Wave Propagation in Non-homogeneous Centrosymmetric Damping Plate Subjected to Impact Series

Abstract

The elastic wave propagation characteristics, especially the local plus resonance phenomenon, affect the stability and the accuracy of the electronic components mounted on the spacecrafts significantly, which implies that the layout of the electronic components in the spacecrafts should be away from the plus resonance domains. Thus, considering two electronic components set symmetrically on a plate fixed on the spacecrafts by eight bolts, the elastic wave propagation properties in the plate are investigated by a structure-preserving approach in this paper. A non-smooth dynamic model is presented to describe the elastic wave propagation in the non-homogeneous centrosymmetric damping plate excited by the impact series acting on the connecting bolts. Then, a structure-preserving approach is proposed to simulate the localized wave propagation phenomenon in the plate based on the generalized multi-symplectic theory. Accompanying with the structure preserving approach, both the local energy dissipation and the generalized multi-symplectic residual are formulated in detail. In the numerical examples, the local plus resonance domains are explored for several load cases. From the numerical results, it can be found that the steady plus resonance domains are symmetric if and only if the impact series is symmetric. It is interesting to observe that, in some cases of the uniform impact series, the local plus resonance domains may exhibit splitting phenomenon or degeneration phenomenon with the time increase. The above-mentioned novel findings can be used to guide the layout optimization of the electronic components in the spacecrafts directly. In addition, the structure-preserving approach developed in this paper proposes a new way to investigate the non-smooth dynamic systems.