Forced vibrations of a layer of a viscoelastic material under the action of a convective wave of shear stresses

A two-dimensional problem of deformation of a layer of a viscoelastic material glued to a solid base by a traveling wave of shear stress is solved. Analytical expressions for two shear compliance components corresponding to two surface displacement components are obtained. It is shown that the dimensionless compliance components depend only on the viscoelastic properties of the material, the ratio of the wavelength to the layer thickness $\lambda/H$, and the ratio of the wave velocity to the propagation rate of shear vibrations $V/C_t^0$. Data on the dynamic compliance in the ranges $0.2<\lambda/H<60.0$ and $0.2<V/C_t^0<5.0$ are given. It is established that, in the range $1.5<\lambda/H<5.0$, the normal component of the shear compliance decreases sharply. Diagrams of the phase shift of the displacement components relative to the phases of the applied oscillatory shear stresses and diagrams of displacements and shifts of their phases over the thickness of the viscoelastic layer are presented.