Nonlinear resonators can have advantages over linear designs including increased sensitivity towards changes in their physical properties and environment, and high quality factors which make them attractive in applications such as mass/chemical sensors or signal filters. Designing nonlinear structures, however, requires much understanding of nonlinear behavior characteristics of structures. Similarly, the proliferation of 3D or additive manufacturing/printing capabilities has opened the doors to deploying nonlinear resonators on scales not possible earlier. However, to obtain consistent nonlinear dynamic performance the designer must perform a careful analysis to explore the existence and repeatability of desired nonlinear behavior. Also, the use of 3D printing with the associated substrate material properties poses its own challenges in regards to device simulation in view of the fact that most of the traditional literature on nonlinear resonators assumes linear material stiffness. In this chapter, the authors discuss computational design methods for structural design, and specifically study the case of 1:2 internal resonances in resonators made of nonlinear (hyperelastic) materials. The design methods allow for development of large number of candidate resonator designs without a required significant nonlinear structural design experience, and the study of the dynamic response of the resonators provides a glimpse in to the 1:2 nonlinear internal resonance exhibited by the candidate resonators.
Part of the book: Nonlinear Systems