裂纹及水介质对薄圆板振动辐射声场特性的影响  

Effects of a crack and water on the characteristics of vibration and sound field radiated by a circular plate

作　　者：石焕文[1] 孙进才[1] 盛美萍[1] 尚志远[2] 

机构地区：[1]西北工业大学航海学院 [2]陕西师范大学应用声学研究所,西安710062

出　　处：《声学学报》2006年第2期158-166,共9页Acta Acustica

基　　金：陕西省自然科学基金(2004A07)中国博士后基金(2005037792)国家自然科学基金(50375121)资助项目

摘　　要：在有限元模态分析的基础上,提取了含人工裂纹的薄板各单元的相关参数,并将瑞利积分离散化,进而计算了裂纹薄板辐射声场的轴向声压分布和r=0．5 m球面上声场分布。结果表明,径向裂纹不仅使模态裂解为关于裂纹的对称模态和反对称模态,而且使声场分布有显著的变化。方法的有效性通过完整圆板辐射声场来验证。该方法可用于求解任意形状穿透裂纹薄板辐射声场的计算。还提出了一种简便计算置于无限大障板上的裂纹薄板水中振动频率以及辐射效率的计算方法。在假定薄板作小振幅振动、水中模态挠度近似为真空模态挠度的条件下,利用瑞利积分得到了因流体压而引起的附加质量密度。进而应用瑞利方法得到了薄板水中振动频率与真空中振动频率、无量纲附加虚质量增量之间的关系。在真空中模态的有限元方法分析数据以及采用适当方法处理奇点积分的基础上,应用离散积分计算了无量纲附加虚质量增量的值。从真空中模态特征频率出发用迭代法直到水中频率收敛为止而得到水中薄板的特征频率,进而计算了薄板的模态辐射效率。方法的有效性通过薄板的无量纲附加虚质量增量与Kwak的结果对比的一致性来验证。Based upon the modal analysis by FEM, some relevant parameters of every element on a clamped thin circular plate with an artificial radial crack are extracted. After the Rayleigh＇s integral is discretlzed, the axial pressure distribution and the distribution of the sound field on the spherical surface r = 0.5 m radiated by the crack plate are computed. It is shown that the radial crack doesn＇t only make the modes split into symmetrical and antisymmetrical modes about the crack except the first mode, but also changes the distribution of the sound field obviously. The validation of the method is illustrated by the sound field radiated by the intact circular plate, and it is suitable for computing sound field radiated by a circular plate with different kind of through crack. Moreover a simple computational method for the vibration frequencies of a circular clamped baffled plate with an artificial crack in water is described. Under the conditions that the plate vibrates in small amplitude and the modal deflection in water equals that in vacuo, the added mass density due to the water pressure is expressed using Rayleigh＇s integral. Then the relationship among vibration frequency of the plate in water and that in vacuo and the Nondimensionalized Added Virtual Mass Incremental （NAVMI） is obtain by utilizing Rayleigh method. Based upon the data of modal analysis for the plate in vacuo by Finite Element Method （FEM） and properly dealing with the integral at singular dot, the value of NAVMI is obtained by discretizing the integral.Moreover the vibration frequencies of the plate are computed using iterative method, which begins with the in vaeuo eigenfrequency and continues until in-water eigenfrequency converges. The present approach is validated by comparison the NAVMI computed here with the results of Reference [Kwak M K. J. Sound Vib., 1997; 201（3）： 293-303].

关 键 词：人工裂纹 辐射声场 圆板振动 水介质 有限元模态分析 声场特性 模态辐射效率 瑞利积分 计算方法 振动频率 

分 类 号：O422.6[理学—声学]