Abstract
This paper investigates the dynamic behavior of a micro-resonator under various levels of Alternating Current (AC) voltage, without a biased Direct Current voltage. The governing equations are developed in the framework of Euler–Bernoulli beam theory, accounting for the effects of damping, fringing field, and mid-plane stretching using von Karman nonlinear strain. The steady-state frequency response of the micro-resonator is derived from the governing equations by the method of multiple scales. The transient response is also derived by the long-time integration. The results of our work reveal that the applied AC voltage and the mid-plane stretching (quantified by a stretching parameter) determine the characteristic feature of the dynamic behavior of the micro-resonator, such as the dynamic pull-in, the frequency response of linear or hardening characteristic. A design diagram in terms of AC voltage amplitude and stretching parameter is developed to show the domains of the different dynamic behavior characteristics. Our results also reveal the significant effects of damping and boundary conditions on the dynamic behavior and the design diagram of the micro-resonator.
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