NONLINEAR BIFURCATION CONTROL OF A PARAMETRICALLY EXCITED CANTILEVER BEAM

摘要

In this paper, the nonlinear characteristics of the parametric resonancerninduced in a cantilever beam are controlled by a linear feedback based on a bifurcationrncontrol. Using the method of multiple scales, the modulation equations governingrnthe slow time variation of the amplitude and phase of the transverse vibration arernderived. In order to change the nonlinear characteristics in the frequency responsernand the bifurcation diagram, the control strategy is designed by using the modulationrnequation and realized by using the piezoelectric actuator that is attached to the surfacernof the beam to produce a bending moment. First, we determine the linear feedbackrngain to modify the modulation equations, which characterize the bifurcation of thernsystem. Secondly, by theoretically analyzing the modulation equations, we show thatrnthe nonlinear characteristics can be changed and the jump in the nonstationary amplitudernresponse can be reduced by the linear feedback based on the bifurcation control.rnFinally, the experiment is performed to discuss the validity of the proposed controlrnmethod. It is experimentally confirmed that discontinuous bifurcation is transformedrninto continuous one, and the jump can be reduced during the quasistationary sweep ofrnthe excitation amplitude.