Self-vibrational Analysis of a Tensegrity

Abstract

A tensegrity structure’s self-vibrational behavior is investigated to validate explanations that the natural frequencies of the tensegrity are composed of the individual natural frequency of strut and cable elements. Tensegrity structure is described as a “self-stressing” object to maintain its equilibrium state. In the equilibrium state, struts are designated to be in compressive state, and cables are designated to be in tensile state. Because all the tensegrity structure elements are connected to preserve the equilibrium state, no boundary condition is needed. To solve this kind of structure by using the conventional finite element procedure is not feasible. Little study has been done to explore the self-vibrational behavior of a tensegrity structure. Previous studies of vibrational tensegrity behavior are limited to specific kind of modular tensegrity (cylinder, sphere) and predefined simple geometric form of tensegrity with some boundary supported nodes to avoid rigid body motion. In this paper, the self-vibrational dynamic equations of the prestressed strut, which is treated as an axially vibrating element, and the prestressed cable, which is treated as a transversally vibrating element, are derived consistently in the frequency domain in the context of spectral element procedure. The Wittrick-Williams procedure uses the determinant value of the equilibrium equation matrix; thus, no singularity problem is encountered. The derived self-vibrational dynamic equations are applicable for general tensegrity form without predefined conditions necessary. A numerical example is presented to demonstrate the efficiency of the present study.