Three-dimensional modeling of the wave dynamics of tensegrity lattices

Abstract

This paper develops effective numerical models to study the wave dynamics of highly nonlinear tensegrity metamaterials. Recent studies have highlighted the geometrically nonlinear response of structural lattices based on tensegrity prisms, which may gradually change their elastic response from stiffening to softening through the modification of mechanical, geometrical, and prestress variables. We here study the nonlinear dynamics of columns of tensegrity prisms subject to impulsive compressive loading. An effective nonlinear rigid body dynamics is employed to simulate the dynamic response of such metamaterials. We illustrate how to pass from the matrix to the vector form of the equations of motions, on accounting for a rigid response of the compressive members (bars). Numerical simulations show that the wave dynamics of the examined metamaterials supports compression solitary pulses with profile dependent on the elastic properties of the tensile members (strings), the given impact velocity, and the applied prestress. We conclude that tensegrity columns can be effectively used as tunable acoustic lenses, which are able to generate acoustic solitary waves with adjustable profile in a host medium.