Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:45

Article

Ghayesh, Mergen H.¹  Balar, Sara² 

[1] McGill Univ, Dept Mech Engn, Montreal, PQ H3A 2K6, Canada

[2] Dr Shariaty Coll, Sch Elect Engn, Tech Sci Dept, Tehran, Iran

关键词: Non-linear vibration;    Multiple scales method;    Visco-elastic beam;    Stability;   

DOI  :  10.1016/j.ijsolstr.2008.08.002

来源: Elsevier

【 摘 要 】

An axially moving visco-elastic Rayleigh beam with cubic non-linearity is considered, and the governing partial-differential equation of motion for large amplitude vibration is derived through geometrical, constitutive, and dynamical relations. By directly applying the method of multiple scales to the governing equations of motion, and considering the solvability condition, the linear and non-linear frequencies and mode shapes of the system are analytically formulated. In the presence of damping terms, it can be seen that the amplitude is exponentially time-dependent, and as a result, the non-linear natural frequencies of the system will be time-dependent. For the resonance case, through considering the solvability condition and Routh-Hurwitz criterion, the stability conditions are developed analytically. Eventually, the effects of system parameters on the vibrational behavior, stability and bifurcation points of the system are investigated through parametric studies. (C) 2008 Elsevier Ltd. All rights reserved.

【 授权许可】

Free