Mechanism of Contact Nonlinearity on the Natural Frequency of Spatial Spherical-Joint-Beam Structures

Spherical joints are widely utilized in space-deployable truss extension arms due to their compact structure, high reliability and excellent flexibility. Spherical joints are often combined with beams to form Spherical-Joint-Beam Structures (SJBS). However, the nonlinear contact effects and discontinuities inherent to spherical joints pose challenges to the dynamic modeling of SJBS, leading to significant errors in predicting the dynamic performance of truss extension arms. To address the aforementioned issues, this paper proposes a continuous modeling method of the spherical joint structure by introducing equivalent material layer (EML) and developing a nonlinear dynamic model of the SJBS. Specifically, this study establishes a theoretical model for the contact force and stiffness of spherical joints based on fractal contact theory, along with an in-depth analysis of the factors influencing contact stiffness. Additionally, mathematical models for key parameters of the EML, such as the elastic modulus, Poisson’s ratio and shear modulus are derived based on energy conservation, then the sensitivity analysis of the EML parameters is conducted. Finally, the dynamic characteristics of the SJBS are systematically investigated, and the accuracy of the theoretical model is validated experimentally through modal experiments. The results indicate that using EML in modal analysis better captures the contact characteristics of the ball joint compared to finite element simulation. The error for the first-order frequency is 9.66%, and for the second-order frequency, it is 12.98%. This study reveals the mechanisms by which geometric nonlinearity and contact nonlinearity influence the natural frequency of the SJBS, providing valuable insights for the application of these structures in the extension arms of large space trusses.