三维声腔模态的等几何计算分析

Modal analysis of three-dimensional acoustic cavity using isogeometric approach

针对复杂空间声场建模问题,本文采用等几何分析研究了三维内部声场的建模与固有特性,基于非均匀有理B样条(non-uniform rational B-spines,NURBS)建立了声腔的几何模型,由Helmholtz方程控制的内部声场同样采用NURBS基函数求解。与传统有限元相比,等几何分析保证了几何模型的精确性,避免了繁琐的网格划分,实现了几何建模与数值仿真的统一。对3种椭圆柱体进行模态计算与分析,其截面分别为椭圆、同心椭圆环和带偏心圆孔的椭圆。数值算例表明等几何分析具有较高的收敛率和计算精度,基函数阶次为3时椭圆柱形声腔的计算结果与解析解吻合良好。椭圆台形声腔的波数随离心率增大而增大,椭圆环柱形声腔的波数变化较为复杂。

Three-dimensional interior acoustic modeling and inherent characteristics are investigated using isogeometric analysis(IGA),which aims at the modeling of the complex acoustic field.The nonuniform rational B-spines(NURBS)employed to exactly build acoustic cavities also serve as the basis for interior acoustic fields governed by the Helmholtz equation.Compared with the traditional finite element method,IGA keeps the accurate geometric model,avoids the traditional tedious meshing step,and unifies the geometric modeling and numerical simulation.This paper presents modal calculation and analysis of elliptical cylindrical cavities,whose cross sections are ellipse,elliptical annulus,and ellipse with an eccentric circular hole,respectively.Numerical examples show that IGA has a fast convergence rate and high calculation precision.The wavenumbers of an elliptical cylindrical cavity obtained by cubic NURBS agree well with the analytical values.For an elliptical truncated cone,the wavenumbers increase as the eccentricity increases.For an elliptical annulus cylindrical cavity,the variation of wavenumbers becomes complex.