Tunable Wave Transmission in Periodic One-Dimensional Tensegrity Architectures

Over the past decades, the investigation of wave transmission through periodic structures has gained interest among researchers, particularly in analyzing frequency band gaps, which have applications in vibration isolation, frequency filtering, etc. Tensegrity structure, a self-equilibrated network of pre-stressed tension and compression elements, enables geometry-driven dynamic control of wave transmission that overcomes previously manufactured-fixed structures and finds growing applications in civil engineering, robotics, space technology, etc. Motivated by this feature, the present study focuses on the numerical study of tunable wave transmission in periodic one-dimensional tensegrity architectures. First, a pre-stressed controlled two-dimensional planar tensegrity structure has been chosen for the analysis. Next, a stable equilibrium configuration was obtained using the minimization principle of its total potential energy by solving a nonlinear optimization solver. Nonlinear, followed by linearized equations of motion, were derived using the Lagrangian approach, and their responses are validated with the dispersion relations obtained by solving the Floquet-Bloch method under impulse load conditions. Two modes of wave transmission, i.e., symmetric and anti-symmetric modes, were identified and analyzed separately. The variation of band gaps over frequencies for each wave transmission mode has been analyzed in detail in a non-dimensional framework.