Shear-wave speeds and elastic moduli for different liquids. Part 1. Theory

D. Joseph, University of Minnesota
Amitabh Narain, Michigan Technological University
O. Riccius, University of Minnesota

© 1986 Cambridge University Press. Publisher's version of record: https://doi.org/10.1017/S0022112086001453

Abstract

In this paper we develop a theory for a rheometrical device for measuring the speed of shear waves into a region at rest. The device is a Couette apparatus with a narrow gap. The outer cylinder is moved impulsively and a time of transit is measured. The linearized theory governing this apparatus is reduced to a perturbation of Stokes’ first problem between parallel planes. A method for determining an effective shear modulus from measured values of the wave speed is discussed and various cases are analysed. An experimental apparatus based on this theory, together with tabular data, is discussed in a companion paper (Part 2, Joseph, Riccius & Arney 1986).