Shape and Material Selection for Optimizing Flexural Vibrations in Multilayered Resonators

Flexural stiffness domains have been determined for optimizing the vibration frequency of a multilayered microresonator. 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 transformers 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