@Article{AAMM-13-1,
author = {Sakhr, Jamal and Chronik, Blaine, A.},
title = {Harmonic Standing-Wave Excitations of Simply-Supported Thick-Walled Hollow Elastic Circular Cylinders: Exact 3D Linear Elastodynamic Response},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2021},
volume = {13},
number = {1},
pages = {18--57},
abstract = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2019-0203},
url = {https://global-sci.com/article/72955/harmonic-standing-wave-excitations-of-simply-supported-thick-walled-hollow-elastic-circular-cylinders-exact-3d-linear-elastodynamic-response}
}