多自由度结构动力方程解析解的改进算法  

Improved analytical algorithm of dynamic formula of a multipledegree-of-freedom system

作　　者：任泽民 凌霄霄 乔金丽 丁冬 孟秋杰 吕超 REN Zemin;LING Xiaoxiao;QIAO Jinli;DING Dong;MENG Qiujie;LU Chao(School of Civil and Transportation Engineering,Hebei University of Technology,Tianj in 300401,China)

机构地区：[1]河北工业大学土木与交通学院,天津300401

出　　处：《河北工业大学学报》2018年第4期68-74,共7页Journal of Hebei University of Technology

基　　金：国家自然科学基金(51675374);河北省自然科学基金(E2014202178)

摘　　要：针对结构动力计算中数值方法不精确以及模态叠加法计算复杂,对结构质量、刚度、阻尼矩阵形式有限制等一系列缺点,提出了多自由度体系运动方程的改进解析算法,推导了改进算法下自由振动时方程的通解形式,并对简谐荷载以及插值形式的地震荷载作用下多自由度体系的运动方程进行了解析求解.文中在求解时对结构的质量、刚度、阻尼矩阵的形式及状态矩阵的正交性不做要求.计算结果与文献中所给结果非常接近,同时将所得解析式代入运动方程时,方程左右两边的误差在10-15量级.数例计算和证明推导过程体现了解的精确性.此解为多自由度体系运动方程解析解的求解方法提供了一个新的思路.Solution of motion equation gotten from numerical method is imprecise. Meanwhile, the mode-superposition method presents great computational complexity and has special requirements on forms of stiflhess matrix, mass matrix and damping matrix. Focusing on those shortages, improved analytical algorithm of dynamic formula of a multiple-degree-of-freedom system is proposed, and general solution for fiee vibration is obtained by improved method. Then analytic solution under harmonic loads and seismic forces based on cubic spline is presented on the premise that there is not a requirement on forms of stiflhess matrix, mass matrix and damping matrix. When we input analytic solution of numerical examples into dynamic formula, error of the equation is about 10^-15. Accuracy of the analytic solution can be demonstrated by the course of proofs and numerical examples. Without doubt, this method brings us an easier way to get analytic solution of dynamic formula of a multiple-degree-of-freedom system.

关 键 词：结构动力方程 多自由度体系 解析解 地震作用 

分 类 号：O325[理学—一般力学与力学基础] O175[理学—力学]