Dynamic performance prediction of an annular tensegrity structure based on similitude method

Abstract

Recently, the deployable antenna structure is designed and built extra larger to address the lack of observation accuracy and high resolution. However, this will bring new challenges for the performance testing of the prototype in a terrestrial environment. Similitude theory is a branch of methodology method that can reflect the basic configuration and characteristic of a reduced scale model. Therefore, this paper briefly introduces a conventional annular tensegrity that can be used by space deployable antennas. The Discrete Similitude Method is proposed to decompose a complex structure into equivalent beam or cable members. The similitude compatibility criteria of members is derived using the Discrete Similitude Method, along with the criteria of consistency of similitude scale factor and conservation of dimension. The criteria of consistency of similitude scale factor and conservation of dimension of the whole structure are also deduced to obtain the scale relationship of dynamic characteristics when the geometrical nonlinearity of beam and cable members are considered. Then, a similitude correction method to address the problem of the distortion in the size, load, and material properties of beam and cable member is proposed to study the dynamic similitude of annular tensegrity structures. The criteria of consistency of distorted coefficients of different beam and cable members are derived. Finally, the comparison of numerical and FEM results is presented to show that the dynamic performance prediction method has a high precision and can guide the design of reduced scale prototype. A 4 m prototype is fabricated and a modal experiment is tested. It is demonstrated that the 1st order natural frequency of the prototype can accurately predict for that of a 100 m oversized prototype.