Modeling of wave processes in a thick-walled viscoelastic spherical shell under impulse load

Abstract

The article investigates the problem of propagation of longitudinal waves in a thick-walled viscoelastic spherical shell under impulse load on its inner surface. The paper presents a numerical-analytical solution to the problem using the Laplace transform. The viscoelasticity model is described through the shear modulus operator relaxing according to the Kelvin – Voigt model without taking into account the relaxation of the volumetric module. The authors highlight important aspects, such as the need to take into account high-frequency oscillations and inertial effects arising from impulse load. Viscoelastic materials exhibit complex behavior depending on the time and frequency of load application, which requires the use of appropriate behaviors. The article presents graphs of the dependence of displacements on a radial variable at different time intervals, which allows us to better understand the reaction of a viscoelastic shell under the influence of a pulsed load. The results of the study can be useful in the development of structures subject to significant short-term loads (pulse effects), such as high-pressure tanks, pipelines, reactors, etc.