Shape and Material Selection for Optimizing Flexural Vibrations in Multilayered Resonators

Abstract—Flexural stiffness domains have been determined for optimizing the vibration frequency of a multilayered microres-onator. It is demonstrated in an efficiency map that, for a given eigenvalue, the flexural properties of a two-materials system, including all possible symmetric and asymmetric multiple-layers arrangements, fall into a domain limited by two curves. These low and upper boundaries describe symmetric three-layers systems consisting of two dissimilar materials. The flexural response model adopted in this paper is based on the Euler–Bernoulli theory, and the results are obtained by extending a scheme for modeling efficiency of monolithic structures (see D. Pasini, “Shape trans-formers for material and shape selection of lightweight beams, ” J. Mater. Design, 2006). Shape parameters are introduced to explore the impact on the resonator vibrations of the cross-section shape, the arrangement, symmetry and number of layers, as well as the materials properties and their volume fraction. The application of the maps to a case study shows that the method can assist to exploit geometry and material potential of microstructures, especially at the concept stage of design. [2006-0137] Index Terms—Design methodology, frequency response, micro-electromechanical systems (MEMS), microresonators, optimiza-tion methods. I