Effect of anti-symmetric mode on dynamic snap-through of curved beam

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Effect of anti-symmetric mode on dynamic snap-through of curved beam

 

Author: Poon, Wai-yin Sam
Title: Effect of anti-symmetric mode on dynamic snap-through of curved beam
Degree: Ph.D.
Year: 2004
Subject: Hong Kong Polytechnic University -- Dissertations
Structural dynamics
Girders -- Vibration
Department: Dept. of Civil and Structural Engineering
Pages: iii, 237 leaves : ill. (some col.) ; 30 cm
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b1781123
URI: http://theses.lib.polyu.edu.hk/handle/200/2834
Abstract: It is well known that the static stability of the initial symmetric buckled mode is significant affected by the onset of anti-symmetric displacement, but the dynamic effects of anti-symmetric modes on dynamic snap-through motion are less understood. The purpose of this investigation is to study the anti-symmetric response of a clamped-clamped buckled beam that is subjected to symmetric sinusoidal excitation. Using the two-mode equations with nonlinear coupling, the autoparametric response of the antisymmetric mode was solved with the aid of Runge-Kutta (RK-4) numerical integration method. The effects of the anti-symmetric mode of vibration on the dynamic snap-through motion were studied. Analytical and numerical studies were also carried out to explore the mechanism of the snap-through motion. Numerical experiments yielded the instability boundaries of dynamic snap-through motion for both single mode and two-mode modeling. Experimental results for a buckled beam were obtained by base excitation with a 6000 N shaker. The measurement of the anti-symmetric modes could be separated from the symmetric mode by special configuration of the strain gauge sensor systems. The analysis results show various characteristic features of phenomenon: (a) autoparametric responses occurred for large static buckled shape when the resonance frequency of symmetric mode was about twice that of anti-symmetric mode; (b) autoparametric responses were dominant at frequency half of the excitation; (c) autoparametric responses of anti-symmetric modes could be as high as the symmetric mode even though the excitation force was symmetric; and (d) autoparametric responses decrease the excitation force that is required to initiate dynamic snap-through motion. A comparison of the simulation results and the experimentally measured data yields excellent results and demonstrates the effectiveness of the modeling approach.

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