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

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.