基于微分求积法求解非粘滞阻尼系统的时程响应  

Time-history analysis of non-viscously damped systems based on the differential quadrature method

作　　者：潘玉华[1] 王元丰[1] 

机构地区：[1]北京交通大学土木建筑工程学院,北京100044

出　　处：《计算力学学报》2011年第4期517-522,529,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(50978015)资助项目

摘　　要：研究一种含有指数型非粘滞阻尼线性多自由度振动系统的时程分析问题。该非粘滞阻尼模型假设阻尼力与质点速度的时间历程相关,数学表述为质点速度与核函数的卷积。由于阻尼模型的改变,常用的数值积分方法(如Newmark-β法、Wilson-θ法)不能直接应用于这种非粘滞阻尼系统。基于一种无条件稳定的微分求积方法,给出了这种非粘滞阻尼系统的逐步积分表达式。与其他文献中的方法相比,该方法无需将系统动力方程扩展成状态空间方程,而是直接对非粘滞阻尼系统的动力方程进行数值计算,具有概念简单,适用范围广,计算精度高的优点。数值算例验证了该方法的有效性。Time-history analysis of multiple-degree-of-freedom linear systems with exponential non-viscous damping is considered.In the non-viscously damped system,the damping forces depend on the time history of velocities,which are represented by convolution integrals between the velocities and exponentially decaying kernel functions.Since the damping model is changed,the classic integration methods,such as Newmark-β method and Wilson-θ method,can not be directly employed in the non-viscously damped systems.Based on an unconditionally stable differential quadrature method,the time step integration algorithms for the non-viscously damped systems are proposed.In contrast with other methods revised in the literature,the proposed method does not need to transform the equations of motion into an extended state-space representation,but can be directly employed to calculate the responds of the non-viscously damped systems,which has the advantages of conceptual simplicity,extensive applicability and high accuracy.Numerical examples are presented to demonstrate the validity of the proposed method.

关 键 词：非粘滞阻尼 指数型阻尼 微分求积法 时程积分 

分 类 号：O322[理学—一般力学与力学基础]