Initial Prestress Distribution and Natural Vibration Analysis of Tensegrity Structures Based on Group Theory

As conventional approaches for morphology and natural vibration analysis do not make full use of the symmetry of structures, the computational cost is significantly raised with increasing number of nodes. In this paper, we propose a simplified technique used to analyze initial prestress distribution and natural vibration of tensegrity structures based on group theory. First, the conditions of symmetry and equilibrium equations for tensegrity structures were established on the basis of the symmetry-adapted coordinate systems found by group theory. Then the initial prestress modes could be found from the null space of the independent sub-matrix of symmetry-adapted equilibrium matrix. Subsequently, the tangent stiffness matrix and the lumped mass matrix were block-diagonalized using symmetry. The generalized eigenvalue problems were simplified by solving the mutually independent subspaces, with the corresponding natural frequencies and vibration modes obtained. Two illustrative examples demonstrate the general procedure, and show the superiority in reducing the difficulty of initial prestress distribution and natural vibration analysis. When compared with numerical results obtained by Abaqus and those of Murakami, the proposed method is shown to be more accurate and efficient.