Analysis Of Nonlinear Vibration Behavior Of The Spacecraft Cable With Coupling Constraints

In order to avoid the problem that cables may be divorced from constraints during spacecraft launch, rules of nonlinear vibration behavior of layin g cables need to be analyzed, so the common restriction condition of the cable inside the spacecraft is selected to study. Based on the inertial coordinate system of cables, force on the cable element is analyzed with elastic mechanics, and then the vibration model of the cable with coupled constraints can be obtained. Ordinary differential equations of cables of in-plane vibration or spatial vibration are obtained by using the Galerkin method. The nonlinear vibration model of cables with coupled constrains is qualitatively and quantitatively analyzed by using the multi-scale method and numerical method. Thus, the nonlinear vibration behavior of cables with different constraints is obtained.Combined with the cable model with the typical constraints of the actual situation, basic hypotheses and relevant parameters are described to establish the partial differential equations of the cable with both ends fixed vibrating in the three-dimensional space. Then, the partial differential equations are discretized by using the Galerkin method. According to the mathematical model of the system, the frequencies of cables vibrating in plane or out of plane are obtained. According to the numerical simulation results, the situation of the vibration frequency of the system changing with its influence factors can be obtained.According to the three-dimensional vibration equations of the cable system, the nonlinear equations of cables vibrating in plane are obtained by translation and elimination of coordinates. Then, the internal resonance and the non resonance of cables are analyzed by using the multi-scale method. The vibration model of the cable with its both ends fixed and its laying route through clamps is built. Then, the vibration model is discretized by using the Galerkin method. Furthermore, the response of cable system vibrating in plane is obtained by using the numerical simulation method and the finite difference method.Through the reduction of the three-dimensional vibration equation of the suspension cable system, the spatial coupling vibration equations of the cable are obtained, and then the equations can be discretized with the Galerkin method. Further, the history responses of cable with coupling vibration in space are obtained by numerical simulation. The fact that cables often exist as the spiral posture and the cable bundle is taken into account, and then the nonlinear behavior of the multi cables system of cables contacting with each other is analyzed on the basis of fretting wear.In order to verify the correctness of the nonlinear vibration model and the numerical simulation results of the nonlinear vibration behavior of the cable in the spacecraft, vibration mode charts, vibration frequencies and time-history response are obtained by finite element analysis of the nonlinear vibration behavior of cables. The results of finite element analysis are compared with the results obtained by numerical simulation, and then the rationality of the nonlinear vibration model and the nonlinear vibration behavior of the spacecraft cable are verified.