The targeted energy transfer (TET) technique could be applied to reduce the low frequency noise by a nonlinear membrane absorber as nonlinear energy sink (NES) inside a tube or an acoustic cavity. The pre-stress of the nonlinear membrane can affect the desired working zone for the TET and also the suppressed amplitude of noise. In order to design the nonlinear membrane according to a given acoustic medium, the influence of the pre-stress of the nonlinear membrane is quantitatively studied in this paper. The analytical formulae over the pre-stress of the membrane are established based on a general model of the system with an acoustic mode of 3D acoustic cavity and one membrane. Meanwhile, the suppressed frequency bandwidth of noise is investigated under different pre-stress levels of the membrane by using harmonic balance method and numerical method. For convenient applications, the radial deformation analysis and the modal analysis of the membrane with the pre-stress are finally performed by finite element method (FEM) to obtain the relationship between the radial displacement and the first mode. It can be helpful to guide design of the pre-stress of the membrane NES according to the desired working zone for the practice engineering application in acoustic field.

有针对性的能量转移（TET）技术可通过非线性膜吸收器（作为管或声腔内部的非线性能量吸收器（NES））来降低低频噪声。非线性膜的预应力会影响TET的所需工作区域，还会影响噪声幅度。为了根据给定的声介质设计非线性膜，本文对非线性膜的预应力的影响进行了定量研究。基于具有3D声腔和一个膜的声模的系统通用模型，建立了膜预应力的解析公式。与此同时，利用谐波平衡法和数值方法，研究了膜在不同预应力条件下的噪声抑制频率带宽。为了方便应用，最后通过有限元方法（FEM）对膜片进行了预应力的径向变形分析和模态分析，从而获得了径向位移与第一模态之间的关系。根据声学领域中的实际工程应用所需的工作区域，指导膜NES的预应力设计可能会有所帮助。