A Unified Approach for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

Abstract: This paper proposes a unified approach for dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a non-minimal description in terms of different combinations of basic points and base vectors to resolve the heterogeneity between rigid bodies and rigid bars in three-dimensional space. This leads to a set of differential-algebraic equations with a constant mass matrix and free from trigonometric functions. Formulations for linearized dynamics are derived to enable modal analysis around static equilibrium. For numerical analysis of nonlinear dynamics, we derive a modified symplectic integration scheme which yields realistic results for long-time simulations, and accommodates non-conservative forces as well as boundary conditions. Numerical examples demonstrate the efficacy of the proposed approach for dynamic simulations of Class-1-to-$k$ general tensegrity structures under complex situations, including dynamic external loads, cable-based deployments, and moving boundaries. The novel tensegrity structures also exemplify new ways to create multi-functional structures.