微分求积法在工程结构动力学中的应用研究

Application of Differential Quadrature Method in Engineering Structural Dynamics

论证了微分求积法和最高精度的高阶有限差分法是等价的,推导出微分求积法权系数的显式表达式,进一步地阐述了如何应用微分求积法求解工程结构动力学偏微分方程.用数值算例给出了微分求积法求解动力学偏微分方程的步骤,并将微分求积解与解析解进行比较,说明了微分求积法的有效性.分析表明,微分求积法是分析工程结构动力学问题的一种简单高效的方法,求解精度高,可给编写程序带来很大方便.

This research has proved that the differential quadrature method is equivalent to the finite difference method ofthe highest accuracy and explicit expressions of differential quadrature weight coefficients are derived. How to apply thedifferential quadrature method to the partial differential equation of engineering structural dynamics has also been stud-ied. Numerical examples are given to illustrate the procedure of using the differential quadrature method to solve dynamic partial differential equations, and differential solution and analytical solution were compared, which justfied the validity of the differential quadrature method. The above research results show that the differential quadrature method is a simple andefficient method for studying the dynamics of engineering structures with high accuracy, and it is very convenient for pro-gramming.