the Character of Forced Vibrations of the Three-layered Orthotropic Plates
in the Mixed-Boundary Problem
The object of study is the forced vibrations of the three-layered orthotropic plate, on the front face of the lower level of which the displacement vector is given which variates harmonically according to time. Between the layers there are conditions of full contact. All the cases when the front face of the upper layer is free or tightly fastened are observed. Formulae are developed to determine the amplitudes of vibrations. A numerical analysis is performed for a number of alternative versions of the three-layered packet. It is shown that when all the three layers are relatively inflexible, then the vibration amplitudes increase from layer to layer, but when the middle layer is smoother, e.g. it is made of rubber material, then the amplitudes abruptly decrease in the third layer. Calculations have been also done for the tough fastening case and it is shown, that the presence of the middle rubber layer significantly decreases the vibration amplitudes in the upper layer. These results prove the necessity of using seismic isolators in a seismic steady construction.