Free vibrations of thin rectangular nano-plates using wave propagation approach

Ilkhani, M.R.; Bahrami, A.; Hosseini-Hashemi, S.H.

Abstract

The wave propagation approach is one of the most powerful techniques used in vibration problems. This method gives the propagation and reflection matrix which is useful for the analysis of mechanical energy transmission in micro/nano devices like energy harvester devices. In this paper, wave propagation approach is used to analyze the free vibrations analysis of thin rectangular macro and nano-plates. Firstly, the propagation and reflection matrices for thin rectangular plates are derived. Then, these matrices are combined to provide a concise and exact approach for obtaining the natural frequencies of the thin rectangular plates. In the macro scale, solution obtained by this approach is exactly the same as those derived by classical method. In Nano-scale, the results are compared with Molecular dynamic simulation of a graphene sheet. Finally, the behavior of reflection coefficients, as an index for energy transmission, under changing the frequency for various nonlocal parameters is studied.

Citation

Ilkhani, M., Bahrami, A., & Hosseini-Hashemi, S. (2016). Free vibrations of thin rectangular nano-plates using wave propagation approach. Applied Mathematical Modelling, 40(2), 1287-1299. https://doi.org/10.1016/j.apm.2015.06.032

• Journal Article Type: Article
• Acceptance Date: Jun 25, 2015
• Online Publication Date: Sep 3, 2015
• Publication Date: Jan 15, 2016
• Deposit Date: Feb 27, 2025
• Journal: Applied Mathematical Modelling
• Print ISSN: 0307-904X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 40
• Issue: 2
• Pages: 1287-1299
• DOI: https://doi.org/10.1016/j.apm.2015.06.032
• Keywords: Rectangular nano-plate, Propagation matrix, Reflection matrix, Vibration analysis, Graphene sheet
• Public URL: https://nottingham-repository.worktribe.com/output/2636741
• Additional Information: This article is maintained by: Elsevier; Article Title: Free vibrations of thin rectangular nano-plates using wave propagation approach; Journal Title: Applied Mathematical Modelling; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.apm.2015.06.032; Content Type: article; Copyright: Copyright © 2015 Published by Elsevier Inc.