of the problem that has no analytical solution is done by the use of the Finite element method. The validity of the developed model is tested on concrete problems and the coincidence with previous studies for layers with infinite length is seen. The effects of change of system parameters are presented.As a second problem, boundary-value problem for bi-layered pre-stressed plate-strip resting on a rigid foundation is considered. The mathematical modeling for the bi-layered case is made and the finite element formulation is presented. The stress distributions on the interface planes are investigated and the influence of the length of the layers to these distributions is presented.Moreover, the influence of pre-stretching of the layer(s) and the frequency of the time-harmonic dynamical load on the stress distribution for both cases is investigated and the numerical results obtained are presented.