On the Use of the Subharmonic Resonance as a Method for Filtration

We study the feasibility of employing subharmonic resonance of order one-half to create a bandpass filter. A filter made up of two clamped-clamped microbeam resonators coupled by a weak beam is employed as a test design. We discretize the distributed-parameter system using the Galerkin procedure to obtain a reduced-order model composed of two nonlinear coupled Ordinary Differentiation Equations (ODEs). It accounts for geometric and electric nonlinearities as well as the coupling between these two fields. Using the method of multiple scales, we determine four first-order nonlinear ODEs describing the amplitudes and phases of the modes. We use these equations to determine closed-form expressions for the static and dynamic deflections of the structure. The basis functions in the discretization are the linear undamped global mode shapes of the unactuated structure. We found that it is impractical to use the proposed filter structure for subharmonic resonance-based filtering since it cannot produce a single-valued response for small excitation amplitudes. On the other hand, it is feasible to use cascaded uncoupled resonators to build a bandpass filter by operating one in the softening domain and the other in the hardening domain.