Nonlinear Dynamic Modeling and Vibration Analysis of a Quadrilateral Cross-Section Tensegrity Prism Considering Gravitational Stiffness: A Comparative Study

Tensegrity systems are lightweight spatial grid structures that are composed of compression and tension elements that can be used in adjustable structures. The primary stability of these structures is achieved by creating pretension conditions between the elements. These systems have low structural damping, which makes them vulnerable to dynamic loads. As a result, it is essential to predict the behavior and extract the dynamic characteristics of these structures to achieve a safe design. This article presents the vibration analysis of a one to four stage tensegrity structure with a square cross-sectional area. A Lagrangian approach and the finite element method were used to extract the nonlinear dynamic equations of the system based on the coordinates of the nodes. For one to fourstage tensegrity systems with fixed cross-sections and heights, the force density method is used as an initial form finding method. Each element's cross-section is designed to have a minimum mass, and dynamic modeling allows for observing elastic/plastic deformations under various boundary conditions, as well as static and dynamic loading on each node, taking gravity stiffness into account. Dynamic simulations in the form of comparative studies have been conducted to investigate natural frequencies, mode shapes, time responses of nodal displacements, elements deformations, and internal forces for one to four-stage tensegrity structures.