An analytical study on the nonlinear vibration of functionally graded beams

作者：Ke, Liao-Liang; Yang, Jie^*; Kiti****chai, Sritawat

来源：Meccanica, 2010, 45(6): 743-752.

DOI：10.1007/s11012-009-9276-1

• Functionally graded materials
• Geometric nonlinearity
• Beam
• Nonlinear vibration

Nonlinear vibration of beams made of functionally graded materials (FGMs) is studied in this paper based on Euler-Bernoulli beam theory and von Karman geometric nonlinearity. It is assumed that material properties follow either exponential or power law distributions through thickness direction. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. The direct numerical integration method and Runge-Kutta method are employed to find the nonlinear vibration response of FGM beams with different end supports. The effects of material property distribution and end supports on the nonlinear dynamic behavior of FGM beams are discussed. It is found that unlike homogeneous beams, FGM beams show different vibration behavior at positive and negative amplitudes due to the presence of quadratic nonlinear term arising from bending-stretching coupling effect.

• 出版日期2010-12
• 单位香港城市大学; 北京交通大学; 中国地震局工程力学研究所