本文選題：子結(jié)構(gòu)試驗(yàn) + 數(shù)值積分��； 參考：《重慶大學(xué)》2016年碩士論文

【摘要】：子結(jié)構(gòu)試驗(yàn)作為一種新興的結(jié)構(gòu)抗震試驗(yàn)方法自提出以來就得到快速發(fā)展。該方法把結(jié)構(gòu)分為兩部分:對(duì)相對(duì)重要或在動(dòng)力荷載下表現(xiàn)出明顯非線性或其他復(fù)雜物理特征的部分進(jìn)行加載,稱為試驗(yàn)子結(jié)構(gòu)(Physical Substructure,PS);而其余部分則用計(jì)算機(jī)進(jìn)行數(shù)值模擬,稱為數(shù)值子結(jié)構(gòu)(Numerical Substructure,NS)。采用子結(jié)構(gòu)實(shí)驗(yàn)方法能夠降低試驗(yàn)規(guī)模,有利于進(jìn)行大比例或足尺試驗(yàn),在真實(shí)模擬結(jié)構(gòu)動(dòng)力響應(yīng)的條件下又能夠節(jié)約大量試驗(yàn)費(fèi)用。子結(jié)構(gòu)試驗(yàn)是試驗(yàn)加載和數(shù)值計(jì)算的混合技術(shù),其中數(shù)值計(jì)算的效率和穩(wěn)定性是子結(jié)構(gòu)試驗(yàn)的關(guān)鍵問題之一。耦合積分方法作為一種高效的積分方法,已被用于擬動(dòng)力試驗(yàn)和多體動(dòng)力學(xué)等方面,在子結(jié)構(gòu)試驗(yàn)中也具有明顯的優(yōu)勢(shì)。本文主要利用數(shù)學(xué)軟件Mathematica編程針對(duì)子結(jié)構(gòu)耦合積分方法進(jìn)行系統(tǒng)的研究。在一種耦合積分方法(GC法)的基礎(chǔ)上,結(jié)合算子分解法(OS法)、Chang法以及CR法,經(jīng)過修改形成了幾種新的耦合積分方法,并對(duì)其從穩(wěn)定性、精度、數(shù)值阻尼比以及頻率誤差等數(shù)值特性方面進(jìn)行了大量的分析與驗(yàn)證。最后基于Bouc-Wen模型和粘滯阻尼器理論對(duì)各耦合積分方法進(jìn)行了數(shù)值模擬。分析結(jié)果表明耦合積分方法的穩(wěn)定性、精度、數(shù)值耗散、頻率失真率等數(shù)值特性除了受積分步長(zhǎng)影響外,還與結(jié)構(gòu)參數(shù)以及子步法直接相關(guān)。對(duì)于不同的參數(shù),不同的耦合積分方法表現(xiàn)出不同的數(shù)值特性,具體為以下幾個(gè)方面:(1)穩(wěn)定性:(實(shí)時(shí))GC-OS法在不同參數(shù)下均穩(wěn)定,(實(shí)時(shí))GC-Chang法和GC-CR法為條件穩(wěn)定,且隨著試驗(yàn)子結(jié)構(gòu)剛度的增大,穩(wěn)定界限降低。隨著子步數(shù)的增大,穩(wěn)定界限有所增大;(2)精度:(實(shí)時(shí))GC-OS法在不采用子步法時(shí)具有二階精度,采用子步法時(shí)為一階精度。(實(shí)時(shí))GC-Chang法和GC-CR法無論是否采用子步法,均為一階精度,同時(shí)子步法的應(yīng)用能夠提高兩者的計(jì)算精度;(3)數(shù)值阻尼比:在低頻階段(實(shí)時(shí))GC-OS法對(duì)試驗(yàn)子結(jié)構(gòu)剛度和子步數(shù)的變化不敏感,在高頻階段數(shù)值阻尼比隨試驗(yàn)子結(jié)構(gòu)剛度的增加而呈遞增趨勢(shì)。(實(shí)時(shí))GC-Chang法數(shù)值阻尼比隨著試驗(yàn)子結(jié)構(gòu)剛度的增加而增大,隨子步數(shù)的增大而降低。GC-CR法對(duì)試驗(yàn)子結(jié)構(gòu)剛度以及子步法的采用最為敏感,隨試驗(yàn)子結(jié)構(gòu)剛度的增大或子步法的采用其數(shù)值阻尼比降低;(4)頻率失真率:各耦合積分方法的頻率誤差均隨采樣頻率增大而增大。(實(shí)時(shí))GC-OS算法基本不受試驗(yàn)子結(jié)構(gòu)剛度和子步數(shù)的影響。(實(shí)時(shí))GC-Chang在試驗(yàn)子結(jié)構(gòu)剛度較大時(shí)會(huì)引起較大的頻率誤差,但不受子步數(shù)的影響。GC-CR對(duì)試驗(yàn)子結(jié)構(gòu)剛度的變化較為敏感,在高頻階段隨試驗(yàn)子結(jié)構(gòu)剛度的增大頻率誤差也呈現(xiàn)出增大的趨勢(shì);在進(jìn)行基于Bouc-Wen滯回模型的位移相關(guān)型子結(jié)構(gòu)耦合積分?jǐn)?shù)值模擬時(shí),GC-OS法、GC-Chang法以及GC-CR法三種算法表現(xiàn)出的性能相差不大,但采用子步法可以使得三者的計(jì)算結(jié)果吻合更好。在進(jìn)行含有線性和非線性粘滯阻尼器的速度相關(guān)型子結(jié)構(gòu)耦合積分?jǐn)?shù)值模擬時(shí),在不采用子步法時(shí),GC-CR算法相對(duì)實(shí)時(shí)GC-OS法和實(shí)時(shí)GC-Chang法會(huì)引入較大的數(shù)值阻尼,隨著計(jì)算的進(jìn)行會(huì)出現(xiàn)響應(yīng)幅值的衰減,在運(yùn)用子步法后幅值衰減現(xiàn)象消失,三種算法計(jì)算精度相近。分析表明文中各耦合積分方法均能夠較好地實(shí)現(xiàn)子結(jié)構(gòu)間的耦合,且子步法的運(yùn)用對(duì)于提高(實(shí)時(shí))GC-Chang法及GC-CR法的穩(wěn)定性和計(jì)算精度能夠起到較好的效果。
[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.

【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：TU352.1

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