In this paper, we investigate theoretically and experimentally dynamics of a buckled beam under high-frequency excitation. It is theoretically predicted from linear analysis that the high-frequency excitation shifts the pitchfork bifurcation point and increases the buckling force. The shifting amount increases as the excitation amplitude or frequency increases. Namely, under the compressive force exceeding the buckling one, high-frequency excitation can stabilize the beam to the straight position. Some experiments are performed to investigate effects of the high-frequency excitation on the buckled beam. The dependency of the buckling force on the amounts of excitation amplitude and frequency is compared with theoretical results. The transient state is observed in which the beam is recovered from the buckled position to the straight position due to the excitation. Furthermore, the bifurcation diagrams are measured in the cases with and without high-frequency excitation. It is experimentally clarified that the high-frequency excitation changes the nonlinear property of the bifurcation from supercritical pitchfork bifurcation to subcritical pitchfork bifurcation and then the stable steady state of the beam exhibits hysteresis as the compressive force is reversed.
Beam is one of the fundamental elements in complex structures. It is very significant to clarify its stability under the various circumstances. In particular, the buckling phenomenon, which is characterized as a pitchfork bifurcation, has accepted much interest by many researchers. In this paper, we propose a stabilization control method for the first-mode buckling phenomenon in the clamped-clamped beam without feedback control. We analyze the stability of a buckled beam under high frequency excitation in linear theory. It is theoretically clarified and experimentally that the high-frequency excitation shifts the bifurcation point (the critical compressive force) and prevents the beam buckling.
Beam is one of the fundamental elements 正 n cQmplex structures . It is very significant to clarif セ its sta . bilitY under the various circumstances , In p 卸 rticular , the buckllng phenomenon7 wh 量 ch ls characterized as a pitchfc )rk bifurcatien , has accepted much interes亀 by many researchers , In this paper, we propose astabilization method fbr the first −mode buckling phenQmenon in the clamped − clamped beam . Fc}r the buckling phenomenon in this system , we propose a stabilization control method without feedback controL High frequency excitation shifts the bifurcation point and carries out the escape from the buckling state . FhJrthermore , the vahd 量 ty of the stabilization method with high frequency excitation is experimentally con 丘 rmed by applying the theore 七 ically Proposed control method to a buckled beam under the compressive 丘〕rce .
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