有限元动力学宽频带计算与连接结构实验建模方法研究
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摘要
为满足航天器结构对结构动力学计算越来越高的精度和计算频率范围要求，本文开展了拓宽结构有限元分析频率范围和连接结构实验建模方法的研究。
限制上限分析频率的主要原因之一是有限元模型的规模超过了计算机的处理能力，而上限分析频率决定了分析的频带宽度。为在保证计算精度的前提下降低模型规模，首先提出了一种具有r阶修正精度的自由界面子结构模态综合法，通过增加修正阶次，可以将足够多的高阶截断模态的影响包含在计算过程中，保证了计算精度。随后，将界面协调条件也推广到r阶，构造了关于广义界面力坐标和广义模态坐标的方程，将高阶截断模态的影响也写为广义模态坐标的形式，从而在消除高阶附着模态之间线性相关问题的同时，使模态降阶后整体结构运动方程中仅包含广义模态坐标，方程的规模不会随修正阶次的上升而上升，提高了模态分析的计算效率。为改善计算效率和计算精度之间的平衡，同时还提出了一种确定修正阶次r的自适应算法。最后对传统的模态截止准则进行了修正，提高了宽频范围内频率响应的计算效率。
对“点连接”结构提出了一种基于频响函数直接识别连接结构动刚度和频响矩阵的“无模型”实验建模方法。为克服实验测量噪声导致的“相对欠传感器”问题，首先建立了四条基本方程，接着以其为依据，提出了一种估计未测自由度频响函数的方法，然后，通过同时将所有估计和实验测试得到的频响信息都纳入到由四条基本方程导出的统一识别方程中，引入了尽可能多的频响信息，达到了抑制实验测试噪声影响并克服其导致的“相对欠传感器”问题的目的。数值和实验算例的计算结果表明，本文提出算法的计算精度显著优于同类算法。
对“线连接”和“面连接”这两类“绝对欠传感器”的连接结构提出了一种“无模型”间接实验建模方法，即首先估计未测自由度运动量信息和界面力，然后由此二者直接构造连接结构单元刚度阵、阻尼阵和质量阵。采用这一方法，首先实现了对“线连接”结构的实验建模，然后对“面连接”结构提出了“虚结构”+“虚连接单元”的等效建模方法，以克服“面连接”结构尺寸大造成的直接构造刚度阵、阻力阵和质量阵的困难。与现行的各种有模型方法相比，即预先构造参数化非线性模型然后识别模型参数的方法，本文提出方法的识别精度不依赖于预先构造的模型准确程度，可以避免识别参数过程中的大规模自由度寻优问题，有利于保证计算精度和计算效率。实验算例的计算结果验证了本文提出的方法。
For satisfying ever raising demands on the structural dynamic computationaccuracy and the upper analysis frequency of spacecraft structures，methods forextending Finite Element Analysis (FEA) to the broadband frequency range andimproving the accuracy of conection structure modeling through experiments areinvestigated in this dissertation.
One major difficulty in carrying out broadband vibration analysis for spacecraftstructure with conventional FEA is caused by the sharp increase in the number ofDegrees of Freedoms (DOFs). For avoiding this sharp increase in the number of DOFswith rational accuracy, an rthorder free interface modal synthesis method is proposed atfirst. With up to rthorder Residual Attachments Modes (RAMs) retained in thecomputation, sufficient influences of higher-order truncated modes can be included inthe computation to ensure the accuracy. Then a set of higher order interfacecompatibility conditions is introduced into computation to eliminate the lineardependence of the retained RAMs for ensuring computation accuracy and to deriveformula of complete structure only in terms of generalized modal coordinates forensuring computation efficiency. To reach a balance between the computation accuracyand the efficiency, a self-adapt algorithm for determining the exact value of r is alsosuggested. Finally, for broadband frequency response analyses, a modified modalcut-off criterion is proposed to reduce the number of the eigenpairs retained in thecomputation and hence improve the computation efficiency.
To overcome the relative insufficient sensor difficulty caused by experimentalmeasurement noise, a non-model method for identifying the dynamic properties of pointtype connection structure with partially measured Frequency Response Functions (FRFs)is proposed. Four basic formulas are derived first and a method for estimatingunmeasured FRFs is developed as the second step of the identification procedure. Thento suppress the influence of measurement noise for overcome the relative insufficientsonsor difficulty, the four basic formulas are integrated together to form a united formformula for utilizing all available data, i.e. all measured and estimated FRFs. With thisapproach, the relative insufficient sonser difficulty can be overcomed and thus the identification accuracy can be improved significantly compared to exisiting methods. Anumerical example and an experimental example are provided to describe theidentification procedure and to show the effectiveness of the proposed method.
For identifying dynamic properties of line type connection and area typeconnection structure, which usually encounters absolute insufficient sensor difficulty, anon-model method is proposed. The strategy of the method is to estimate the motioninformation, i.e. acceleration, velocity and displacement, of unmeasured DOFs andjunction forces firstly, and then connection stiffness matrix, damp matrix and massmatrix are constructed with these estimated motion information and junction forces.With this strategy, line type connection structure can be modeled; however, modelingarea type connection still faces challenge due to the dimension of the connectionstructure is too large to directly construct stiffness matrix, damp matrix and mass matrix.Thus an equal modelling method is developed to model such kind of connection withVirtual Structure (VS) and Virtual Connection Element (VCE). Compared to variouscurrent modeling methods with predefined or presumed connection models, theidentification accuracy of the proposed method does not depends on the accuracy of thepredefined or presumed models, and large-scale optimization procedure can also beavoided. An experimental example is provided to describe the identification procedureand show the effectiveness of the proposed method.
