A Non-Conforming Approximate Solution To A Specially Orthotropic Axisymmetric Thin Shell Subjected To A Harmonic Displacement Boundary Condition

Abstract

In this paper an approximate closed form solution is developed to a specially orthotropic axisymmetric cylindrical thin shell subjected to a harmonic boundary condition. Modified Love-Timoshenko equations that model a shell forced by a longitudinal harmonic boundary condition at one end and grounded by a mechanical spring and damper at the other are used to formulate this boundary value problem. The shell equations and the boundary conditions correspond to a tension-dependent shell testing configuration with a longitudinal shaker at one end and a rope termination at the other. The approximate steady state closed form solution to the boundary value problem is then constructed, resulting in the equations of motion in the longitudinal and circumferential directions. It is shown that the circumferential motion of the shell is driven by the longitudinal motion. When the closed form solutions derived here are compared to finite element results for the thin shell problem, very close agreement is observed. However, the closed form solution has the advantage of being computationally more efficient than the finite element analysis. Additionally, the effects of the system parameters are explicit to the closed form solution and only implicit to the finite element solution.