Oscillations of a rigid strip on a viscoelastic half-plane under the vertical load

The oscillations of a rigid strip on a viscoelastic half-plane under the action of a vertical load are considered. The strip is exposed to a time-dependent vertical force. The aim of this study is to develop a problem-solving technique and an algorithm to determine the normal response of the base and the displacement of the strip and viscoelastic half-plane. The contact stress of the half-plane is specified as a series expansion by Che-byshev polynomials of the first kind. The Lamb problem for a viscoelastic plane is solved using the method of double Laplace and Fourier transforms. The problem of oscillations of rigid and viscoelastic beam slabs on a viscoelastic half-plane is considered using the Fourier series method. It is concluded that the Fourier series and Fourier transform methods allow analytical solving of dynamic contact problems for arbitrary viscoelastic kernels. However, when applying this methodology, certain restrictions are placed on the type of loading function. The determination of displacements and stresses from the obtained analytical expressions is a separate and rather complicated computational problem. Thus, the dynamic contact problem is solved using numerical methods.