Damping formulations for jointed deployable space structures

Abstract

Both the friction caused by the preload in locked joints and the impact caused by clearance in unlocked joints cause energy dissipation in jointed deployable structures. The energy dissipation of locked joints is studied by analyzing the force on the infinitesimal body of the joint. The jointed beam with an unlocked joint is simplified into an impact mass-spring model with clearance, which considers the coefficient of restitution of impact. The energy dissipations of the joint caused by friction and clearance are transformed into damping ratios by Taylor expansion. Then, the effects of pressure, clearance and the dynamic parameters on the damping of joints are analyzed by utilizing the damping ratio formulation. The damping ratio increases with the preload and the clearance. To validate the damping ratio formulation of joints, experiments on a single jointed beam with preload and double jointed beams with clearance are conducted. Comparison between the experimental results and the model simulation results shows that the friction and impact damping models are accurate for the dynamic calculation of deployable structures. Furthermore, the damping ratio formulations can be directly introduced into the design and dynamic analysis of deployable structures.

Nonlinear Dynamic Modeling and Analysis of an L-Shaped Multi-Beam Jointed Structure with Tip Mass

“…The natural frequencies of the L-shaped multi-beam jointed structure are denoted in ascending order by ω 1 , ω 2 , • • • , which are the positive roots of the frequency equation det(H(ω)) = 0. Once the natural frequency ω s is obtained, the eigenvector ψ (s) can be obtained by Equation (26). Then, the s − th global mode shapes for the L-shaped multi-beam jointed structure can be determined by Equation (24).…”

“…Concerning the multi-beam structure connected with joints, there have many studies on the effect of the joint on the nonlinear dynamic behavior of the system, which mainly focuses on flexible-joint manipulators [ 16 , 17 , 18 , 19 , 20 , 21 , 22 ] and deployable structures [ 23 , 24 , 25 , 26 , 27 , 28 , 29 ]. For the flexible-joint manipulator, the joint flexibility mainly comes from the harmonic reducer.…”

“…Bowden and Dugundji [ 25 ] proposed a geometric joint participation factor to quantify the contribution of the damping in the joints to the modal damping of the whole structure. Zhang et al [ 26 ] presented a damping ratio formulation to investigate the effects of pressure, clearance, and dynamic parameters on the damping of joints. Guo et al [ 27 ] systematically investigated the effects of the stiffness, the damping location, and the clearance of the joint on the dynamics of the jointed deployable structure by the finite element model and experimental method.…”