带倾斜薄板的梯形声场建模及其振声特性分析  

Modeling of a trapezoidal sound field covered by an inclined panel and its vibro-acoustic analysis

作　　者：陈跃华[1,2] 靳国永 刘志刚[2] 王延召[3] CHEN Yuehua;JIN Guoyong;LIU Zhigang;WANG Yanzhao(Faculty of Maritime and Transportation,Ningbo University,Ningbo 315211,China;College of Power and Energy Engineering,Harbin Engineering University,Harbin 150001,China;State Key Laboratoty for Environlnentul Protection of Power Grid,China Electric Power Research institute,Wuhan 430074,China)

机构地区：[1]宁波大学海运学院,浙江宁波315211 [2]哈尔滨工程大学动力与能源工程学院,黑龙江哈尔滨150001 [3]中国电力科学研究院电网环境保护国家重点实验室,湖北武汉430074

出　　处：《哈尔滨工程大学学报》2018年第7期1186-1190,共5页Journal of Harbin Engineering University

基　　金：国家自然科学基金项目(51505237);宁波市自然科学基金项目(2017A610081);宁波大学王宽诚幸福基金资助

摘　　要：针对带倾斜薄板的梯形声场声学建模问题,提出了一种基于Chebyshev-变分原理的非规则声场-结构耦合系统建模方法,建立了弹性边界约束下倾斜薄板-梯形封闭声场耦合模型。将结构位移和声场声压分别表示成多重Chebyshev级数形式,按照利兹方法分别求解结构和声场的拉格朗日泛函,得到耦合系统的特征方程并求得系统的固有频率和模态。与有限元结果的对比验证了本文方法的正确性,并就结构边界条件及声场倾斜角度对耦合系统固有频率的影响进行了分析。分析结果表明:倾斜角的存在增强了声场模态的不规则程度,倾角的增大使得耦合系统板控频率依次递减,而腔控频率的变化趋于复杂;薄板倾斜边界约束的释放使得耦合系统各阶固有频率显著减小。To model a trapezoidal sound field covered by an inclined panel,a modeling method for irregular sound field-structure coupling systems was proposed based on the Chebyshev-variational theory. A coupled model of inclined panel-trapezoidal enclosed sound field is established under elastic restrained conditions. The vibration displacement and sound pressure are separately expressed as multiple Chebyshev polynomials. The Lagrangian functional of the structure and sound field are solved according to the Ritz method. The acoustic characteristic equation of the coupling system is obtained,and the natural frequency and mode shapes of the system are acquired. By comparing with the finite element results,the accuracy of the present method is validated. In addition,considering the boundary conditions of the structure and the inclination angle of the sound field,the influence of the natural frequency of the coupled system is analyzed. It reveals that the existence of the inclination enhances the irregularity of the modal of sound field,and with an increase of the inclination,the panel-controlled frequency of the coupled system decreases successively,while the change of the cavity-controlled natural frequencies becomes complex. Furthermore,the release of the inclined boundary restraints of the panel results in an obvious decrease of the natural frequencies of each order of the system.

关 键 词：梯形声场 非规则声场 Chebyshev级数 变分法 振声特性 结构-声耦合 

分 类 号：TU311.3[建筑科学—结构工程]