The flexible back cavity (FBC) plate silencer is composed of an FBC and a flexible inner plate. Through the coupling of the sound field with the flexible inner and outer plates, the transmitted sound energy of the downstream is reduced, and it has a good broadband muffling effect at low frequencies. In order to obtain the transmission loss (TL) of the FBC plate silencer under arbitrary boundary conditions, this paper establishes the acoustic-vibration coupling model of the FBC plate silencer based on the energy principle. Translational restraints and rotational restraints are used to simulate the arbitrary boundary conditions of the flexible plate, and then the influence of the boundary conditions of the flexible plate on the TL is analyzed. The results show that the results of the proposed method are in good agreement with the finite element method (FEM) results. The structural boundary restraint has a significant influence on the acoustic characteristics of the system, and the rotational restraints suppress the muffling effect. By appropriately releasing the translational restraints, a better low-frequency broadband muffling effect can be achieved, with the minimum muffling frequency reduced by 44.8% and the muffling bandwidth broadened by 57.4%.

柔性背腔（FBC）板式消声器由FBC和柔性内板组成。通过声场与柔性内外板的耦合，减少下游传输的声能，在低频下具有良好的宽带消声效果。为了获得FBC板式消声器在任意边界条件下的传输损失（TL），本文基于能量原理建立了FBC板式消声器的声振耦合模型。采用平移约束和旋转约束模拟柔性板的任意边界条件，分析柔性板边界条件对TL的影响。结果表明，该方法的结果与有限元法（FEM）的结果吻合较好。结构边界约束对系统的声学特性有显着影响，旋转约束抑制消声效应。通过适当释放平移约束，可以获得更好的低频宽带消声效果，最小消声频率降低44.8%，消声带宽展宽57.4%。