Dynamics of Microbeams under Multi-Frequency Excitations

This paper presents an investigation of the dynamics of microbeams under multiple harmonic electrostatic excitation frequencies. First, the response of a cantilever microbeam to two alternating current (AC) source excitation is examined. We show by simulations the response of the microbeam at primary resonance (near the fundamental natural frequency) and at secondary resonances (near half, superharmonic, and twice, subharmonic, the fundamental natural frequency). A multimode Galerkin method combined with the Euler-Bernoulli beam equation, accounting for the nonlinear electrostatic force, has been used to develop a reduced order model. The response of the cantilever microbeam to three AC source excitation is also investigated and shown as a promising technique to enhance the bandwidth of resonators. Finally, an experimental study of a clamped-clamped microbeam is conducted, demonstrating the multi-frequency excitation resonances using two, three, and four AC sources.