摘要
本文在将修正的Ritz向量直接叠加法(MWYD法,原称MRVDS法)的思想与Lanczos坐标法结合的基础上,提出了完整的Lanczos向量叠加法和Ritz向量叠加法,并用统一的理论框架,比较系统地阐明了Lanczos向量叠加法,Ritz向量叠加法和振型叠加法的基本原理、主要步骤和各自的特点。文中提出了结构的成比例阻尼矩阵及其特殊形式—Rayleigh阻尼矩阵在Ritz子空间和Lanczos子空间的具体表达式以及无耦合单自由度运动方程的具体形式,结合进MWYD算法的优点和近来发展的误差估计方面的研究成果,提出了经过改进完善的Lanczos向量叠加算法。该法不仅可用于单向动力荷载,也可用于双向三向动力荷载;不仅适用于具有相同振型阻尼比的系统,也适用于具有Rayleigh阻尼的系统;它还可以利用误差估计式根据给定的精度要求及时控制产生初始Lanczos向量的数日。最后,文中简要地总结了Lanczos向量叠加法对于振型叠加法和Ritz向量叠加法的优越性。
In this paper,a complete Lanczos Vector Superposition method (the LVS method) is presented.Its algorithm,the expression of the Rayleigh damping matrix in the Lanczos subspace and the way to determine its elements are given.It could be used not only for one direction of dynamic loading but also for dynamic loadings with two or three components.It is suitable to both systems,with equal damping ratios and with Rayleigh damping; and reliable no matter the problem solved is with or without multiple eigenvalues.In addition,An error estimation formula presented by Pierre Leger et al.is adopted and described,so that it is possible to control the generation process of the Lanczos vectors according to specified accuracy demand.Finally,its advantages over the MS method and the MWYD method are summarized,
出处
《地震工程与工程振动》
CSCD
北大核心
1991年第1期37-50,共14页
Earthquake Engineering and Engineering Dynamics
基金
国家自然科学基金
