Accurate modeling and analysis of a bio-inspired isolation system: with application to on-orbit capture

The accurate dynamical model of a bio-inspired isolation (BII) system with complete consideration of the kinetic and potential energies of all components is established for the first time. Owing to the inclusion of energies pertaining to the rods and joints in the modeling process, the equations of motion of the accurate BII model are virtually governed by a set of implicit ordinary differential equations (IODEs), which is totally different from the simplified model whose governing equations are standard ODEs. Since the accurate model cannot be transformed into the explicit form, viz. ẋ=f(x,t), it cannot be handled via the traditional numerical integration methods, e.g. the Runge-Kutta method. In order to conquer this difficulty, the harmonic balance method and the Matlab's ODE15i code are employed to solve the periodic and aperiodic solutions, respectively. More importantly, the comparisons of dynamical responses as well as isolation performance between the accurate and simplified BII models are conducted in two situations. For the situation when system exhibits simple responses, the accurate and the simplified models generate qualitatively the same pattern of results. The only discrepancy is that the latter model produces an overestimated vibration. For the complex responses, an essential distinction occurs between the two models, indicating that using the accurate BII model is extremely important. Furthermore, the efficiency of the BII isolator is verified through comparing with the traditional spring-mass-damper (SMD) system. The influences of system parameters, such as damping, layer number, assembly angle, spring stiffness, etc., on the isolation performance have been investigated. Finally, numerical examples verify the efficiency of the present BII isolator in both ground and space environments.