Nonlinear dynamic modeling and responses of a cable dragged flexible spacecraft

Abstract

The space debris removal system (SDRS) of tethered space tug is modelled as a cable dragged flexible spacecraft. The main goal of this paper is to develop a dynamic modeling approach for mode characteristics analysis and forced vibration analysis of the planar motion of a cable dragged flexible spacecraft. Solar arrays of the spacecraft are modelled as multi-beams connected by joints with additional rotating spring where the nonlinear stiffness, damping and friction are considered. Using the Global mode method (GMM), a novel analytical and low-dimensional nonlinear dynamic model is developed for vibration analysis of SDRS to enhance the design capacity for better fulfillment of space tasks. The linear and nonlinear partial differential equations that governing transverse vibration of solar arrays, transverse and longitudinal vibrations of cable are derived, along with the matching and boundary conditions. The natural frequencies and analytical global mode shapes of SDRS are determined, and orthogonality relations of the global mode shapes are established. Dynamical equations of the system are truncated to a set of ordinary differential equations with multiple-DOF. The validity of the method is verified by comparing the natural frequencies obtained from the characteristic equation with those obtained from FEM. Interesting mode localization and mode shift phenomena are observed in mode analysis. Dynamic responses of the system excitated by fluctuation of attitude control torque and short-time attitude control torque are worked out, respectively. Nonlinear behaviors are observed such as hardening, jump and super-harmonic resonances. Residual vibration of the overall system with considering the varous values of nonlinear stiffness, damping coefficient and friction coefficient has shown that the nonlinearity of joints has a great influence on the vibration of the overall system.