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.
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October 2011
Research Papers
On the Use of the Subharmonic Resonance as a Method for Filtration
Eihab M. Abdel-Rahman
Eihab M. Abdel-Rahman
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Bashar K. Hammad
Ali H. Nayfeh
Eihab M. Abdel-Rahman
J. Comput. Nonlinear Dynam. Oct 2011, 6(4): 041007 (11 pages)
Published Online: April 12, 2011
Article history
Received:
April 24, 2010
Revised:
October 30, 2010
Online:
April 12, 2011
Published:
April 12, 2011
Citation
Hammad, B. K., Nayfeh, A. H., and Abdel-Rahman, E. M. (April 12, 2011). "On the Use of the Subharmonic Resonance as a Method for Filtration." ASME. J. Comput. Nonlinear Dynam. October 2011; 6(4): 041007. https://doi.org/10.1115/1.4003031
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