Chaos prediction in MEMS-NEMS resonators

Different nonlinearities in micro-electro-mechanical resonators lead to various nonlinear behaviors such as chaotic motion which can affect the resonator performance. As a result, it is important to properly identify and analyze the chaotic regions in resonators. In this paper, a novel method is proposed for prediction of the chaos in the micro- and nano-electro-mechanical resonators. Based on the proposed method, first an accurate analytical solution for the dynamics behavior of the nano-resonators is derived using the multiple scales method up to the second order. The results obtained by this analytical solution are validated by comparing them with the numerical ones. Using the analytical frequency response and the homoclinic orbit characteristics, we have developed an analytical criterion for prediction of the chaos in the resonator. The bifurcation diagram for different cases revealed an appropriate agreement between the results of the proposed technique and the numerical method, while the results of the Melnikov method are far from being acceptable in the prediction of chaos region. In addition to better accuracy of the proposed technique, it is simple and requires low computation cost in comparison with the Melnikov method which requires complicated integral calculation. This quick and efficient method can be used in the design of the micro-resonators as well as determination of its optimum operational conditions.