结构动力响应中急动度的计算

A Numerical Method for Calculation of Structural Jerk Responses

急动度(jerk)在工程实践中具有重要的意义.将径向基函数逼近与配点法相结合,发展了一种能够有效求解动力响应的数值算法.该方法使用径向基函数插值来逼近真实的运动规律,能够用于急动度和急动度(三阶)方程的计算,弥补了传统的数值方法无法计算急动度的不足.并针对微分方程的特点,提出了改进的多变量联合插值函数,同时添加与微分方程同阶的初值条件,可显著减小数值震荡.算例表明,该方法具有计算过程简单、精度高的特点,同时对急动度方程也有很好的适用性.

Jerk is of great significance in engineering practice. A numerical method for solving jerk responses was constructed through combination of the radial basis function （RBF） approximation and the collocation method. The proposed method was used to calculate the jerk and the 3rd-order jerk equations, and the RBF interpolation was adopted to approximate the real motion rule, which made good the defect that the traditional methods can＇ t be used to calculate the jerk. Aimed at the numerical characteristics of the dynamic differential equations, an improved RBF expression of multivariable joint interpolation combining the all-order derivatives of the variable was presented. The initial-value condition of the same order with the differential equation was added to obviously decrease the numerical oscillation. The results of the numerical examples indicate that the proposed method has the advantages of a simple calculation process, high accuracy and high applicability to jerk equations.