The objective of this manuscript is to elucidate the role of topology on the nonlinear response of resonators. The resonators are composed of two beams and designed to exhibit two-to-one internal resonances. The manuscript explores the sensitivity to variations in the topological parameters, i.e., the relative orientation, and the ratio of lengths and heights, on the modal frequencies of the structure. The nonlinear governing equations are solved using the method of multiple scales when the system is excited near the first and second resonances. The occurrence of bifurcations and modal interactions has been shown both numerically and experimentally and related to the topological parameters. The effect of the topology on modal saturation has also been studied.

该手稿的目的是阐明拓扑在谐振器非线性响应中的作用。谐振器由两个光束组成，并设计为表现出一对一的内部谐振。该手稿探讨了对拓扑参数变化的敏感性，即结构的模态频率上的相对方向以及长度与高度的比率。当系统在第一和第二共振附近被激发时，使用多尺度方法求解非线性控制方程。数值和实验都表明了分叉和模态相互作用的发生，并且与拓扑参数有关。还研究了拓扑对模态饱和的影响。