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

Di Wang,Miaoxia Xie,Yueming Li

doi:10.1155/2015/157208

Abstract

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.

Highlights

With the great development of hypersonic crafts which are usually subjected to extremely aerodynamic heating and high-frequency exciting during working, there is a great need for the high-frequency dynamic analysis of structures in thermal environments.Thermal environments have a series of effects on material properties, geometry shapes, stress state, and so on
Ganesan and Dhotarad [1] developed a numerical method for the vibration analysis of thermally stressed plates in which the thermal stresses were evaluated by the finite element method and these stress values were used in a dynamic analysis of the plate performed by either the finite difference method or variation methods
We study the thermal effects on power transmission and reflection coefficient and develop an approximate approach to analyze the energy density distribution of coupled plates in nonuniform thermal environments: first, the thermal analysis and thermal stress analysis are conducted; based on the temperature and thermal stresses derived above, the energy distribution of the structure could be obtained

Summary

Introduction

With the great development of hypersonic crafts which are usually subjected to extremely aerodynamic heating and high-frequency exciting during working, there is a great need for the high-frequency dynamic analysis of structures in thermal environments. Park et al [13] developed the power flow model of in-plane waves in thin plates and flexural waves in finite orthotropic plates They derived the energy governing equation of flexural waves in Timoshenko beam [14, 15], Mindlin plate [16], and RayleighBishop rod [17] which take shear distortion and rotatory inertia acting an important role in high-frequency range into consideration. Zhang et al developed an alternative energy finite element formulation for interior acoustic spaces and thin plates considering the wave response as a summation of incoherent orthogonal waves [18] They expanded the EFEM to analyze the energy distribution of stiffened plates under heavy fluid loading [19]. Though EFEM has been developed well since 1980s, only Zhang et al [23] researched on the thermal effects on the high-frequency vibration They derived the energy density governing equation of beams and verified the accuracy. The numerical example of the coupled plate in nonuniform thermal environments shows that the approach could describe well the thermal effects on the level and distribution of energy density

Derivation of Wavenumber and Group Velocity with

Validation and Discussion

Conclusion