Vibration analysis of a FGM beam based on energy finite element method

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (3) : 119-124.

WANG Di1, ZHU Xiang1.2,LI Tianyun1.2,HE Xing1,GAO Shuang1

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Abstract

Functionally graded materials (FGMs) are more and more widely used in engineering because of their excellent structural properties and important application value. Here, bending vibration characteristics of FGM beams and coupled beams were analyzed based on the energy finite element method. In order to get the energy density and energy flow, FGM beam energy density control equation and energy finite element matrix equation as well as coupled beam energy finite element matrix equation were deduced, respectively. Taking a simply supported FGM beam as an example, its energy density was computed with the energy finite element method and the traditional finite element method, respectively. The two energy densities were compared to verify the correctness of the proposed energy FE method. Then the energy density and energy flow of the coupled FGM beam were solved. Finally, the energy distribution features of the beam were obtained. This study provided a theoretical basis for the vibration characteristics analysis of complex FGM structures based on the energy finite element method.

Key words

functionally graded material (FGM) beam / energy finite element method / coupled beam / energy density / energy flow

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WANG Di1, ZHU Xiang1.2,LI Tianyun1.2,HE Xing1,GAO Shuang1. Vibration analysis of a FGM beam based on energy finite element method[J]. Journal of Vibration and Shock, 2018, 37(3): 119-124

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