有限尺寸V型薄板功率流透射损失研究

Research on transmission loss of power flow through a finite V-shaped plate

基于薄板理论,采用回传射线矩阵法研究了两对边简支任意角连接有限尺寸V型薄板的功率流透射损失。引入对偶坐标系,在力作用点和板接缝处对结构进行离散,同时考虑弯曲波动与面内波动效应,根据结构连接处的位移协调条件、力平衡条件以及两端边界条件得到V型薄板结构的散射矩阵。根据对偶坐标系的内在物理关系得到整体相位矩阵,最后推导出结构的回转射线矩阵。在此基础上,建立了V型薄板结构的动态响应分析模型以及功率流分析模型,通过对简谐点激励力作用下结构的动态响应进行对比分析,证明回传射线矩阵法具有很高的求解精度与求解效率。最后,分析了V型薄板结构功率流传导问题,研究了不同角度、不同板厚和不同阻尼损耗因子的V型薄板的功率流透射损失变化规律。

Based on the Kirchhoff thin plate theory,the method of reverberation ray matrix（MRRM）is employed to study the transmission loss of power flow through a finite V-shaped plate.The V-shaped plate is supposed to be simply supported at two opposite edges and coupled with an arbitrary angle at the joint.Both of the effects of the flexural and in-plane waves are concerned.The V-shaped plate is discretized into different parts at the excitation point and the joint.A dual local coordinate system is established for each part of the discretized model.Accordingly,the scattering matrix of the V-shaped plate is obtained from the continuity and equilibrium conditions at the joint and the boundary conditions at each end.Subsequently,the phase matrix is derived from the inherent relations among the variable vectors expressed in the dual local coordinate system.Then the reverberation matrix of the V-shaped plate is derived.Therefore,a model for dynamic response analysis of the V-shaped plate is established.Then the dynamic response of a V-shaped plate subjected to a harmonic point force is analyzed by MRRM,and the calculation results are compared with those obtained by FEM.It is found that MRRM is of high accuracy and efficiency.Finally,power flow of the V-shaped plate is calculated,and the effects of coupling angle,plate thickness and damping loss factor on transmission loss of power flow through the V-shaped plate are also investigated.