Lumped parameter model for longitudinal in-plane resonators with zig-zag elastic elements

Tuned vibration absorbers have long been used as a mean to suppress vibration. Despite their simplicity and effectiveness, they have a significant drawback, which is their limited effective bandwidth. Recent research efforts have been focused on development of solutions for passive vibration suppression that are effective over a wide frequency range, which resulted in the invention of metastructures. Metastructures contain local resonators that are distributed along the structure and tuned to specific frequencies. In many applications the addition of significant mass to the structure in the form of resonators is prohibitive, hence resonators must be integrated into structural members. Given the dimensional constraints set by the size and geometry of the cross-section of the structural member, design and integration of local resonators into structural members becomes a non-trivial problem. Here we consider the case of longitudinal vibrations. The proposed metastructure will contain in-plane resonators acting as distributed vibration absorbers. In this research, zigzag elastic elements connected to a small mass will be used to function as in-plane resonators. The reason for using a zig-zag geometry for elastic elements is that it enables realizing low enough stiffness within a confined space to achieve low resonant frequencies. Such resonators could be integrated into structural members using conventional manufacturing methods. We describe the development of a lumped parameter model that could be used as a tool for design and optimization of in-plane resonators, while being more efficient computationally than traditional finite element models. We verify the developed model by comparing its predictions with results obtained using finite element models.