On the Dynamics of Tensegrity Bridges

Abstract

This paper describes the nonlinear dynamics of planar tensegrity bridges designed for minimal mass. The three-dimensional bridge benefits by the planar analysis in the most important manner relating to topology of material. We start with the minimal mass bridge, counting both structural mass and deck mass, and then derive the nonlinear dynamics to study dynamic behavior of the minimal mass bridge. Suggested design criteria include static and dynamic response. The minimal mass tensegrity has an optimal complexity (number of elements), and we show how the dynamic response influences the best choice of complexity, in comparison with the optimal complexity of the static design. The structures are first designed with minimal mass criteria, accounting for equilibrium and static stability conditions, and subsequently, we investigate the dynamics of such structures subject to constraints on displacements and loads perturbations. We employ an efficient approach to rigid body dynamics in matrix form, modified to include cable masses. We also show how to pass from the matrix to vector form of the dynamics. The equations of motion are derived analytically using Newtonian methods, and include damping and bar length constraints. Prestress of cables is added to tune stiffness. We show an application for artificial gravity space habitats.

Rigidity percolation in a random tensegrity via analytic graph theory

“…Our analytic approach for finding tensegrity rigidity can help guide the engineering of tensegrity structures, such as towers ( 13 ), bridges ( 40 ), domes ( 41 ), or others ( 42 ), as their demand continues to grow. It can also help our understanding of how complex biological tensegrities ( 12 ) arose through successive generations of random mutation and natural selection.…”