On the forced vibrations of elastic bodies in contact

The forced vibrations of two elastic bodies having a surface of contact are investigated within the framework of the classical, linear theory of elasticity. The representations for the displacements and stresses consist of two parts, namely, a quasi-static and a dynamic portion. The generalized orthogonality condition and a convenient, simple expression for the generalized forces are derived. As a specific example of this general theory, the forced thickness—stretch problem is solved for a two-layer plate system. Plots of the natural frequencies of vibration as a function of the ratio of the thicknesses of the plates and of the variation of the displacement of the lower face and the interfacial stress as a function of time are given.