中文摘要：

动力方程的数值求解关系结构响应计算的真实准确和结构设计的安全可靠，一直是国内外研究人员十分关注的问题。钟方勰教授提出的精细积分法对求解齐次的动力方程很简便，但对于非齐次结构动力方程，采用数值积分的处理办法可以避免直接用精细积分法带来的矩阵的求逆或逆阵不存在问题，大大减少了计算量，并且方便编程。运用牛顿-柯特斯数值积分公式、高斯数值积分公式、龙贝格数值积分、龙格-库塔方法等积分方法，分别求解非齐次动力方程，并对计算结果进行了全面细致的数值验证和最大的相对误差比较。通过比较分析，认为高斯数值积分公式是相对计算精度较高、计算效率较好的积分方法。因此为在多种数值积分方法中选用高斯数值积分公式求解动力方程提供了理论分析的依据。

英文摘要：

The numerical solution of dynamic equation is on intimate terms with true and accurate response of the structure and design of safety and reliability, which has been a matter of great concern to researchers at home and abroad. The precise integration method, which was proposed by Professor Zhong Wan-xie, for solving the dynamic equation is very simple and homogeneous, but for non-homogeneous structure of the equation, numerical integration approach avoided inverse matrix or inverse problems exist by direct using the precise integration, significantly reduce the amount of calculation, and to facilitate programming. This article utilizes Newton-Cotes numerical integration formula, the Gauss numerical integration formula, the Romberg numerical integration, Runge-kutta method, and so on integral methods, have carried on the comprehensive careful value confirmation to the inhomogenous item and the biggest erroneous comparison. Through the comparative analysis, obtains the Gauss numerical integration formula is the relative higher computation accuracy and efficiency integral method. Therefore for selected the Gauss numerical integration formula solution dynamic epuation in many kinds of numerical integration method to provide the theoretical analysis basis.