【摘要】：非線性單元的存在給結(jié)構(gòu)動(dòng)響應(yīng)的計(jì)算及試驗(yàn)辨識(shí)帶來(lái)巨大的挑戰(zhàn)。本文研究的對(duì)象為工程中廣泛存在的局部非線性結(jié)構(gòu),即結(jié)構(gòu)具有整體自由度較多但非線性單元的個(gè)數(shù)遠(yuǎn)小于整體自由度數(shù)量的特點(diǎn)。雖然只包含若干非線性單元,然而結(jié)構(gòu)的整體動(dòng)力學(xué)特性卻表現(xiàn)出非線性,這就需要同時(shí)求解大規(guī)模非線性微分方程組才能獲得結(jié)構(gòu)的響應(yīng)。本文以局部非線性結(jié)構(gòu)的動(dòng)力學(xué)計(jì)算和試驗(yàn)辨識(shí)問(wèn)題為研究對(duì)象,重點(diǎn)探討提高計(jì)算效率的降階算法、試驗(yàn)過(guò)程的辨識(shí)方法和非線性單元定位過(guò)程中的基本理論與方法。研究了局部非線性結(jié)構(gòu)的頻域響應(yīng)計(jì)算過(guò)程,提出了一種基于相對(duì)坐標(biāo)的降階方法。該方法首先通過(guò)將物理坐標(biāo)描述的動(dòng)力學(xué)方程變換到結(jié)構(gòu)線性部分的模態(tài)坐標(biāo)下進(jìn)行截?cái)?然后通過(guò)坐標(biāo)變換又進(jìn)一步降階到僅與非線性單元相關(guān)的相對(duì)坐標(biāo)上進(jìn)行求解。整個(gè)降階過(guò)程不僅避免了對(duì)結(jié)構(gòu)動(dòng)剛度矩陣直接求逆,而且還在很大程度上減少了需要求解的非線性代數(shù)方程的個(gè)數(shù)。此后,通過(guò)三個(gè)數(shù)值算例與文獻(xiàn)中的其它方法進(jìn)行比較,驗(yàn)證了該降階方法的正確性與可行性,并以柔性基礎(chǔ)對(duì)非線性隔振器的影響分析為例展示了其工程應(yīng)用。研究了單自由度非線性結(jié)構(gòu)的試驗(yàn)辨識(shí)過(guò)程,提出了一種利用頻域試驗(yàn)數(shù)據(jù)對(duì)單自由度非線性結(jié)構(gòu)進(jìn)行辨識(shí)的等效動(dòng)剛度圖法,該方法不以預(yù)先假設(shè)非線性單元的類型為前提,是一種非參數(shù)型方法。隨后,利用四組包含典型非線性類型的數(shù)值算例驗(yàn)證了該辨識(shí)方法的可行性,探討了不同基函數(shù)的選取對(duì)辨識(shí)過(guò)程和辨識(shí)結(jié)果的影響。在此基礎(chǔ)上,將其應(yīng)用到實(shí)際非線性阻尼器單機(jī)的地面試驗(yàn)過(guò)程中,利用頻域試驗(yàn)數(shù)據(jù)對(duì)阻尼器的模型和參數(shù)進(jìn)行辨識(shí)。結(jié)果表明,該方法不僅能較好的擬合參與辨識(shí)的試驗(yàn)結(jié)果,并且可以預(yù)測(cè)其它激勵(lì)幅值下未參與辨識(shí)的頻域響應(yīng)。探討了多自由度結(jié)構(gòu)中非線性單元的定位過(guò)程,提出了一種不以預(yù)先假設(shè)非線性單元類型為前提、僅利用頻域試驗(yàn)數(shù)據(jù)定位不可測(cè)非線性單元的方法。該方法通過(guò)引入模型降階的思路首先將非線性單元引起的非線性力向量通過(guò)降階的方式投影到可測(cè)自由度上,稱作降階偽力。通過(guò)比較各自由度上降階偽力的大小和相位性質(zhì)來(lái)得到更多的信息并最終還原得到非線性力向量,以定位非線性單元。依據(jù)一個(gè)20個(gè)自由度的質(zhì)量-彈簧模型,只考慮其奇數(shù)自由度可測(cè)的情況,探討了該定位方法的效果,同時(shí)分析了建模誤差和測(cè)量噪聲對(duì)定位過(guò)程的影響。結(jié)果表明,該定位方法能同時(shí)定位多個(gè)非線性單元,且定位的過(guò)程對(duì)建模誤差和測(cè)量噪聲不敏感。在此基礎(chǔ)上,利用具有非線性連接的固支梁試驗(yàn)對(duì)定位過(guò)程進(jìn)行分析,展示了利用真實(shí)的試驗(yàn)結(jié)構(gòu)測(cè)試數(shù)據(jù)定位不可測(cè)非線性單元的過(guò)程,并且與其它方法進(jìn)行比較,驗(yàn)證了該方法的可行性與正確性。
[Abstract]:The existence of nonlinear elements brings great challenges to the calculation of dynamic response and experimental identification of structures. The object of this paper is the local nonlinear structure, which is widely existed in engineering, that is, the structure has the characteristics that the total degree of freedom is more, but the number of nonlinear elements is far less than the number of global degrees of freedom. Although there are only a number of nonlinear elements, the global dynamic characteristics of the structure are nonlinear, which requires solving the large-scale nonlinear differential equations simultaneously in order to obtain the response of the structure. In this paper, the dynamic calculation and experimental identification of local nonlinear structures are studied, and the order reduction algorithm, the identification method of experimental process and the basic theory and method of nonlinear element location are discussed. In this paper, the frequency domain response of local nonlinear structures is studied, and an order reduction method based on relative coordinates is proposed. The method is firstly truncated by