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

被引：57

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

页码：715 / 724

页数：10

共 22 条

[1] Timoshenko beam-column with generalized end conditions on elastic foundation: Dynamic-stiffness matrix and load vector [J].

Arboleda-Monsalve, Luis G. ;

Zapata-Medina, David G. ;

Aristizabal-Ochoa, J. Dario .

JOURNAL OF SOUND AND VIBRATION, 2008, 310 (4-5) :1057-1079

[2] Parametrically excited non-linear traveling beams with and without external forcing [J].

Chakraborty, G ;

Mallik, AK .

NONLINEAR DYNAMICS, 1998, 17 (04) :301-324

[3] On the comparison of Timoshenko and shear models in beam dynamics [J].

Challamel, Noel .

JOURNAL OF ENGINEERING MECHANICS, 2006, 132 (10) :1141-1145

[4] Solvability condition in multi-scale analysis of gyroscopic continua [J].

Chen, Li-Qun ;

Zu, Jean W. .

JOURNAL OF SOUND AND VIBRATION, 2008, 309 (1-2) :338-342

[5] Nonlinear free transverse vibration of an axially moving beam: Comparison of two models [J].

Chen, Li-Qun ;

Yang, Xiao-Dong .

JOURNAL OF SOUND AND VIBRATION, 2007, 299 (1-2) :348-354

[6] Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models [J].

Chen, LQ ;

Yang, XD .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2005, 42 (01) :37-50

[7] Multidimensional Lindstedt-Poincare method for nonlinear vibration of axially moving beams [J].

Chen, S. H. ;

Huang, J. L. ;

Sze, K. Y. .

JOURNAL OF SOUND AND VIBRATION, 2007, 306 (1-2) :1-11

[8] Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity [J].

Ghayesh, M. H. ;

Khadem, S. E. .

INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 2008, 50 (03) :389-404

[9] Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams [J].

Ghayesh, Mergen H. ;

Balar, Sara .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2008, 45 (25-26) :6451-6467

[10] Dynamics of transversely vibrating beams using four engineering theories [J].

Han, SM ;

Benaroya, H ;

Wei, T .

JOURNAL OF SOUND AND VIBRATION, 1999, 225 (05) :935-988

← 1 2 3 →