Analysis of linear visco-elastic spherical waves based on ZWT constitutive equation

For the explosion and shock loading in the 1-100 s time scale, the linear visco-elastic ZWT constitutive equation under a three-dimensional stress state was derived by ignoring the relaxation effect of the low-frequency Maxwell element and the nonlinear spring element. Based on the basic kinetic equation of the spherical wave and the linear visco-elastic ZWT constitutive equation, the third-order wave equation depicted by the displacement u was obtained. The absorption and dispersion phenomena of the spherical wave propagation in the visco-elastic solid were analyzed. Conclusions are as follows: the attenuation factor of the high-frequency spherical wave is inclined to constant, and its phase velocity to that of high-frequency longitudinal wave; the attenuation factor of the low-frequency spherical wave is in direct proportion to the square 2 of the circular frequency, and its phase velocity is inclined to that of the lowfrequency longitudinal wave; the phase velocity of the lowfrequency spherical wave is less than that of the high-frequency spherical wave, and the ratio between them is related to the Poisson ratio as well as the elastic modules of the ZWT and Maxwell elements.