Nonlinear Dynamics Investigation of Beam-Tensegrity Structures

This study presents a finite element method (FEM) for the nonlinear and linearized dynamics of tensegrity structure, including beams, based on the Lagrangian method. The displacements and rotations of the nodes are applied as global generalized coordinates. The nonlinear beam-tensegrity dynamics with or without constraints are derived first. Then, static equations in three standard forms are presented, in terms of generalized global coordinates, force density, and force vectors. Finally, the linearized dynamics and model analysis equations of the beam-tensegrity structure with or without constraints are given. The general nonlinear FEM dynamics of the beam-tensegrity system proposed in this study have the following abilities: 1. Accurate nonlinear dynamic and static analyses with elastic deformation of elements in the system. 2. Various types of boundary conditions for the system, such as some specified DoFs are fixed, static or dynamic external forces (i.e., the gravitational force or some forces applied to the specified DoFs). 3. Accurate modal analysis, including the natural frequency of the system and its corresponding modes. Three examples were investigated to verify the proposed approach, and the results were compared with those of the analytical method and the commercial software ANSYS. This study provides new insights into the nonlinear and linearized dynamics, statics, and model analysis of beam-tensegrity structures.