Propagation of Elastic Waves in Plates and Bars of Solid Material with Low Shear Modulus

Abstract

Sound propagation in solid media of finite cross section is very complicated in the general case, due to the fact that the boundary conditions can be fulfilled only by superposition of both longitudinal and transverse waves. It can be shown that this picture will be much clearer for rubber-like materials (with low shear modulus, the Poisson constant being nearly 0.5), because the velocity of the transverse waves is much smaller than that of the longitudinal waves. As long as all dimensions normal to the axis are small compared with half the wavelength of the longitudinal wave, the dispersion of the phase velocity is given by the shear modulus as in an incompressible medium with finite shear modulus. Above this frequency limit the influence of the bulk modulus overcomes that of the shear modulus; and if energy losses exist, it will alone determine the behavior. The phase velocity then will nearly be equal to that of the different modes of the longitudinal wave in a liquid column. Measurements of phase velocity and attenuation confirm that below this limiting frequency the damping is determined by the loss factor of the shear modulus, while above the limit a much lower damping exists, a result of the smaller influence of the shear modulus.