【作者】 牛建辉；

【导师】 李建康； 解幸幸；

【作者基本信息】 江苏大学 ， 固体力学， 2003， 硕士

【摘要】 工程实际中普遍采用有限元分析方法和试验模态分析技术进行结构动力分析，这两种技术都各有优缺点，近年来，有人提出把有限元方法和试验模态分析技术有机的结合起来，相互取长补短，分析计算结构的动力特性。本文即在这种思想的指导下，从时域角度出发，以试验及计算数学模型得到的动态响应序列为对象，提取系统的动力信息，建立适用于动力分析的相关分析方法，并据此进行有限元计算模型(离散化的数学模型)和试验模型的相关性分析。 实际问题中常常得到的是一个时间间隔为Δt的单变量的时间序列，它是许多物理因子相互作用的综合反映，蕴藏着参与运动的全部变量的痕迹，传统的时序分析是直接从这个序列去形式地分析它的时间演变，一维分析必然丧失许多有用信息，相空间重构方法的特点是把一维标量数据构造成高维矢量，支起状态的几何空间，在相空间中展示系统全部动力信息。本文正是根据相空间重构的特点，对响应时间序列进行分析，利用符号动力学、重构相空间等方法，提出一种有理论依据的系统数学模型关联度分析方法，从而达到修正计算数学模型，使其更符合实际系统状态的目的。研究的具体物理背景是：以结构有限元分析动态计算模型所求出的响应与实际结构在瞬态激励下产生的试验响应数据为分析对象，对这两个序列进行重构相空间，即将序列构造成向量，对数学模型与实际结构进行整体相关度分析，分析其间的符合程度。同时，利用这种方法特别针对复杂结构进行了较仔细和深入的探讨，分析了这种方法的特点和适用性，验明了这种相关分析方法的可行性，从而为结构动态分析中有限元计算模型的可靠性判别和修改提供了依据。本文所研究和讨论的响应相关分析理论是对时域内模型相关理论的补充，同时也是把非线性相关理论与时序分析理论及结构动力分析相结合的一次大胆尝试。更多还原

【Abstract】 Structural dynamic analysis in engineering has two basic methods- finite element analysis method and test model analysis technology, they all have their own advantage and defect, recently , some put forward to combine finite element analysis method and test model analysis technology, take length mutually and mend short, in order to analyse and calculate the dynamical character of the structure. It is in this texts that under the guidance of this kind of thought, set out from the angle of time domain, take the aim of dynamic response array which receives from testing and computational mathematical model, Draw the systematic dynamic information, set up the relevant analytical method suitable for dynamical analysis, and go on the relevant analysis between the finite element calculating model( the dispersed mathematics model) and test model.What the practical problems is often gotten is a single variable time series whichhas a time interval of △t ,reflect by a lot of interactive physics factor, containing themark of all variates participating in movement, traditional time series analysis is to analyse going from this array to the form directly it’s time develops, one dimension analysis loses useful information, the characteristics of phase space reconstruction method is to construct one dimension scalar quantity to high dimension vector, prop the geometry space of the state, show all dynamical information of system in phase space.The characteristic that just constructs again according to the phase space in this text, analyse the time series of responding, use the relevant knowledge of symbol dynamics and reconstruct phase space, put forward a kind of relation degree analysis method of the systematic mathematics model which has theory basis, so reach the correction of calculation mathematics model, make it accord with the actual systematic state. The specific physical background of research is : we take theresponse data calculated from structural finite element analysis dynamical computing model and the test respond data of the actual structure produced under the transient state encourage as the analysis object, reconstruct phase space for this two sequences, construct sequences to vector, then carry out relation degree analysis between the mathematics model and real structure and analyse the accordance At the same time, using this kind of method, have carried out more careful and thorough discussion especially according to complex structure, have analysed applicability and the characteristic of this kind of method, and identified the feasibility of this kind of related analysis method, and have offered a basis differentiating the reliability of the finite element calculation model in structural dynamic analysis and modifying . This paper study and discuss respond related analysis theory is the supplement of theory and perfection for the model relation theory in the time domain, at the same time is also a helpful try on combining nonlinear theory and sequence analysis theory and structural dynamic analysis.更多还原