任意形振动源表面振速分布的重建

Velocity Reconstruction of Vibrating Sources with Arbitrarily Shaped Surfaces

从Helmholtz积分方程出发,利用奇异值分解技术和统计计算方法,导出了任意形振动源表面振速重建公式.文中首先利用边界元方法对Helmholtz积分方程进行离散化,其中采用了线性插值的平面三角形单元和四边形单元,每个单元上的表面积分采用二维高斯积分.为了消除或减小各种附加噪声对重建结果的影响,对最小二乘解的残量进行了方差估计,并在给定的约束条件下,确定合适的阻尼因子来修正奇异值,从而改善了最小二乘解.数值结果表明,本文的方法是可行的、有效的.

Based on the Helmholtz integral equation, the velocity reconstruction formulas of vibrating sources with arbitrarily shaped surface are established, utilizing the technique of Singular Value Decomposition (SVD) and the statistical calculating method.In this paper,the Helmholtz integral surface is replaced by a number of interconnected flat triangular elements and flat quadrilateral elements with linear plotted function.The element surface integration is performed by means of two-dimensional Gaussion quadrature.In order to eliminate or reduce the contribution of noise to velocity reconstruction results, the method proposed by Veronesi and Maynard is devoloped.Through estimating the remainder of Least-Square, and among the mathematical constraints, we defined a resistance facil to modify the singular values for improved solution of the Least-Square problem.The numerical results show that the method is effective, and render it attractive.