Form-Finding and Free Vibration Analysis of a Class-One Triplex Tensegrity Prism

This paper deals with form-finding and free vibration analysis of a pre-stressed class-one triplex tensegrity structure. The form-finding is performed via a two-step procedure, the nodal coordinates connectivity matrix, and structural element force density determination. Accordingly, the possible states for the nodal coordinates and the structural force density of the triplex prism have been determined by trial and error (based on topology and member type knowledge) to satisfy the force density, and equilibrium matrices rank requirements. Based on different structural topologies, the equation of the motion in the frequency domain for free vibration analysis of the system is derived using the spectral element approach and dynamic shape functions. Simulations are provided for different system heights and the top-bottom aria ratios and compared with the finite element method. The numerical simulations in the form of a comparative study of the natural frequencies of triplex tensegrity prism with different heights and cross-sections represent the system’s robustness with different topologies for single or