Relations Between Modulus and Compliance

Abstract

Connections between some of the gross features of a modulus and the corresponding compliance are easy to obtain by using the reciprocal relation between their s-multiplied transforms. In the present chapter we first consider some exact relations that can be obtained by considering the behavior of the transforms for small values of the transform parameter. We then consider some approximate but more detailed relations that can be obtained by using linear approximations to the response functions on a log-log plot. The main object of these considerations is to develop enough qualitative understanding that, given one response function in graphical or numerical form, graphs of all others can be sketched immediately with fair quantitative accuracy. More refined numerical techniques which can give arbitrarily accurate results are not discussed because they do not lead to any qualitative understanding of the situation.