Bandgap tunability in strongly and weakly nonlinear periodic tensegrity structures

This study explores bandgap formation in periodic nonlinear tensegrity structures within a non-dimensional framework. Nonlinear equations of motion were derived for a general tensegrity structure and rendered non-dimensional. Band structures were predicted using both perturbation and harmonic balance methods, with perturbation limited to the weakly nonlinear regime. Although the formulation accommodates general two- and three-dimensional lattices, the analysis focuses on a one-dimensional D-bar tensegrity chain as an example. Nonlinearity is introduced via a cubic constitutive law in the strings, capturing hardening or softening behavior. All combinations of nonlinearity type and location are investigated under varying wave amplitudes to assess their impact on bandgap characteristics. In the weakly nonlinear case, excellent agreement is observed between perturbation and harmonic balance method results. Amplitude-dependent bandgaps exhibit shifting, shrinking and widening, while in the strongly nonlinear regime, more pronounced effects such as the roton effect and complete closure and significant shifts in bandgap location and width emerge.