​​Dynamic Modeling, Analysis and Testing of Tensegrity Structures

Tensegrity structures, known for their lightweight and reconfigurability, face challenges in achieving desired dynamic responses due to the absence of robust tools for dynamic modeling and testing. Traditional methods often oversimplify structural members, neglecting internal displacements, leading to inaccurate predictions, especially at high frequencies. Additionally, conventional testing uses transducers that introduce undesired effects.

To address these challenges, this research aims to establish a platform for tensegrity structures’ dynamic modeling and testing. The study focuses on (1) a modeling method for vibration analysis, (2) a method for morphing analysis incorporating internal displacements, and (3) a non-contact testing system using three-dimensional laser vibrometry and digital image correlation for validation and indirect force measurement.

Application of tensegrity structures: (a) deployable tensegrity reflector for small satellites; (b) Kurilpa Bridge in Brisbane, Australia; (c) SUPER-ball; (d) tensegrity metamaterials.

Vibration Analysis of Tensegrity Structures

This research develops a nonlinear dynamic modeling method known as the Cartesian spatial discretization (CSD) method for vibration analysis of tensegrity structures. The CSD method introduces an innovative technique to integrate member internal displacements into the modeling of these structures. This approach counters the common oversimplifications in traditional methods. By including member internal displacements, the CSD method delivers enhanced precision in vibration analysis, especially at high frequencies. Moreover, employing a global Cartesian coordinate system, the CSD method simplifies the assembly process in deriving the equations of motion for the entire tensegrity structure.

Simulation results of the CSD method (a) initial configuration of the planar Snelson’s tensegrity structure; (b) history of convergence of the last natural frequency; (c) frequency responses of node four; and (d) displacement of node three in the x-direction at the excitation frequency of 15000 Hz.

Morphing Analysis of Tensegrity Structures

This research explores a nonlinear dynamic modeling method, termed the extended Cartesian spatial discretization (ECSD) method, for the morphing analysis of tensegrity structures. The ECSD method introduces a unique approach to seamlessly integrate member internal displacements linked to the slack-to-taut transition of cable members during the morphing process, especially when encountering large structural deformations and swift nodal motions. Consequently, the ECSD method can accurately predict the dynamic responses of tensegrity structures. Using the global Cartesian coordinate system, the ECSD method automatically incorporates rigid-body motions of members, optimizing its efficiency for large deformations. Building upon the foundation of the CSD method, the ECSD further introduces: 1) nonlinear dynamic modeling of members’ damping forces, and 2) nonlinear modeling of slack cable members.​

Simulation results of the proposed ECSD method: (a) initial configuration of the planar Snelson’s X tensegrity structure with cable five being slack; nodal displacements in the x-direction of the structure (b) node two, (c) node three, and (d) node four.

​Non-Contact Dynamic Testing of Tensegrity Structures

We introduce a non-contact dynamic testing system for tensegrity structures using 3D laser vibrometry (3D-LV) and a 3D high-speed digital image correlation (DIC) system. These methods will validate both the CSD and ECSD modeling approaches and facilitate indirect measurement of member internal forces. Additionally, a novel technique, leveraging a deep neural network (DNN), will be developed to estimate these forces without built-in transducers, using modal parameters from the non-contact systems as input data.

Dynamic testing of tensegrity structures: (a) experimental setup for vibration measurement by the 3D high-speed DIC system; (b) measured FRF; (c) schematic for morphing measurement; and (d) experimental setup for vibration measurement using the 3D-LV.

References

  1. Yuan, S.* and Zhu, W., 2023. A Cartesian spatial discretization method for nonlinear dynamic modeling and vibration analysis of tensegrity structures. International Journal of Solids and Structures, 270, p.112179. doi: 10.1016/j.ijsolstr.2023.112179
  2. Yuan, S. and Zhu, W., 2022, October. A New Approach to Nonlinear Dynamic Modeling and Vibration Analysis of Tensegrity Structures. In ASME International Mechanical Engineering Congress and Exposition (Vol. 86670, p. V005T07A104). American Society of Mechanical Engineers. doi: 10.1115/IMECE2022-94746