Nonlinear dynamic and deployment analysis of clustered tensegrity structures using a positional formulation FEM

This paper addresses the dynamic analysis of the clustered tensegrity structures via the framework of the positional formulation finite element method (FEM). The nodal coordinates are chosen as the generalized coordinates. The rod element and multi-nodes clustered cable element are first formulated. A comprehensive dynamic model for investigating the dynamic properties of the clustered tensegrity is then developed. The dynamic model is subsequently modified for the structural vibration analysis and modal analysis. The results of the modal analysis show that each order of natural frequency of a clustered tensegrity is lower than that of its corresponding classical tensegrity, indicating that the structure tends to be more flexible if a classical tensegrity is transformed into a clustered tensegrity. The results of the nonlinear deployment analysis show that the motion characteristics differ from those of the quasi-static analysis as the actuation speed increases. To pursuit a fast actuation speed to actuate the structure, mere quasi-static analysis in the existing literature is inadequate, and dynamic effects must be taken into account. The proposed method provides an effective tool to capture the dynamic properties, such as the determination of an appropriate actuation speed, and to actuate the clustered tensegrity.