Towards validated dynamic models for tensegrity structures: Parametric modelling, vibration testing, and model updating of a hexagonal prism

Abstract

Tensegrity structures are self-equilibrium systems connected by compression rods and tension strings. They represent a promising structural type in aerospace applications due to the lightweight advantage. Conventional transducers, such as accelerometers, are difficult to apply to the rods or strings, making it challenging to measure the dynamic behaviours of tensegrity structures. It has hindered model updating studies and the accurate modelling of these structures, which are of great interest from an industrial point of view. Additionally, state-of-the-art model updating methods, which routinely adjust parameters such as geometric dimensions or elastic modulus for engineering structures, may be inadequate to apply to a tensegrity structure, as its structural stiffness depends on both material properties and prestress in rods and strings. To address these challenges, this paper presents a systematic approach towards validated dynamic models for tensegrity structures. First, a parametric finite element (FE) model is established, and sensitivity analyses of nodal positions, elastic modulus and prestress levels on the natural frequencies of the prism are carried out. Numerical simulations show that the prestress level is a critical factor that affects its natural frequencies. Second, full-field vibration testing of the prism is carried out. A single-point excitation is employed to obtain the frequency response functions, from which three natural frequencies and modal damping ratios are identified. Next, full-field mode shapes of the prism are measured by dwelling the excitation at each of the identified natural frequencies and tracking the full-field vibrations using a non-contact motion capture system. Third, a novel model updating method for tensegrity structures is proposed by utilising the test results. The measured full-field mode shapes are paired with those FE predictions using a modified cross-modal assurance criterion (cross-MAC), with special treatment to account for degenerated modes attributed to the symmetry of the structure. Subsequently, the test/analysis discrepancies of the natural frequencies for the paired modes are minimised by adjusting the prestress levels of strings in the FE model. As shown by the results, the updating process effectively reduces the test/analysis discrepancies of the natural frequencies from 29.2 % to 5.3 %. It also estimates the prestress values as 18.54 N and 22.01 N for the horizontal and diagonal strings, respectively. Finally, direct tension measurements of the strings are carried out as a validation tool for the proposed model updating method. Discrepancies in the prestress levels of the strings, ranging from 13.44 % to 27.72 %, confirm the feasibility of the proposed method. The parametric model, experimental data, and model updating codes are openly available to serve as a benchmark for accurate modelling of tensegrity structures.