Rest length controlled tunable band structure in periodic tensegrity metastructure – a numerical study using a novel consistent stiffness and mass formulation

Abstract

Elastic wave propagation in various periodic metastructures and its application to wave filtering, vibration isolation, acoustic cloaking, etc., have gained significant attention among researchers in recent years. Despite the presence of band gaps, traditional lattice structures lack dynamic tunability. The solution lies in using tensegrity as unit cells. This article presents analysis of tunable wave propagation through a metastructure formed by tessellation of a 2D tensegrity unit cell in one dimension. Equations of motion of the unit cell are derived with consideration of flexibility and distributed mass of the bars, which is often neglected in the literature. The formulation is extended for wave dispersion analysis using the Floquet–Bloch theory. Next, the order of the formulation is reduced for decoupled analysis of symmetric and antisymmetric modes. The dispersion relations for different modes have been validated with nonlinear as well as linearized frequency response analysis under impulse load. Next, the effect of rest length of strings and alternating arrangement of bars on band gaps is studied in detail.