Steady state response of nonlinear vibration of axially accelerating viscoelastic rayleigh beam

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Journal of Vibration and Shock ›› 2012, Vol. 31 ›› Issue (5) : 135-138.

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Steady state response of nonlinear vibration of axially accelerating viscoelastic rayleigh beam

DING Hu1，CHEN Li-qun1,2

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Abstract

The sub-harmonic resonance of axially accelerating nonlinear viscoelastic Rayleigh beams are investigated via an approximate analytical method with differential quadrature method verification. The mathematical model of transverse vibration of deformations infinitesimal beams is established by calculus of variations. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The solvable conditions of parametric vibration for sub-harmonic resonance are established via the methods of multiple scales. Therefore the steady state periodic response is presented for accelerating viscoelastic Rayleigh beams with simple supports boundary conditions. Numerical examples show the effects of the nonlinear coefficient and the viscoelastic coefficient on the steady state response are studied individually. The differential governing equation for transverse vibration of an axially moving slender Rayleigh beam is numerically solved via differential quadrature method. The numerical calculations confirm the analytical results. Numerical examples demonstrate that the approximate analysis results are with rather high precision.

Key words

Rayleigh beam / parametric resonance / nonlinear / Multi-scale method / Differential quadrature method

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DING Hu;CHEN Li-qun;. Steady state response of nonlinear vibration of axially accelerating viscoelastic rayleigh beam[J]. Journal of Vibration and Shock, 2012, 31(5): 135-138