阶梯圆柱形耦合声场的特征正交-里兹法建模及声学特性分析  

Modeling and acoustic characteristics analysis of stepped cylindrical coupling sound field using Characteristic Orthogonal Ritz method

作　　者：钟锐 谢非 秦斌 王青山 ZHONG Rui;XIE Fei;QIN Bin;WANG Qing-shan(State Key Laboratory of High Performance Complex Manufacturing,Central South University,Changsha 410083,China;School of Traffic&Transportation Engineering,Central South University,Changsha 410083,China)

机构地区：[1]中南大学高性能复杂制造国家重点实验室,长沙410083 [2]中南大学交通运输工程学院,长沙410083

出　　处：《计算力学学报》2021年第6期729-738,共10页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(51705537)资助项目.

摘　　要：针对阶梯圆柱形耦合声场建模问题,提出基于特征正交-里兹能量原理的声学建模方法。该方法利用二维特征正交多项式和周向傅里叶级数表征阶梯圆柱形耦合声场子分段的声压函数,从能量角度考虑邻近子声场间声学连续性条件,并结合里兹法获得耦合声场的声学特性。基于本建模方法对不同分段的耦合声场开展声学特性分析,结果表明,本建模方法在保证计算准确性的基础上有效提高了计算效率,且对任意阶梯分段的圆柱形耦合声场普遍适用;圆柱形耦合声场固有频率会随着腔体外径增大而普遍增大,而腔深的影响规律相反;降低声学边界阻抗可抑制声学响应幅值,为此类声场的噪声控制提供了设计依据。Aiming at the modeling problem of stepped cylindrical coupling acoustic field,an acoustic modeling method is proposed on the basis of characteristic orthogonal Ritz energy principle.In the method,two-dimensional characteristic orthogonal polynomials and circumferential Fourier series are used to characterize the sound pressure function of the sub segments of the stepped cylindrical coupled sound field.The acoustic continuity conditions between adjacent sub fields are considered from the energy point of view,and the acoustic characteristics of the coupled sound field are obtained by combining Ritz method.Based on the modeling method,the acoustic characteristics of the coupled sound field with different segments are analyzed.The results show that the modeling method can effectively improve the calculation efficiency while ensuring the calculation accuracy,and it is generally applicable to the cylindrical coupling acoustic field with arbitrary step segments.The natural frequencies of the cylindrical coupled sound field will generally increase with the increase of the outer diameter of the cavity,while the influence trend of the cavity depth is the opposite.Reducing the acoustic boundary impedance can suppress the acoustic response,which provides a design basis for noise control of this type of sound field.

关 键 词：阶梯圆柱形 耦合声场 特征正交-里兹法 声学建模 声学特性 

分 类 号：O242.1[理学—计算数学] O422.2[理学—数学]