FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED TIMOSHENKO BEAM USING DYNAMIC STIFFNESS METHOD

Tran Van Lien; Nguyen Tien Khiem; Ngo Trong Duc

Tran Van Lien Faculty of Building and Industrial Construction, National University of Civil Engineering (NUCE)
Nguyen Tien Khiem Institute of Mechanics, Vietnam Academy of Science and Technology
Ngo Trong Duc Design Consultant and Investment of Construction - Ministry of Defense

Abstract

In this paper, free vibration of a functionally graded material (FGM) beam is investigated based on the Timoshenko beam theory and dynamic stiffness method. Material properties vary continuously throughout the thickness direction according to the volume fraction constituent deﬁned by power law function. First, a consistent theory of vibration is established for FGM Timoshenko beam taking into account the actual position of neutral axis that is a useful tool for analysis of coupled vibration in the beam. Then, frequency equation obtained provides an efficient method for free vibration analysis of FGM Timoshenko beam. The theoretical development has been illustrated and validated by numerical examples.

Keywords: FGM; timoshenko beam; natural frequency; dynamic stiffness method;

Received: July 21^th, 2016, revised: August 4^th, 2016, accepted: October 13^th, 2016

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