Vibration analysis of axially functionally graded beams with the composite element model

LIU Jike; LV Zhongrong

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Vibration analysis of axially functionally graded beams with the composite element model

LIU Jike,LV Zhongrong * #

School of Engineering, Sun Yat-sen University, Guangzhou 510006, P.R. China

*Correspondence author

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Funding: National Natural Science Foundation of China （No.11172333, 11272361, 11572356）, Guangdong Province Science and Technology Program （No.2014A020218004）, Guangdong Province Natural Science Foundation （No.2015A030313126）, Doctoral Program Foundation of Ministry of Education of China （No.20130171110039）

Opened online: 5 January 2017

Accepted by: none

Citation: LIU Jike,LV Zhongrong.Vibration analysis of axially functionally graded beams with the composite element model[OL]. [ 5 January 2017] http://en.paper.edu.cn/en_releasepaper/content/4715329

This paper presents a simple yet accurate approach to analyze the free and forced vibrations of axially functionally graded (AFG) beams. The governing equations of the beam is derived by Lagrange's equations and then discretized by the composite element method. Numerical simulations are presented to show the effects of Young's modulus variation, mass density variation, and slenderness ratios, on the dynamic characteristics of the AFG beams. The natural frequencies obtained from the proposed method are found to be in close agreement with those from finite element and other methods. The forced vibration responses of the AFG beam are also calculated from the proposed method and compared with those obtained from the finite element method (FEM). Time histories from both methods are found to match very well. This further indicates the correctness of the present method for forced vibration analysis of the AFG beam.

Keywords:solid mechanics; composite element; free and forced vibrations; response; axially functionally graded beam

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