Nonlinear dynamical behaviors of axially accelerating large deflection thin plates

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Journal of Vibration and Shock ›› 2012, Vol. 31 ›› Issue (11) : 11-15.

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Nonlinear dynamical behaviors of axially accelerating large deflection thin plates

LIU Jin-tang1，YANG Xiao-dong1，Wen Bang-chun2

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Abstract

The stability and bifurcations of axially accelerating plates with large transverse deflections are investigated. The governing equations of an axially accelerating plate are derived through D’Alembert’s principle based on von Kàrmàn’s nonlinear plate theory. The Galerkin metod is employed to discretize the governing partial differential equations into a set of ordinary differential equations. By numerical method, the bifurcation diagrams are presented with respect to some parameters such as mean velocity, velocity amplitude and amplitude of exciting. The dynamical behaviors are identified based on the Poincaré map and the Largest Lyapunov Exponent. Periodic, quasi-periodic and even chaotic motions are located in the bifurcation diagram for the transverse vibration of the axially moving plate.

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Axially Accelerating Plates / Nonlinear Vibration / Largest Lyapunov Exponent / Bifurcation / Chaos

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LIU Jin-tang;YANG Xiao-dong;Wen Bang-chun. Nonlinear dynamical behaviors of axially accelerating large deflection thin plates[J]. Journal of Vibration and Shock, 2012, 31(11): 11-15