Tensegrity system dynamics in fluids

Hydrodynamic loads are critical in the design of marine tensegrity structures. While dynamic models of tensegrity structures have been developed over the years, the effects of fluid-added mass on their dynamics have not been thoroughly analyzed, nor has the damping torque introduced by constraints been modeled. In this paper, we develop an integrated tensegrity-fluid interaction model that accounts for all possible forces and torques within the system. Fluid-added mass is explicitly expressed in the equations of motion alongside the tensegrity structure’s mass, enabling a direct estimation of the natural frequencies of the tensegrity-fluid system through a linearized model. Additionally, we model the fluid-induced torque on individual rods and the damping torque resulting from positional constraints. To avoid singularities in the coordinate representation, we use vectors for the rods and their mass centers instead of Euler angles to describe the rods’ motion. The equations of motion are further modified to minimize numerical errors and reduce computational costs. Our model is applicable to general tensegrity systems with or without constraints. We demonstrate the effects of fluid-added mass and viscosity on the behavior of tensegrity structures through simulations of two specific structures: a tensegrity prism and an icosahedron. Considerable changes in system behavior are observed in the presence of fluid.