A study of the nonlinear response of a resonant microbeam to an electric actuation

An investigation into the response of a resonant microbeam to an electric actuation is presented. A non-linear model is used to account for the mid-plane stretching, a DC electrostatic force, and an AC harmonic force. Design parameters are included in the model by lumping them into nondimensional parameters. A perturbation method, the method of multiple scales, is used to obtain two first-order nonlinear ordinary-differential equations that describe the modulation of the amplitude and phase of the response and its stability. The model and the results obtained by the perturbation analysis are validated by comparing them with published experimental results. The case of three-to-one internal resonance is treated. The effect of the design parameters on the dynamic responses is discussed. The results show that increasing the axial force improves the linear characteristics of the resonance frequency and decreases the undesirable frequency shift produced by the nonlinearities. In contrast, increasing the mid-plane stretching has the reverse effect. Moreover, the DC electrostatic load is found to affect the qualitative and quantitative nature of the frequency-response curves, resulting in either a softening or a hardening behavior. The results also show that an inaccurate representation of the system nonlinearities may lead to an erroneous prediction of the frequency response.