Higher Approximation to Relaxation Spectra from Dynamic Measurements

Abstract

General methods of successive approximations to calculate the relaxation spectrum from data of dynamic mechanical measurements are worked out using an inversion theorem of integral equations of the Stieltjes type. The idea underlying the methods is essentially the same as that used by Schwarzl and Staverman in their treatment of stress relaxation data. It is shown that the delta‐function method of Schwarzl and Staverman and of Leaderman is not a unique process of successive approximations to obtain relaxation spectra from dynamic data. Conditions to obtain a series of best approximations in terms of the delta‐function method are discussed.