A nonlinear model is developed to investigate the blade vibration-induced acoustic resonance in a linear cascade. The Euler equations are solved by using high-order computational aeroacoustics techniques. To satisfy no-penetration wall boundary conditions for vibrating blades, a semi-implicit time-accurate body force model is developed. Leading-edge singularity at resonance is remarkably strong, and so the balance of globally high-order quality (less dissipation) and numerical stability is significant. The adaptive discontinuity-capturing filtering is introduced as a local operation to achieve the good balance. To validate our model, the benchmark case of the Parker $\beta$ acoustic resonance induced by the vibrating cascade of flat plates is revisited. Compared to the linearized theory and viscous flow solution, our inviscid model economically achieves a good prediction both for the unsteady loading and the near-field sound pressure for the small blade vibration amplitude of $Y_m/c=0.4\%$. When it comes to a larger vibration amplitude of $Y_m/c=2.0\%$, nonlinearity on the unsteady lift and sound pressure appears in our results, and it cannot be considered in the linearized theory. The results, to some extent, are also consistent with the viscous flow solution. The study well verifies the capability of our nonlinear model in predicting this category of linear and nonlinear sound-vortex/structure interaction problems.

开发了一个非线性模型来研究线性级联中叶片振动引起的声共振。欧拉方程是通过使用高阶计算航空声学技术求解的。为了满足振动叶片的无穿透壁边界条件，建立了半隐式时间精确体力模型。共振时的前沿奇异性非常强，因此全局高阶质量（较少的耗散）和数值稳定性之间的平衡非常重要。引入自适应不连续性捕获滤波作为本地操作，以实现良好的平衡。为了验证我们的模型，Parker的基准案例$\beta$再次讨论了由平板振动产生的声共振。与线性化理论和粘性流解相比，我们的无粘性模型在非恒定载荷和近场声压方面都能很好地预测叶片小振幅时的非稳态载荷和近场声压。${ÿ}_{米}/C=0.4％$。当涉及到更大的振动幅度时${ÿ}_{米}/C=2.0％$，不稳定的升力和声压的非线性会出现在我们的结果中，而在线性化理论中则无法考虑。结果在某种程度上也与粘性流动解决方案一致。这项研究很好地验证了我们的非线性模型预测此类线性和非线性声涡/结构相互作用问题的能力。