Free vibration analysis on a simply-supported rhombus plate by using transfer matrix method

DOI

10.2991/iccte-17.2017.11How to use a DOI?

Keywords

rhombus plate; transfer matrix method; perturbation method; a first order ordinary differential matrix equation

Abstract

In this paper, the transfer matrix method is firstly used to analyze the free vibration of a simply-supported rhombus plate. Firstly, using coordinate transformation formula, the solution domain for a rhombus plate is converted into a rectangular one, and the governing equations and the corresponding boundary conditions for the plate in the transformed rectangular domain are obtained. Then, combined with the Fourier series expansion and the perturbation theory, the equation is written in a first order ordinary differential matrix form. Next, the transfer matrix method is used to solve the matrix equations, in order to get the natural frequencies of the free vibration plate. Finally, numerical results are compared with the ones obtained by the finite element method. Example results show that when the difference between the rhombus angle and the corresponding rectangular angle is in a small range, the transfer matrix method proposed in this paper can be applied to analyze the dynamic characteristics of a rhombus plate.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Canli Liu
AU  - Liyun Yuan
AU  - Junpeng Wang
AU  - Zhenqiang Cao
AU  - Run Sun
PY  - 2017/07
DA  - 2017/07
TI  - Free vibration analysis on a simply-supported rhombus plate by using transfer matrix method
BT  - Proceedings of the 2017 2nd International Conference on Civil, Transportation and Environmental Engineering (ICCTE 2017)
PB  - Atlantis Press
SP  - 58
EP  - 66
SN  - 2352-5401
UR  - https://doi.org/10.2991/iccte-17.2017.11
DO  - 10.2991/iccte-17.2017.11
ID  - Liu2017/07
ER  -