Vibration and elastic wave propagation in spatial flexible damping panel attached to four special springs

Investigation of the characteristics of the vibration and elastic wave propagation in the ultra-large ultra-flexible damping spatial structures is the precondition for the active control of the dynamic response of the spatial structure from the viewpoint of the wave absorption perspective. The difficulties of the analysis on the characteristics of the vibration and elastic wave propagation in the spatial structures result from the following two aspects: one is the coupling effects between the attitude control, the orbit dynamics and the structural vibration exciting the elastic waves; and another is the non-smooth factors including the on-off controllers and the geometric constraints between the components of the structure. Employing the complex structure-preserving approach, the vibration and wave propagation characteristics in the spatial flexible damping panel attached to four special springs are investigated in this paper. Considering the coupling between the structural vibration, the attitude dynamics and the orbit dynamics, a dynamic model is established for the spatial flexible damping panel-spring-mass system. Compared with the dynamic model proposed in previous work, the springs suspending the panel are considered as unilateral non-smooth constraints to describe the zero constraints when some tethers are slack during certain time periods in the tethered satellite system described by the dynamic model presented in this paper. Relying on the local structure-preserving properties of the generalized multi-symplectic method and the excellent long-term numerical behaviour of the symplectic method, the complex structure-preserving method is employed. Some novel vibration and wave propagation characteristics in the spatial flexible damping panel attached to four special springs with different initial attitude angles are revealed, which include the damping characteristics of the elastic wave propagation in the spatial panel and the interaction process of the elastic waves, especially the resonance phenomena between the elastic waves obliquely propagating in the panel. The complex structure-preserving method presented in this paper is proved as an effective approach to deal with the non-smooth coupling dynamic systems and the vibration and wave propagation characteristics revealed can be used to guide the structural design as well as the material selection for the tethered satellite system.