【作者】 田学民；

【导师】 李乔；

【作者基本信息】 西南交通大学 ， 桥梁与隧道工程， 2003， 博士

【摘要】 许多工程结构在强烈随机外激励下都将进入弹塑性变形状态，表现出滞后特性，结构的振动表现为非线性随机振动，因此必须用非线性模型来描述结构，并用非线性随机振动的理论和方法来进行分析。一般来说，结构受到的外激励(地震、风波浪等)属于Markov过程，结构的随机反应也属于Markov过程。在随机振动分析中，这些外激励可当作Gauss过程或滤波Gauss过程，但由于结构的非线性，结构的反应一般并不完全属于Gauss过程。因此，本文基于FPK方程和伊藤随机微分方程，研究了滞后结构物的随机地震反应和随机滤波问题的基本方法，并利用等效线性化法和矩方程法，研究了非线性结构随机地震反应分析和随机滤波分析的近似解法及它们的工程应用。作者主要完成了以下四个方面的工作。 首先，对双线形滞后特性的微分表达式进行了研究，提出了一种新的微分表达式，并给出了证明。本文提出的表达式不仅形式简单，而且便于编程，计算速度快。在此基础上，又提出了双线形滞后体系的随机分段线性化法和双线形滞后体系的随机分段线性滤波器。 其次，通过FPK方程和伊藤随机微分方程，推导和建立了一般非线性工程结构物的单自由度、多自由度随机振动微分方程和随机滤波微分方程。 第三，对非线性结构随机振动近似分析方法中的随机等效线性化法和矩方程法进行了研究。通过已建立的非线性结构物随机振动方程，纳入滞后特性微分表达式，利用随机等效线性化法和矩方程法，计算了工程结构物的随机地震反应。通过大量计算并与Monte Carlo法及其它计算结果比较分析得知，对一般工程结构物，等效线性化法的计算精度能够满足工程应用的要求。 第四，分别按随机等效线性滤波器和作者提出的随机分段线性滤波器，基于受到地震激励的圆钢管混凝土结构物的观测数据，进行了单自由度和多自由度的滤波分析，并与模拟结果进行了对比。研究表明，作者提出的随机分段线性滤波器较等效线性滤波器计算程序简单得多，便于推广应用、而且效率高。这两种滤波器都能很好地去除观测噪声，对实际应用中可能发生的不正确估计观测噪声强度的情况，和不正确估计地震激励强度的情况，两种滤波器都是稳定可靠的。更多还原

【Abstract】 Under strongly random exterior excitation, most structures will undergo elastic-plastic stage and show hysteretic characteristics, the vibration of structure expresses nonlinear random feature. Therefore nonlinear model must be utilized in order to describe the behavior of this kind of structure, also the theory and methodologies of nonlinear random vibration are necessary for analyzing their response. Generally speaking, exterior excitations that act on structure such as earthquake and wind wavelet, etc. are Markov procedure. The random response of structure as well as exterior excitations is Markov procedure. These exterior excitations can be treated as Gauss procedure or filtering Gauss procedure. But because of the nonlinearity, the response of structure is not absolute Gauss procedure. Therefore, basic methodologies for stochastic seismic and filtering responses of nonlinear structure are studied, the approximate solution methodologies and their practical applications are investigated in the dissertation employing equivalent linearization and moment equations method based on FPK equations and Ito stochastic differential equations. The research works are mainly concerned with the following aspects:Firstly, the differential expression of bilinear hysteretic is studied and a new differential expression is developed, then they are demonstrated. The equations introduced which in simple form can be utilized easily to code a procedure. On this basis, sectionalized linearization of bilinear hysteretic structural characteristics and bilinear hysteretic filtering of structural system are put forward.Secondly, random vibration and random filtering differential equations of SDOF and MDOF nonlinear structure are established and deduced employing FPK equations and Ito stochastic differential equations.Thirdly, the methodologies of equivalent linearization and moment equations method in the approximate method for random vibration of nonlinear structure are studied. Random seismic responses of civil engineering structure arecalculated by employing stochastic vibration equations and moment equations methods of nonlinear structures established and stochastic equivalent linearization. In this procedure of calculation, differential expression of hysteretic characteristics and seismic excitation are taken into consideration. Through a great deal of calculation and comparison with the results of Monte Carlo and other methodologies, a conclusion can be drawn that the precision in the calculation of equivalent linearization can satisfy the needs of practical civil applications for general engineering structures.Lastly, based on the observed data of the concrete-filled tubular structures under seismic excitation, filtering analysis of SDOF and MDOF is done respectively by the methods of stochastic equivalent linearization and sectionalized linearization introduced by the author. The simplicity and efficiency of the proposed methodologies are demonstrated by the comparison. The research indicates that the random sectionalized linearization methodology introduced by the author is more simple and efficient than stochastic equivalent linearization method, so it is convenient for generalizing. The study reveals that all these two filtering can eliminate noise efficiently, they are reliable in the case that the strength of observed noise and seismic excitation estimated incorrectly in practice.更多还原