transforming the dynamic equations described by physical coordinates into the modal coordinates of the linear part of the structure, and then further reducing the order to the relative coordinates related to nonlinear elements by coordinate transformation. The whole order reduction process not only avoids the direct inverse of the dynamic stiffness matrix of the structure, but also reduces to a great extent the number of nonlinear algebraic equations that need to be solved. Then, by comparing three numerical examples with other methods in literature, the correctness and feasibility of the method are verified. The analysis of the influence of flexible foundation on nonlinear vibration isolator is taken as an example to demonstrate its engineering application. In this paper, the experimental identification process of nonlinear structures with single degree of freedom is studied, and an equivalent dynamic stiffness graph method is proposed to identify nonlinear structures with single degree of freedom using frequency domain test data. The method does not presuppose the type of nonlinear elements. It is a nonparametric method. Then, the feasibility of the method is verified by four numerical examples with typical nonlinear types, and the influence of the selection of different basis functions on the identification process and the identification results is discussed. On this basis, the model and parameters of the damper are identified by frequency domain test data. The results show that the proposed method can not only fit the experimental results well, but also predict the frequency domain responses of other excitation amplitudes that are not involved in the identification. This paper discusses the localization process of nonlinear elements in multi-degree-of-freedom structures, and proposes a method for locating undetectable nonlinear elements only using experimental data in frequency domain without presupposing the type of nonlinear elements. By introducing the idea of model reduction, the nonlinear force vector caused by nonlinear element is projected to the measurable degree of freedom in the way of order reduction, which is called reduced pseudo force. By comparing the magnitude and phase properties of the reduced pseudo-force on each degree of freedom, more information is obtained and the nonlinear force vector is finally reduced to locate the nonlinear element. Based on a mass-spring model with 20 degrees of freedom, the effect of the method is discussed, and the influence of modeling error and measurement noise on the positioning process is analyzed. The results show that the method can locate many nonlinear elements simultaneously and the positioning process is not sensitive to modeling errors and measurement noise. On this basis, the positioning process of fixed beam with nonlinear connection is analyzed, and the process of locating undetectable nonlinear elements with real test data is demonstrated, and compared with other methods. The feasibility and correctness of the method are verified.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O342

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