Parametric resonance of axially moving Timoshenko beams with time-dependent speed

被引：54
|
作者：
Tang, You-Qi [2 ]
Chen, Li-Qun [1 ,2 ]
Yang, Xiao-Dong [3 ]
机构：
[1] Shanghai Univ, Dept Mech, Shanghai 200436, Peoples R China
[2] Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China
[3] Shenyang Inst Aeronaut Engn, Dept Engn Mech, Shenyang 110034, Peoples R China
来源：
NONLINEAR DYNAMICS | 2009年 / 58卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Parametric resonance; Axially moving Timoshenko beams; Method of multiple scales; Steady-state response; STEADY-STATE RESPONSE; NONLINEAR VIBRATION; TRANSVERSE VIBRATION; STABILITY; MODES; FREQUENCIES;
D O I：
10.1007/s11071-009-9512-1
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, parametric resonance of axially moving beams with time-dependent speed is analyzed, based on the Timoshenko model. The Hamilton principle is employed to obtain the governing equation, which is a nonlinear partial-differential equation due to the geometric nonlinearity caused by the finite stretch of the beam. The method of multiple scales is applied to predict the steady-state response. The expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by using the Lyapunov linearized stability theory. Some numerical examples are presented to demonstrate the effects of speed pulsation and the nonlinearity in the first two principal parametric resonances.
引用
收藏
页码：715 / 724
页数：10
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