On propagation of small non-stationary disturbances in linear viscoelastic fluids

Summary A representation is given for the solutions of linearized equations describing a flow of compressible viscoelastic fluids, the spherical part of tensor of stresses corresponding to the rheological Voigt body, while the deviator part corresponds to the Maxwell, Oldroyd and Kelvin-Voigt body of any order. Two independent equations for the propagation of longitudinal and transverse disturbances are obtained.The Laplace transform is applied to study the propagation of plane non-stationary longitudinal and transverse waves in linear viscoelastic fluids, where the spherical part of the tensor of stresses corresponds to the elastic body, while the deviator part corresponds to the Maxwell body. The problem of inversion is reduced to the numerical solution of the linear homogeneous Volterra integral equation of the second kind with a discontinuous kernel.