The transient amplitude of the viscoelastic travelling string: An integral constitutive law

The problem considered is an initially stressed viscoelastic string subjected to steady state and harmonic variation of axial motion. The string material is assumed to be constituted by the hereditary integral type. The partial differential-integral equation of motion is derived first. Then by applying Galerkin's method, the governing equation is reduced to a set of second order non-linear differential-integral equations which are solved by finite difference numerical integration procedures. The viscoelastic string with a linear spring-dashpot model is considered as the Voigt element in series with a spring (three-parameter model). The qualitative aspect of parametric excitation due to the non-uniform travelling velocity of a viscoelastic string is investigated. Finally, the results are compared with those obtained by a constitutive law of a differential type method. The effects of elastic and viscoelastic parameters, constant and non-constant transport speeds, the wave propagation speed ratio, and the non-linear term on the transient amplitudes are also investigated. (C) 1997 Academic Press Limited.