局部非线性结构的动力学计算与试验辨识研究

发布时间：2018-08-06 13:16

【摘要】：非线性单元的存在给结构动响应的计算及试验辨识带来巨大的挑战。本文研究的对象为工程中广泛存在的局部非线性结构,即结构具有整体自由度较多但非线性单元的个数远小于整体自由度数量的特点。虽然只包含若干非线性单元,然而结构的整体动力学特性却表现出非线性,这就需要同时求解大规模非线性微分方程组才能获得结构的响应。本文以局部非线性结构的动力学计算和试验辨识问题为研究对象,重点探讨提高计算效率的降阶算法、试验过程的辨识方法和非线性单元定位过程中的基本理论与方法。研究了局部非线性结构的频域响应计算过程,提出了一种基于相对坐标的降阶方法。该方法首先通过将物理坐标描述的动力学方程变换到结构线性部分的模态坐标下进行截断,然后通过坐标变换又进一步降阶到仅与非线性单元相关的相对坐标上进行求解。整个降阶过程不仅避免了对结构动刚度矩阵直接求逆,而且还在很大程度上减少了需要求解的非线性代数方程的个数。此后,通过三个数值算例与文献中的其它方法进行比较,验证了该降阶方法的正确性与可行性,并以柔性基础对非线性隔振器的影响分析为例展示了其工程应用。研究了单自由度非线性结构的试验辨识过程,提出了一种利用频域试验数据对单自由度非线性结构进行辨识的等效动刚度图法,该方法不以预先假设非线性单元的类型为前提,是一种非参数型方法。随后,利用四组包含典型非线性类型的数值算例验证了该辨识方法的可行性,探讨了不同基函数的选取对辨识过程和辨识结果的影响。在此基础上,将其应用到实际非线性阻尼器单机的地面试验过程中,利用频域试验数据对阻尼器的模型和参数进行辨识。结果表明,该方法不仅能较好的拟合参与辨识的试验结果,并且可以预测其它激励幅值下未参与辨识的频域响应。探讨了多自由度结构中非线性单元的定位过程,提出了一种不以预先假设非线性单元类型为前提、仅利用频域试验数据定位不可测非线性单元的方法。该方法通过引入模型降阶的思路首先将非线性单元引起的非线性力向量通过降阶的方式投影到可测自由度上,称作降阶伪力。通过比较各自由度上降阶伪力的大小和相位性质来得到更多的信息并最终还原得到非线性力向量,以定位非线性单元。依据一个20个自由度的质量-弹簧模型,只考虑其奇数自由度可测的情况,探讨了该定位方法的效果,同时分析了建模误差和测量噪声对定位过程的影响。结果表明,该定位方法能同时定位多个非线性单元,且定位的过程对建模误差和测量噪声不敏感。在此基础上,利用具有非线性连接的固支梁试验对定位过程进行分析,展示了利用真实的试验结构测试数据定位不可测非线性单元的过程,并且与其它方法进行比较,验证了该方法的可行性与正确性。
[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.
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O342

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