The Propagation of Sinusoidal Small-Amplitude Waves in a Deformed Viscoelastic Solid I

摘要

An isotropic viscoelastic solid is first subjected to a static pure homogeneous deformation. A plane sinusoidal wave is propagated in it. The amplitude of this wave is sufficiently small so that terms of second degree in the displacement gradients associated with it may be neglected in comparison with those of first degree. The secular equation for a wave propagating in any direction with respect to the principal axes of the static strain is obtained. Certain relations between the complex slownesses for the principal waves and the principal stresses, which are independent of the precise form of the constitutive equation, are obtained. These generalize some previously obtained formulae for an elastic material due to Ericksen.