The coupling effect between the vibration of the electric components and the wave propagation is the critical factor that should be considered in the optimization on the layout of the electric components in the spacecrafts. Different from the case considered in our previous job, the layout of the electronic components on the spacecraft is always asymmetric, thus, investigating the wave propagation characteristics in an asymmetric plate is more meaningful than that in a symmetric one. As a companion job of the previous investigation on the wave propagating in a non-homogeneous centrosymmetric damping plate subjected to the impact series, the wave propagation characteristics in a non-homogeneous asymmetric circular plate are studied in this paper. Considering the asymmetry of the layout of the electronic components, the controlling equation of the wave propagating in the non-homogeneous circular plate is proposed. And then, the first-order approximate symmetric form of the controlling equation is obtained based on the multi-symplectic reduced-order idea. Employing the Preissmann method, a structure-preserving scheme is constructed to simulate the wave propagation in the plate. To reproduce the superimposed effects of the resonance phenomenon, the integration of the wave forms in the plate is performed in a long-time interval in the numerical experiments and some meaningful superimposed results of the resonance regions are presented for several impact combinations. The main contribution of this paper is proposing a structure-preserving approach to provide the superimposed results of the resonance regions in the non-homogeneous asymmetric plate that can be used in the layout optimization of the electronic components in the spacecraft directly.

电气元件的振动与波传播之间的耦合效应是航天器电气元件布局优化中应考虑的关键因素。与我们之前工作中考虑的情况不同，航天器上电子元件的布局总是不对称的，因此，研究非对称板中的波传播特性比研究对称板更有意义。作为先前对受到冲击序列的非均匀中心对称阻尼板中波传播的研究的配套工作，本文研究了非均匀非对称圆板中的波传播特性。考虑到电子元器件布局的不对称性，提出了波在非均匀圆盘中传播的控制方程。然后，基于多辛降阶思想得到控制方程的一阶近似对称形式。采用普赖斯曼方法，构造了一个结构保持方案来模拟波在板中的传播。为了重现共振现象的叠加效应，在数值实验中以较长的时间间隔对板中的波形进行积分，并针对几种冲击组合给出了共振区域的一些有意义的叠加结果。