Dynamic modelling and Chaos control for thin plate oscillator Using Bubnov-Galerkin integral method

Thin plate system based on acoustic vibration plays an important role in micro nano manipulation and exploration of nonlinear science. In this paper, starting from the actual thin plate system driven by acoustic wave signals, combining the mechanical analysis of thin plate micro element and the approximation approach Bubnov-Galerkin integral method, the governing equation of a forced vibration square thin plate is derived. Of note, the reaction force of the thin plate vibration system is defined as f=αΙwΙ resembling the Hooke’s law. And then by solving amplitude frequency response function of the thin plate oscillator using the harmonic balance method, the amplitude-frequency curves under the action of distinct parameters are analyzed with two different vibration modes through numerical simulation. Further, the conservative chaotic motions in the thin plate oscillator is demonstrated by the theory and numerical method. Drawing the dynamics maps indicating the system states reveals the evolution laws of the system. Through expounding the effect of force fields and system energy, the underlying mechanism of chaos is interpreted. Additionally, the phenomenon of chaos occurred in the oscillator is controlled by the method of velocity and displacement states feedback, which is meaningful for the engineering application.