Research On Multistability And Some Other Behaviors Of Mechanical Vibrating Systems

Multistability is very common in mechanical vibration system,such as relative rotation system,multistage gear transmission system driven by synchronous motor,micro-resonator vibration system,vibration energy harvesting system,etc.Multistability is avoid in relative rotation system,microresonator vibration system,multistage gear transmission system,due to it could easy to cause mechanical vibration instability;but it is expected for vibration energy harvesting system,which can widen the working frequency band.Therefore,it is significant to study the multistability for better design of mechanical vibration system structures and the use of vibrating systems.To this end,this paper takes bilateral capacitive electrostatic driven microresonator and two degrees of freedom and three steady state piezoelectric cantilever energy harvester as the research object,and conducts the analysis and application of the mechanism of complex dynamic behavior based on the multistability.Firstly,establish a dynamic model for the microresonator vibration system,and use the multi-scale method to analyze the periodic response of the system and divide the basins of attraction numically to study the evolution of the system under different external excitation.It is found that the change of external excitation frequency can lead to bi-stability and vibration jump;the change of external excitation amplitude can lead to multistability,vibration jump,hidden attractors and chaotic behavior.Secondly,select a typical piezoelectric cantilever vibration energy harvester,establish a dynamic model,analyze the local bifurcation,study the mechanism of fractal and chaos through the global bifurcation theory,and verify the results with numerical method.It is found that the change of external excitation amplitude can lead to the system basins of attraction fractals as well as the appearance of large periodic attractors and chaos.This paper has certain application value in the design of electrostatic driven microresonant devices and piezoelectric driven energy harvesting devices.