摘要
为了避免划分网格,应用Hermite径向基函数点插值配点法(HRPIC)求解消声器横向本征方程,应用该方法计算的圆形和跑道圆横截面本征波数分别与解析结果和有限元计算结果吻合较好。进而分析影响域尺寸,问题域内计算点数目以及径向基函数的形状参数对本征波数计算误差的影响。结果表明,本征波数的计算误差在一定范围内会随着影响域尺寸和问题域内节点数目的增大而减小,但是不会一直减小,存在最优的数值,无量纲的形状参数直接影响本征波数的计算精度。最后比较Hermite径向基函数点插值配点法与有限元法的计算速度。
The collocation method with point interpolation and Hermite radial basis function(HRPIC) is employed in the numerical analysis of the 2-D eigen-equations of silencers.The eigen-wave numbers of the circular and oval cross sections are computed using this method and the results are found to agree well with those of the analytical method and general finite element method.Furthermore,the effects of size of the influence domain,number of computation nodes and the shape parameters of the radial base-functions on the calculation accuracy are evaluated.The results show that the relative error of the eigenvalue decreases with the increasing of the number of computational nodes and the size of influence domain in an effective range,but it increases instead beyond the range.So,there must be optimal values for the number of the computational nodes and the size of the influence domain.The dimensionless shape parameter directly affects the calculation accuracy of the eigenvalue.Finally,the computational speed of HRPIC method is compared with that of general FEM.
出处
《噪声与振动控制》
CSCD
2018年第1期36-41,共6页
Noise and Vibration Control
基金
国家自然科学基金资助项目(11504119)
