Two-dimensional viscoelastic beam element for ultra-large space structures based on absolute nodal coordinate formulation

Abstract

Internal damping is an important factor in the dynamic behaviors of ultra-large space structures in zero damping space environment. To precisely describe the damping, this paper proposes a two-dimensional viscoelastic Euler-Bernoulli beam element based on absolute nodal coordinate formulation and Kelvin-Voigt damping model, where the damping stress is linearly dependent on the stress rate. Firstly, a precise generalized damping force model is developed using the principle of virtual work. A simplified generalized damping force model is then proposed to improve simulation efficiency by neglecting the axial damping force and a part of the transverse damping force. Numerical simulations show that the proposed damping force models will not affect the rigid-body motion of the beam. Then, a simple formula is presented to estimate the damping ratio of the beam for different parameters, which shows good agreement with the logarithmic decrement method in simulations. Finally, the effects of viscoelastic damping on the dynamic behaviors of a Sun-facing beam in space are investigated. Simulation results reveal that the viscoelastic damping can greatly reduce the vibration amplitude of the beam near the resonance frequencies.