在任意动力荷载作用下具有有效自由度的非线性系统的一些解析算法(英文)  

Some Analysis Algorithms for Nonlinear Systems with Finite Number of Degrees of Freedom Under Arbitrary Dynamic Effects

作　　者：Y.T.契尔诺夫 

机构地区：[1]莫斯科建筑工程大学土木工程系,俄罗斯莫斯科129337

出　　处：《北京建筑工程学院学报》2010年第2期26-31,共6页Journal of Beijing Institute of Civil Engineering and Architecture

摘　　要：具有有限自由度的非线性动力系统(线性系统为其特例)的动力设计方法,通过非线性连接装置(具有非线性特性的阻尼器、或者是阶跃性地启动和退出工作的联系)与其它的单元和结构连接.在这种算法中,与线性系统对应的算符写于运动方程的左边,而非线性算符置于方程的右边.具有这种形式的运动方程的解可以表示为线性系统振型的叠加,从而可以把方程分解为n个类似于单自由度系统的具有非线性项lr的方程.利用Duhamel积分,得到的方程转化为n个非线性积分方程.虚拟力值在每一个步长上通过叠代得到了进一步的精确化.在本文中展示的非线性隔振系统设计结果及其它一些问题的解答,尤其是具有阻尼器的系统的设计,展示了在任意荷载作用下,在强非线性系统的设计中本算法具有很好的收敛性和精度.The paper shows the method of dynamic design of nonlinear systems with finite number of degrees of freedom and,as a special case,of linear systems,which are jointed with the additional elements and constructions（dampers with nonlinear characteristics or stepping-into-work or stepping-out-of-work links） by nonlinear links.During the development of design algorithm,the operator,corresponding to some linear system,is written down in the left side of the motion equation,and nonlinear components are rearranged to the right side of the equation.The solution of this equation,represented in a such form,can be written down as an expansion in eigenforms of linear system and resolved into n systems of equations,similar to the motion equations of systems with a single degree of freedom related through nonlinear terms lr.Using the Duhamel integral,obtained system can be reduced to the system of n nonlinear integral equations.External and fictitious loads are replaced by polylines,and during equation solving we use one-type formulas on every step of time.The fictitious load value is precised by iterations on every step of time.The results of nonlinear vibroisolated system design,shown in the paper,and the solutions of some other questions,in particular the design of a system with a damper,demonstrate a good convergence and a high accuracy of numerical algorithms also in the design of strongly nonlinear systems under arbitrary effects.

关 键 词：动力设计 多自由度非线性系统 积分方程 

分 类 号：TU311.3[建筑科学—结构工程]