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IMA Journal of Applied Mathematics Advance Access originally published online on October 6, 2008
IMA Journal of Applied Mathematics 2009 74(1):85-96; doi:10.1093/imamat/hxn012
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Non-linear responses of a one-sided constrained beam with base excitation

Q. Qian and L. Wang{dagger}

Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China

{dagger} Email: wanglinfliping{at}sohu.com

Received on November 20, 2007; Revision received March 13, 2008. Accepted on April 9, 2008

The paper discussed the non-linear responses of a buckled beam under base excitation and constrained by a one-sided motion restraint. The geometric non-linearity due to axial extension is taken into account. We apply the Galerkin method to the governing partial differential equation of the transverse motion to obtain a general model of n degrees of freedom (nDOF). The results of dynamic response for the 1DOF mode of a pinned-pinned beam are presented for the system both with and without one-sided motion restraint. The regular and irregular motions of the 1DOF model for the beam are represented in the forms of time trace, phase plot, bifurcation diagram and power spectra. An in-depth study based on an energy approach is done to illustrate the non-linear responses resulting from the multiplicity of resonant solutions. It is shown that the effect of the motion restraint on the dynamics of the system is significant.

Keywords: non-linear response; buckled beam; base excitation; motion restraint; energy approach.


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