Free damped oscillations in viscoelastic materials

Abstract

In a recent paper Struik has shown how approximate values of the dynamic viscoelastic functions for a material subjected to undamped oscillatory shear may be correctly deduced from observations on the free damped oscillation of a system in which the restoring force is provided by that material. On the assumption that the material has a discrete positive spectrum of relaxation times and negligible inertia, he was able to obtain bounds to the errors in the values of the dynamic functions as calculated from certain simple formulae involving the frequency and logarithmic decrement of the damped oscillations. In the present paper the work is carried a stage further by the calculation of attainable limits to the errors, and these are appreciably narrower than Struik's bounds. Further, it is shown that the results apply equally to cases in which the internal inertia of the material is important, provided there is no other elastic member in the oscillating system. The justification for assuming a discrete positive spectrum of relaxation times is briefly discussed.