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