Anti-symmetric mode vibration of a curved beam subject to autoparametric excitation

This paper details study of the antisymmetric response to the symmetric sinusoidal excitation of a clamped–clamped buckled beam. The autoparametric responses of the antisymmetric modes are obtained from a two-mode equation with nonlinear coupling, which is solved using the Runge–Kutta numerical integration method. The effects of the antisymmetric mode vibration on the dynamic snap-through motion are studied. The theoretical results conclude that (i) the autoparametric responses occur for large static buckled shapes when the resonance frequency of the symmetric mode is about twice that of antisymmetric mode, (ii) autoparametric responses are dominant at a frequency that is half that of the excitation, (iii) the autoparametric responses of antisymmetric modes are as high as the symmetric mode although the excitation force is symmetric, and the autoparametric responses decrease the excitation force that is required to initiate the dynamic snap-through motion. The experimental results for a buckled beam were obtained by base excitation with a 6000 N shaker. The measurement of the antisymmetric modes was separated from the measurement of the symmetric mode by the special configuration of the strain gauge sensor systems. A comparison of the simulation results and the measured data shows a reasonable agreement, and demonstrates the effectiveness of the modeling approach.