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Shock and Vibration
Volume 2015 (2015), Article ID 157208, 14 pages
Research Article

High-Frequency Dynamic Analysis of Plates in Thermal Environments Based on Energy Finite Element Method

1State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China
2School of Mechanical and Electrical Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China

Received 20 November 2014; Accepted 18 January 2015

Academic Editor: Tai Thai

Copyright © 2015 Di Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The energy density governing equation to analyze the high-frequency dynamic behavior of plates in thermal environments is derived in this paper, in which the thermal effects are considered to change the membrane stress state and temperature dependent material properties of plates. Then the thermal effects on the energy reflection and transmission coefficients are dealt with hereof. Based on the above, an EFEM (energy finite element method) based approximate approach for the energy analysis of coupled plates under nonuniform thermal environments is proposed. The approach could be conducted by three steps: (1) thermal analysis, (2) thermal stress analysis, and (3) forming element matrixes, joint matrixes, and the whole EFEM formulation for the energy analysis. The same mesh model is used for all the three steps. The comparison between EFEM results and classical modal superposition method results of simply supported plates in various uniform thermal environments and coupled plates in nonuniform thermal environments demonstrated that the derived energy governing equation and the proposed approach described well the smooth time- and locally space-averaged energy density. It is found that the distributions and levels of energy density are affected by thermal effects, and the variation trends are related to exciting frequency.