Volume 13, Issue 1
Harmonic Standing-Wave Excitations of Simply-Supported Thick-Walled Hollow Elastic Circular Cylinders: Exact 3D Linear Elastodynamic Response

Adv. Appl. Math. Mech., 13 (2021), pp. 18-57.

Published online: 2020-10

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• 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.

• Keywords

Thick-walled hollow elastic cylinders, simply-supported thick cylindrical shells, harmonic standing-wave boundary stresses, forced vibration, linear elastodynamic response.

• AMS Subject Headings

74H45, 74J05, 35Q74, 74B05

• Copyright

COPYRIGHT: © Global Science Press

• Email address

jsakhr@uwo.ca (Jamal Sakhr)

bchronik@uwo.ca (Blaine A. Chronik)

• BibTex
• RIS
• TXT
@Article{AAMM-13-18, author = {Sakhr , Jamal and A. Chronik , Blaine }, 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 = {2020}, volume = {13}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0203}, url = {http://global-sci.org/intro/article_detail/aamm/18338.html} }
TY - JOUR T1 - Harmonic Standing-Wave Excitations of Simply-Supported Thick-Walled Hollow Elastic Circular Cylinders: Exact 3D Linear Elastodynamic Response AU - Sakhr , Jamal AU - A. Chronik , Blaine JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 18 EP - 57 PY - 2020 DA - 2020/10 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2019-0203 UR - https://global-sci.org/intro/article_detail/aamm/18338.html KW - Thick-walled hollow elastic cylinders, simply-supported thick cylindrical shells, harmonic standing-wave boundary stresses, forced vibration, linear elastodynamic response. AB -

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.

Jamal Sakhr & Blaine A. Chronik. (2020). Harmonic Standing-Wave Excitations of Simply-Supported Thick-Walled Hollow Elastic Circular Cylinders: Exact 3D Linear Elastodynamic Response. Advances in Applied Mathematics and Mechanics. 13 (1). 18-57. doi:10.4208/aamm.OA-2019-0203
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