Bandgap structure of tensegrity mass–spring chains equipped with internal resonators

Abstract

This work studies the dispersion relation of a Maxwell type mass–spring chain formed by lumped masses and the parallel arrangement of two different types of tensegrity prisms. Use is made of the Bloch–Floquet theory of discrete systems in association with a linearized model of the response of the tensegrity units under compression loading. Such a modeling is aimed at studying the propagation of compression waves under small perturbations of the initial equilibrium state of the system. For a given value of the cable’s prestress, the tensegrity systems connecting the lumped masses react as elastic springs, which exhibit axial deformations accompanied by relative twisting rotations of the terminal bases. The twisting motion of the chain affects the expression of the kinetic energy, and is accounted for by introducing a suitable definition of equivalent masses. The bandgap structure of the analyzed system is analytically determined and numerical results are obtained for a chain formed by physical models tensegrity θ=1 prisms aligned in parallel with minimal tensegrity prisms. The given results highlight the highly tunable frequency bandgap properties of tensegrity mass–spring chains exhibiting internal resonance capabilities.