面向动力子结构试验的耦合积分方法研究

发布时间：2018-04-20 02:10

本文选题：子结构试验 + 数值积分　；参考：《重庆大学》2016年硕士论文

【摘要】：子结构试验作为一种新兴的结构抗震试验方法自提出以来就得到快速发展。该方法把结构分为两部分:对相对重要或在动力荷载下表现出明显非线性或其他复杂物理特征的部分进行加载,称为试验子结构(Physical Substructure,PS);而其余部分则用计算机进行数值模拟,称为数值子结构(Numerical Substructure,NS)。采用子结构实验方法能够降低试验规模,有利于进行大比例或足尺试验,在真实模拟结构动力响应的条件下又能够节约大量试验费用。子结构试验是试验加载和数值计算的混合技术,其中数值计算的效率和稳定性是子结构试验的关键问题之一。耦合积分方法作为一种高效的积分方法,已被用于拟动力试验和多体动力学等方面,在子结构试验中也具有明显的优势。本文主要利用数学软件Mathematica编程针对子结构耦合积分方法进行系统的研究。在一种耦合积分方法(GC法)的基础上,结合算子分解法(OS法)、Chang法以及CR法,经过修改形成了几种新的耦合积分方法,并对其从稳定性、精度、数值阻尼比以及频率误差等数值特性方面进行了大量的分析与验证。最后基于Bouc-Wen模型和粘滞阻尼器理论对各耦合积分方法进行了数值模拟。分析结果表明耦合积分方法的稳定性、精度、数值耗散、频率失真率等数值特性除了受积分步长影响外,还与结构参数以及子步法直接相关。对于不同的参数,不同的耦合积分方法表现出不同的数值特性,具体为以下几个方面:(1)稳定性:(实时)GC-OS法在不同参数下均稳定,(实时)GC-Chang法和GC-CR法为条件稳定,且随着试验子结构刚度的增大,稳定界限降低。随着子步数的增大,稳定界限有所增大;(2)精度:(实时)GC-OS法在不采用子步法时具有二阶精度,采用子步法时为一阶精度。(实时)GC-Chang法和GC-CR法无论是否采用子步法,均为一阶精度,同时子步法的应用能够提高两者的计算精度;(3)数值阻尼比:在低频阶段(实时)GC-OS法对试验子结构刚度和子步数的变化不敏感,在高频阶段数值阻尼比随试验子结构刚度的增加而呈递增趋势。(实时)GC-Chang法数值阻尼比随着试验子结构刚度的增加而增大,随子步数的增大而降低。GC-CR法对试验子结构刚度以及子步法的采用最为敏感,随试验子结构刚度的增大或子步法的采用其数值阻尼比降低;(4)频率失真率:各耦合积分方法的频率误差均随采样频率增大而增大。(实时)GC-OS算法基本不受试验子结构刚度和子步数的影响。(实时)GC-Chang在试验子结构刚度较大时会引起较大的频率误差,但不受子步数的影响。GC-CR对试验子结构刚度的变化较为敏感,在高频阶段随试验子结构刚度的增大频率误差也呈现出增大的趋势;在进行基于Bouc-Wen滞回模型的位移相关型子结构耦合积分数值模拟时,GC-OS法、GC-Chang法以及GC-CR法三种算法表现出的性能相差不大,但采用子步法可以使得三者的计算结果吻合更好。在进行含有线性和非线性粘滞阻尼器的速度相关型子结构耦合积分数值模拟时,在不采用子步法时,GC-CR算法相对实时GC-OS法和实时GC-Chang法会引入较大的数值阻尼,随着计算的进行会出现响应幅值的衰减,在运用子步法后幅值衰减现象消失,三种算法计算精度相近。分析表明文中各耦合积分方法均能够较好地实现子结构间的耦合,且子步法的运用对于提高(实时)GC-Chang法及GC-CR法的稳定性和计算精度能够起到较好的效果。
[Abstract]:As a new method of structural seismic test, substructure test has been developed rapidly since it was proposed. This method divides the structure into two parts: the parts which are relatively important or have obvious nonlinear or other complex physical characteristics under dynamic loads are loaded, called Physical Substructure (PS), and the rest of the structure. The part uses the computer to simulate the numerical substructure (Numerical Substructure, NS). Using the substructure experiment method can reduce the scale of the test, it is beneficial to the large scale or full scale test, and can save a lot of test cost under the condition of the real simulation of the dynamic response of the structure. The substructure test is the test loading and the numerical value. The efficiency and stability of numerical calculation are one of the key problems in the substructure test. The coupling integral method, as an efficient integral method, has been used in the pseudo dynamic test and multibody dynamics, and has obvious advantages in the substructure test. This paper mainly uses the mathematical software Mathematica compilation. On the basis of a coupled integral method (GC method), combined with the operator decomposition (OS) method, Chang method and CR method, several new coupling integration methods are formed, and the numerical characteristics such as stability, precision, numerical damping ratio and frequency error are made. A large number of analysis and verification are carried out. Finally, the numerical simulation of the coupling integration method is carried out based on the Bouc-Wen model and the viscous damper theory. The results show that the stability, precision, numerical dissipation and frequency distortion rate of the coupled integration method are directly related to the structural parameters and the substep method, except the effect of the integral step length. For different parameters, different coupling integration methods show different numerical characteristics, which are the following aspects: (1) stability: (real time) GC-OS method is stable under different parameters, (real time) GC-Chang method and GC-CR method are stable, and with the increase of the stiffness of the test substructure, the stability limit is reduced. With the increase of the number of sub steps, stability is stable. The limit limits have increased; (2) precision: (real time) GC-OS method has two order precision without substep method, using substep method as one order precision. (real time) GC-Chang method and GC-CR method are first order accuracy regardless of whether substep method is adopted or not; and the application of substep method can improve the calculation precision of both; (3) numerical damping ratio: in low frequency phase (real) The GC-OS method is not sensitive to the change of the stiffness and the number of substructures of the test substructure, and the numerical damping ratio of the high frequency phase increases with the increase of the stiffness of the test substructure. (real time) the numerical damping ratio of the GC-Chang method increases with the increase of the stiffness of the test substructure, and decreases the stiffness of the test substructure with the increase of the number of the substructures with the increase of the number of sub steps and the.GC-CR method. The substep method is most sensitive, with the increase of the stiffness of the test substructure or the reduction of the numerical damping ratio of the substep method; (4) the frequency distortion: the frequency error of the coupling integration method increases with the sampling frequency. (real time) the GC-OS algorithm is basically unaffected by the experimental substructure stiffness and the number of substeps. (real time) GC-Chang in the test When the stiffness of the substructure is large, the frequency error will be larger, but it is sensitive to the change of the stiffness of the test substructure without the influence of the number of substructures. In the high frequency phase, the frequency error of the structure stiffness increases with the increase of the structure stiffness of the test substructure; the displacement related substructure coupling fraction based on the Bouc-Wen hysteresis model is carried out. In the value simulation, the performance of the three algorithms, GC-OS method, GC-Chang method and GC-CR method, shows little difference in performance, but the substep method can make the three calculation results better. In the numerical simulation of the coupling integral of the velocity dependent substructure with linear and nonlinear viscous dampers, the GC-CR algorithm is relative when the substep method is not used. The real time GC-OS method and the real-time GC-Chang method will introduce the larger numerical damping. With the attenuation of the response amplitude, the attenuation of the amplitude is disappearing after the application of the substep method. The three algorithms are similar in calculation accuracy. It can improve the stability and accuracy of the GC-Chang method and GC-CR method.

【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TU352.1

【参考文献】