Vinh Pham Chi, Malischewsky Peter G
Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, 334 Nguyen Trai Str., Thanh Xuan, Hanoi, Viet Nam.
Ultrasonics. 2007 Dec;47(1-4):49-54. doi: 10.1016/j.ultras.2007.07.002. Epub 2007 Jul 27.
In the present paper an improved approximation for the Rayleigh wave velocity in isotropic elastic solids is obtained using the method of least squares. It is of Bergmann's form, i.e. the form of the ratio of two binomials. It is shown that this approximation is the best one of the Rayleigh wave velocity, in the sense of least squares, with respect to the class of functions whose elements are the ratio of two binomials. This approximation is much more accurate than Bergmann's one. Its maximum percentage error is 10 times smaller than that of Bergmann's. It is 7.6 times better than the one obtained recently by Royer and Clorennec [D. Royer, D. Clorennec, An improved approximation for the Rayleigh wave equation, Ultrasonics 46 (2007) 23-24]. An approximation of Bergmann's form for the squared Rayleigh wave velocity is also derived and its maximum percentage error is 5 times smaller than that of Royer and Clorennec's approximation. Some polynomial approximations with very high accuracy are also obtained.
在本文中，使用最小二乘法获得了各向同性弹性固体中瑞利波速度的一种改进近似。它具有伯格曼形式，即两个二项式之比的形式。结果表明，就最小二乘法而言，对于元素为两个二项式之比的函数类，这种近似是瑞利波速度的最佳近似。这种近似比伯格曼的近似精确得多。其最大百分比误差比伯格曼的小10倍。它比罗耶尔和克洛伦内克最近得到的结果[D. 罗耶尔，D. 克洛伦内克，瑞利波动方程的一种改进近似，《超声学》46 (2007) 23 - 24]好7.6倍。还推导了瑞利波速度平方的伯格曼形式近似，其最大百分比误差比罗耶尔和克洛伦内克的近似小5倍。还得到了一些精度非常高的多项式近似。