限制上限分析频率的主要原因之一是有限元模型的规模超过了计算机的处理能力，而上限分析频率决定了分析的频带宽度。为在保证计算精度的前提下降低模型规模，首先提出了一种具有r阶修正精度的自由界面子结构模态综合法，通过增加修正阶次，可以将足够多的高阶截断模态的影响包含在计算过程中，保证了计算精度。随后，将界面协调条件也推广到r阶，构造了关于广义界面力坐标和广义模态坐标的方程，将高阶截断模态的影响也写为广义模态坐标的形式，从而在消除高阶附着模态之间线性相关问题的同时，使模态降阶后整体结构运动方程中仅包含广义模态坐标，方程的规模不会随修正阶次的上升而上升，提高了模态分析的计算效率。为改善计算效率和计算精度之间的平衡，同时还提出了一种确定修正阶次r的自适应算法。最后对传统的模态截止准则进行了修正，提高了宽频范围内频率响应的计算效率。
对“点连接”结构提出了一种基于频响函数直接识别连接结构动刚度和频响矩阵的“无模型”实验建模方法。为克服实验测量噪声导致的“相对欠传感器”问题，首先建立了四条基本方程，接着以其为依据，提出了一种估计未测自由度频响函数的方法，然后，通过同时将所有估计和实验测试得到的频响信息都纳入到由四条基本方程导出的统一识别方程中，引入了尽可能多的频响信息，达到了抑制实验测试噪声影响并克服其导致的“相对欠传感器”问题的目的。数值和实验算例的计算结果表明，本文提出算法的计算精度显著优于同类算法。
对“线连接”和“面连接”这两类“绝对欠传感器”的连接结构提出了一种“无模型”间接实验建模方法，即首先估计未测自由度运动量信息和界面力，然后由此二者直接构造连接结构单元刚度阵、阻尼阵和质量阵。采用这一方法，首先实现了对“线连接”结构的实验建模，然后对“面连接”结构提出了“虚结构”+“虚连接单元”的等效建模方法，以克服“面连接”结构尺寸大造成的直接构造刚度阵、阻力阵和质量阵的困难。与现行的各种有模型方法相比，即预先构造参数化非线性模型然后识别模型参数的方法，本文提出方法的识别精度不依赖于预先构造的模型准确程度，可以避免识别参数过程中的大规模自由度寻优问题，有利于保证计算精度和计算效率。实验算例的计算结果验证了本文提出的方法。
For satisfying ever raising demands on the structural dynamic computationaccuracy and the upper analysis frequency of spacecraft structures，methods forextending Finite Element Analysis (FEA) to the broadband frequency range andimproving the accuracy of conection structure modeling through experiments areinvestigated in this dissertation.
One major difficulty in carrying out broadband vibration analysis for spacecraftstructure with conventional FEA is caused by the sharp increase in the number ofDegrees of Freedoms (DOFs). For avoiding this sharp increase in the number of DOFswith rational accuracy, an rthorder free interface modal synthesis method is proposed atfirst. With up to rthorder Residual Attachments Modes (RAMs) retained in thecomputation, sufficient influences of higher-order truncated modes can be included inthe computation to ensure the accuracy. Then a set of higher order interfacecompatibility conditions is introduced into computation to eliminate the lineardependence of the retained RAMs for ensuring computation accuracy and to deriveformula of complete structure only in terms of generalized modal coordinates forensuring computation efficiency. To reach a balance between the computation accuracyand the efficiency, a self-adapt algorithm for determining the exact value of r is alsosuggested. Finally, for broadband frequency response analyses, a modified modalcut-off criterion is proposed to reduce the number of the eigenpairs retained in thecomputation and hence improve the computation efficiency.
To overcome the relative insufficient sensor difficulty caused by experimentalmeasurement noise, a non-model method for identifying the dynamic properties of pointtype connection structure with partially measured Frequency Response Functions (FRFs)is proposed. Four basic formulas are derived first and a method for estimatingunmeasured FRFs is developed as the second step of the identification procedure. Thento suppress the influence of measurement noise for overcome the relative insufficientsonsor difficulty, the four basic formulas are integrated together to form a united formformula for utilizing all available data, i.e. all measured and estimated FRFs. With thisapproach, the relative insufficient sonser difficulty can be overcomed and thus the identification accuracy can be improved significantly compared to exisiting methods. Anumerical example and an experimental example are provided to describe theidentification procedure and to show the effectiveness of the proposed method.
For identifying dynamic properties of line type connection and area typeconnection structure, which usually encounters absolute insufficient sensor difficulty, anon-model method is proposed. The strategy of the method is to estimate the motioninformation, i.e. acceleration, velocity and displacement, of unmeasured DOFs andjunction forces firstly, and then connection stiffness matrix, damp matrix and massmatrix are constructed with these estimated motion information and junction forces.With this strategy, line type connection structure can be modeled; however, modelingarea type connection still faces challenge due to the dimension of the connectionstructure is too large to directly construct stiffness matrix, damp matrix and mass matrix.Thus an equal modelling method is developed to model such kind of connection withVirtual Structure (VS) and Virtual Connection Element (VCE). Compared to variouscurrent modeling methods with predefined or presumed connection models, theidentification accuracy of the proposed method does not depends on the accuracy of thepredefined or presumed models, and large-scale optimization procedure can also beavoided. An experimental example is provided to describe the identification procedureand show the effectiveness of the proposed method.
引文
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