This article investigated the stability of transverse hydrogen injection combustion caused by the plate vibration. The finite-rate method is used to simulate the combustion. The unsteady flow field in the unstable phase of combustion is extracted. The unstable mode of the shock wave structure and the flame structure during the stage of combustion instability, the spatial and temporal characteristics of the dominant modes, as well as their stability are analyzed based on the dynamic mode decomposition (DMD) method. The results indicate that, according to the sequence of energy, the extracted first six orders modes of the shock wave structure and the flame structure have relatively low frequency with a negative growth rate and small numerical value, which presents a trend of weak convergence. The characteristics of the dominant structure of DMD modes show that the plate vibration has great effects on the reflected shock wave structure near the plate and on the upper wall surface, as well as the flame structure near the plate. According to the sequence of the mode energy and the growth rate, respectively, the extracted first six orders modes have relatively high frequency. Simultaneously, the structures of the modes extracted by the sequence of mode energy are more regular, while those extracted by the sequence of growth rate are more disorderly. The unstable shock wave structure is mainly manifested by the reflected shock wave in the vibration region and the shock wave structure reflected by the upper wall surface. The unstable flame structure is mainly concentrated near the vibration region and downstream areas.

本文研究了平板振动引起的横向喷氢燃烧的稳定性。有限速率法用于模拟燃烧。提取燃烧不稳定阶段的非定常流场。基于动态模态分解(DMD)方法分析了燃烧不稳定阶段冲击波结构和火焰结构的不稳定模态、主导模态的时空特征及其稳定性。结果表明，根据能量顺序，提取的激波结构和火焰结构的前六阶模态频率较低，增长率为负，数值较小，呈现弱收敛趋势。DMD模式的主导结构特征表明，板振动对板附近和上壁面的反射激波结构以及板附近的火焰结构有很大影响。分别根据模态能量和增长速率的顺序，提取的前六阶模态频率较高。同时，模式能量序列提取的模式结构更规则，而增长率序列提取的模式结构更无序。不稳定的激波结构主要表现为振动区域内反射的激波和上壁面反射的激波结构。不稳定的火焰结构主要集中在靠近振动区域和下游区域。