Journal of Applied Mathematics
Volume 2012 (2012), Article ID 659872, 17 pages
Research Article

Nonlinear Dynamics of an Electrorheological Sandwich Beam with Rotary Oscillation

1Department of Mechanical Engineering, Hunan Institute of Engineering, Xiangtan 411101, China
2State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China

Received 29 August 2012; Accepted 28 November 2012

Academic Editor: Vasile Marinca

Copyright © 2012 Kexiang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The dynamic characteristics and parametric instability of a rotating electrorheological (ER) sandwich beam with rotary oscillation are numerically analyzed. Assuming that the angular velocity of an ER sandwich beam varies harmonically, the dynamic equation of the rotating beam is first derived based on Hamilton's principle. Then the coupling and nonlinear equation is discretized and solved by the finite element method. The multiple scales method is employed to determine the parametric instability of the structures. The effects of electric field on the natural frequencies, loss factor, and regions of parametric instability are presented. The results obtained indicate that the ER material layer has a significant effect on the vibration characteristics and parametric instability regions, and the ER material can be used to adjust the dynamic characteristics and stability of the rotating flexible beams.