Abstract
The radial propagation of the steady-state wave motion is studied for a pre-stressed cylindrical shell composed of the isotropic compressible neo-Hookean material. The radial static deformation of the cylindrical shell and radial wave motion of the pre-stressed cylindrical shell are investigated. The mathematical model is established as a class of boundary value problems of the second-order nonlinear ordinary differential equation (ODE). Based on the theory of the large elastic deformation superposed by the small harmonic deformation, a radial dynamic displacement is added to the pre-stressed cylindrical shell. The existence of the steady-state wave motion is conducted. Numerical solutions are obtained by using the multiple shooting method. In addition, the influences of the static load, material and structural parameters on the steady-state wave motion are discussed. Numerical results indicate that as the static load increases, the frequency of the steady-state wave motion increases and the amplitude decreases in the compressible hyperelastic cylindrical shell. The material parameter plays a significant role in the frequency and amplitude of the steady-state wave motion.
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