Predicting the Resonance Frequency of Nonreciprocal Structure with Unsymmetric Stiffness under Harmonic Loading

Given the broad promise of nonreciprocity for a wide range of applications in engineering, it is important to examine the dynamic characteristics of nonreciprocal structures. In contrast to conventional nonlinear yet reciprocal systems with symmetric restoring force, bilinear nonreciprocal systems exhibit stiffness asymmetry that breaks deformation symmetry and induces direction-dependent dynamic response. This study reveals that the resonance of the bilinear nonreciprocal system under harmonic loading cannot be avoided but is instead shifted. We propose two approaches to the prediction of the shifted resonance frequency. The resonance prediction of a single-degree-of-freedom (SDOF) nonreciprocal system under harmonic loading is first studied and then its extension to a generalized SDOF nonreciprocal system is investigated. The effectiveness of the two proposed approaches in predicting the resonance frequency is demonstrated through a series of numerical examples. Results show that the two proposed approaches can successfully predict the shifted resonance frequency of structures with different levels of nonreciprocity. The findings from this study can be used as a basis to identify the resonance frequency of a wide range of nonreciprocal structures for various engineering applications.