On the theory of visco-elasticity: a thermodynamical treatment of visco-elasticity, and some problems of the vibrations of visco-elastic solids

Abstract

The problem of the damping of vibrations in a solid which is imperfectly elastic was introduced to me by Professor E. A. MILNE. Sir CHARLES SHERRINGTON had asked Professor MILNE for his assistance in the analysis of an experiment which Dr. J. C. ECCLES was performing at the Oxford Physiological Laboratories, on the damping of forced longitudinal vibrations in a muscle. It was proposed, in the first place, to assume that in this experiment muscle displays dynamical properties of the same character as a non-living solid—a similarity between the dynamical behaviour of muscle and that of rubber and glass had already been noticed. According to this view the damping of vibrations in the muscle would be due to the “ imperfectness of elasticity ” of the muscle; and in order to work out the analysis of the experiment, it is necessary to know the expression for the tension at any point of the muscle at any instant during its straining . An examination of the scientific literature dealing with the imperfectness of elasticity of solids did not indicate an immediate solution of the problem.