基于拓展单位分解有限元法分析声波在多域场内的响应  

Analysis of acoustic wave response in complex multiple domains based on the enriched partition of unit finite element method

作　　者：李鸿秋[1] 姜金辉[2] 陈国平[2] 智淑亚[1] LI Hong-qiu;JIANG Jin-hui;CHEN Guo-ping;ZHI Shu-ya(College of Mechanical and Electrical Engineering, Jinling Institute of Technology, Nanjing 211169, Jiangsu, China;State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu, China)

机构地区：[1]金陵科技学院机电工程学院,江苏南京211169 [2]南京航空航天大学结构力学和控制国家重点实验室,江苏南京210016

出　　处：《声学技术》2019年第5期481-487,共7页Technical Acoustics

基　　金：江苏省自然科学基金资助(BK20151099);金陵科技学院科研基金资助(JIT-B-201219);江苏省高校优秀中青年教师和校长境外研修计划资助

摘　　要：基于拓展单位分解有限元方法,将平面波函数和贝塞尔函数作为基函数进行拓展。将亥姆霍兹方程离散,求解时不变情况下多域场内声波的响应,并分析基函数对求解精度的影响。将波动方程的时间导数利用二阶中心差分方法离散,得到方程的隐式表达式,划分时间步迭代求解时变情况下声波在多域场内的响应,分析迭代时间间隔对计算精度的影响,与典型算例的精确解进行比较,验证精确性。结果表明,平面波函数作为拓展基函数,利用二阶中心差分法离散时间导数,分析时不变以及时变情况下多域场内高波数声波的响应问题,具有较高的计算精度和计算效率。Based on the enriched partition of unity finite element method, the plane wave functions or Bessel functions are enriched as basis functions to discretize Helmholtz equation, the response of acoustic wave in complex multiple domains under time-independent condition is solved and the effect of basis functions on solution accuracy is analyzed. The two-order central difference method is used to discrete time derivative of the wave equation for implicit solution and the time step iterative method is used to solve the response of acoustic wave in complex multiple domains under time-dependent condition. By taking the plane wave function enriched as basis function and using the two-order central difference method to discrete time derivative, the responses of high wavenumber acoustic waves in complex multiple domains under time-dependent and time-independent conditions are calculated. Also, the effect of iterative time interval on calculation accuracy is analyzed. Typical examples are used to compare the calculation results with the exact solu- tions and to verify the method in this paper having high accuracy and efficiency.

关 键 词：波动方程 亥姆霍兹方程 单位分解有限元 拓展方法 时变和时不变 

分 类 号：O429[理学—声学]