Harmonic Standing-Wave Excitations of Simply-Supported Thick-Walled Hollow Elastic Circular Cylinders: Exact 3D Linear Elastodynamic Response
Year: 2021
Author: Jamal Sakhr, Blaine A. Chronik
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 1 : pp. 18–57
Abstract
The forced-vibration response of a simply-supported isotropic thick-walled hollow elastic circular cylinder subjected to two-dimensional harmonic standing-wave excitations on its curved surfaces is studied within the framework of linear elastodynamics. Exact semi-analytical solutions for the steady-state displacement field of the cylinder are constructed using recently-published parametric solutions to the Navier-Lame equation. Formal application of the standing-wave boundary conditions generates three parameter-dependent $6\times6$ linear systems, each of which can be numerically solved in order to determine the parametric response of the cylinder's displacement field under various conditions. The method of solution is direct and demonstrates a general approach that can be applied to solve many other elastodynamic forced-response problems involving isotropic elastic cylinders. As an application, and considering several examples, the obtained solution is used to compute the steady-state frequency response in a few specific low-order excitation cases. In each case, the solution generates a series of resonances that are in exact correspondence with a unique subset of the natural frequencies of the simply-supported cylinder. The considered problem is of general theoretical interest in structural mechanics and acoustics and more practically serves as a benchmark forced-vibration problem involving a thick-walled hollow elastic cylinder.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0203
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 1 : pp. 18–57
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
Keywords: Thick-walled hollow elastic cylinders simply-supported thick cylindrical shells harmonic standing-wave boundary stresses forced vibration linear elastodynamic response.