Non-dimensional linear analysis of one-dimensional wave propagation in tensegrity structures

This study presents a methodology for analyzing wave propagation in tensegrity lattices within a non-dimensional framework. Two strategies are employed to predict pass bands and bandgaps. The first examines wave dispersion through a single representative unit cell, using dispersion curves to identify bandgaps and pass bands. The second models the structure as a finite system, using modal analysis to compute the steady-state response to harmonic loads and plot the frequency response function. Two unit cells are analyzed: a two-dimensional D-bar unit and a three-dimensional tensegrity prism. The study investigates axial and in-plane bending wave propagation in a D-bar chain and axial wave propagation in a prism chain. After non-dimensionalizing the equations of motion, key parameters such as ratios of stiffness per unit length, mass per unit length, and prestress are identified. Its is shown that varying these parameters shifts the bandgap locations and widths. Prestress has minimal effect in the D-bar case, while a slight shift in the first bandgap is observed in the prism. The predictions from unit cell and finite structure analyses show good agreement.