On Elastic Continua With Hereditary Characteristics

In a previous paper (1) the free and forced vibrations of systems of one degree of freedom with hereditary damping characteristics were discussed. In the present paper the classical equations of motion for elastic media are extended on the basis of the general linear stress-strain law involving hereditary damping. These equations are applied to the case of free radial vibrations of a sphere. Furthermore, the free vibrations of strings, the free transverse vibrations of beams, and the free vibrations of rectangular and circular membranes are studied under the assumption of hereditary damping.