单侧触水复杂形状薄板的自由振动特性分析  

Analysis of free vibration characteristics of complicated shape plate contacting with water on one side

作　　者：李清盛 李天匀[1,2,3] 朱翔 张帅[1] 聂睿 LI Qingsheng;LI Tianyun;ZHU Xiang;ZHANG Shuai;NIE Rui(School of Naval Architecture and Ocean Engineering,Huazhong University of Science and Technology,Wuhan 430074,China;Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration,Shanghai 200240,China;Hubei Key Laboratory of Naval Architecture&Ocean Engineering Hydrodynamics,Wuhan 430074,China)

机构地区：[1]华中科技大学船舶与海洋工程学院,湖北武汉430074 [2]高新船舶与深海开发装备协同创新中心,上海200240 [3]船舶与海洋水动力湖北省重点实验室,湖北武汉430074

出　　处：《中国舰船研究》2023年第5期194-206,共13页Chinese Journal of Ship Research

基　　金：国家自然科学基金资助项目(51839005,51879113)。

摘　　要：[目的]旨在研究单侧触水弹性边界下复杂形状薄板的自由振动特性。[方法]选取包络复杂形状薄板域的矩形域并将薄板位移用矩形域内的改进傅里叶级数表示,结合Rayleigh积分建立表面声压和薄板位移的关系,并将积分式转换到局部极坐标中以避免奇异性,针对局部极坐标中该变限积分中的边界曲线难以获得显式表达式的问题,用“以直代曲”的方式处理结构边界曲线以简化Rayleigh积分,基于能量原理建立了分析单侧触水复杂形状薄板自由振动特性的半解析方法。[结果]给出了单侧触水矩形薄板、圆形薄板和一些复杂形状薄板的算例,与有限元及文献结果对比验证了该方法的收敛性和准确性,并讨论了弹性边界对薄板附加虚拟质量增量因子(added virtual mass incremental,AVMI)的影响规律,各阶AVMI因子在边界位移弹簧无量纲化刚度为103附近出现最大值,此时结构受流体影响相对最大。[结论]该方法适应性较强,计算效率较高,揭示了流体中复杂形状薄板的自由振动规律,具有一定的工程指导意义。[Objectives]This paper aims to study the free vibration characteristics of complicated shape plate coupled with fluid under elastic boundary conditions.[Methods]To this end,the rectangular domain enveloping the complicated shape plate domain is selected,and the plate displacement is expressed by the improved Fourier series in the rectangular domain.Combined with the Rayleigh integral,the relationship between the plate displacement and the surface sound pressure is established,and the integral formula is transformed into polar coordinates to avoid singularity.Aiming at the problem that it is difficult to obtain the explicit expression of the boundary curve in the variable limit integral in local polar coordinates,the structural boundary curves are treated by"replacing curve with straight"to simplify the Rayleigh integral.Based on the energy principle,a semi analytical method for analyzing the free vibration characteristics of complicated shape plate contacting with water on one side is established.[Results]The numerical examples of rectangular plate,circular plate and some complicated shape plates are given.Compared with the finite element method and literature results,the convergence and accuracy of the method are verified,and the influence of elastic boundary conditions on the added virtual mass incremental(AVMI)factor of plate is discussed.The AVMI factor of each mode reaches the maximum near the dimensionless displacement spring stiffness of 103.At this time,the structure is relatively most affected by the fluid.[Conclusions]This method has strong adaptability and high calculation efficiency.It reveals the free vibration law of complicated shape plate coupled with fluid,and has certain engineering guiding significance.

关 键 词：复杂形状 薄板 声振耦合 Rayleigh积分 改进的傅里叶级数 

分 类 号：U663.1[交通运输工程—船舶及航道工程] TB532[交通运输工程—船舶与海洋工程]