混合界面直接分支模态综合法

在直接分支模态综合法(本质上属自由界面模态综合法)的基础上,提出并深入研究了混合界面直接分支模态综合法。混合界面法将复杂庞大的结构取做主体部件,而将与此主体部件相连的其余部分视为分支部件。对主体部件采用自由界面,分支部件则采用固定界面。各子结构之间完全独立计算,并且通过计入主、从子结构的剩余模态矩阵的办法来补偿所舍去的高阶模态分量,保证了计算精度。本方法从工程应用的实际出发,通过模拟航空发动机机匣管路系统的数值算例,验证了混合界面法的正确性。     

具有连接区的混合子结构模态综合法

本文提出具有连接区的间接对接的混合界面子结构模态综合法，讨论了位移协调和力与位移双协调两种对接模式。     

子结构Ritz向量综合法

讨论了在动态子结构法中应用静态Ｒｉｔｚ向量替代模态向量时所应考虑的基本问题，即如何合理地定义荷载空间分布向量｛ｆ（ｓ）｝，以避免在子结构中出现低阶模态不连续分布的情况。文中给出了在自由子结构和约束子结构内进行Ｒｉｔｚ变换的一般形式及修正公式。算例表明：应用子结构Ｒｉｔｚ向量综合技术能有效地提高线性结构模态分析的计算效率     

模态分析与动态子结构方法新进展

综述在模态分析与动态子结构方法研究的一些最新进展.首先回顾经典的位移展开定理和模态叠加原理.为了加速经典方法的收敛速度、提高计算效率, 进一步介绍两个新的结构位移展开定理(采用固定界面模态的位移展开新定理, 给出采用低阶固定界面模态的高精度位移展开式;采用混合模态的位移展开新定理, 给出采用低阶混合模态表示的高精度位移展开式)和相应的动力学新解法.相应上述3个位移展开定理, 介绍采用解析推导的方法构造出3类动态精确子结构方法, 各种子结构模态综合法实质上都是它们的某种近似与变化形式, 从而形成系统的动态子结构分析技术.上述介绍的模态分析与动态子结构方法新进展与经典模态分析技术一起形成结构动力学分析技术的系统理论.      

碰撞激发弹塑性波传播的动态子结构方法

通过建立弹塑性碰撞动态子结构模型, 推导了模态坐标下的控制方程,提出了模拟柔性结构碰撞激发弹塑性波传播的动态子结构方法, 并对其中的主模态的存在性和主模态截断的收敛性进行了证明. 通过对柔性杆纵向碰撞和柔性梁横向碰撞两个算例的计算, 并将计算结果与理论解和三维动力有限方法计算结果进行了对比, 验证了该方法的数值收敛性和计算碰撞弹塑性波传播的有效性.      

航天器与运载火箭耦合分析相关技术研究进展

本文以载荷分析为主要内容, 概述航天飞行器结构动力学研究的一些进展. 首先介绍航箭(航天器/运载火箭简称为航箭) 耦合系统载荷分析基本思想. 然后介绍以下3 个方面的载荷分析方法: (1) 采用基础激励理论初始载荷分析的近似方法; (2) 考虑航箭耦合影响的航天器/运载耦合系统分支模态综合法. 导出采用约束模态质量界面加速度的航天器载荷计算方法; 当仅考虑静定约束特殊情况时, 退化的方程与Chen 采用有限元法导出的方程相同. 给出新航天器载荷瞬态分析技术, 即一个以前的航天器/运载耦合系统载荷结果可以用来获得相同运载火箭发射一个新航天器结构的必要的载荷信息. (3) 考虑航箭耦合影响的航天器/运载耦合系统模态综合法. 包括: 固定界面模态综合法, 以及航天器/运载耦合的界面综合动态响应计算新方法. 最后, 介绍验证载荷分析技术. 简要讨论验证技术的重要性, 提出了采用试验与理论相结合的结构动态试验仿真技术,该方法包括了一套修正数学模型的新技术, 称之为子结构试验建模综合技术. 该方法已应用于复杂的结构建模. 在进行CZ-2E 运载火箭实尺模态试验之前, 用建议的模态试验仿真技术给出CZ-2E 模态参数的预示结果, 并与随后获得的实际模态试验结果相比, 两个结果彼此之间高度一致. 这个结果证明了模态试验仿真技术已成功地预示了CZ-2E 运载火箭的模态参数, 验证了建议的模态试验仿真技术的可靠性. 讨论了振动台振动试验仿真技术. 介绍了振动台振动试验仿真的几个关键技术. 包括: 有限元模型修正技术, 40 t 振动台系统台面控制仿真方法和D 卫星振动台振动试验仿真.      

核反应堆主系统管道的动力特性研究

本文系统研究了核反应堆主系统管道在局部破裂工况下的动力特性及非线性动力响应。采用统一动力子结构方法建立复杂管系的动力计算模型,采用Lanczos法和Arnoldi法分别求解系统的实、复特征值问题,分析了流速大小对系统固有频率的影响,在给定破口处的流体排放力后,采用Lanczos基矢量与模态综合相结合的自由度减缩技术,兼用伪力法、摄动法等技巧,求解管道系统的非线性动力响应。计算表明,采用本文的理论方法所研制的软件对核安全设计审批具有实用价值。文中给出了主系统管道的若干算例。     

组合神经网络在结构损伤检测中的应用

子结构的动态响应变化与整体结构相比,对结构内部损伤反应更为敏感。组合神经网络可以克服单个神经网络功能的单一局限性,实现更加全面综合的仿真识别功能。本文首先运用双协调自由界面模态综合法对结构进行模态分析,获取各子结构及整体结构的模态信息。然后,通过组合BP神经网络将损伤子结构与整体结构的模态频率变化率组合起来进行结构损伤检测。该方法在改善网络训练性能的同时,提高了检测结果的准确性和可靠性。文章最后通过数值算例验证了该方法的可行性和有效性。     

输液螺旋管系振动的动力子结构分析

本文推导了反对称阻尼振动系统的动力约束子结构法，利用反对称阻尼性质避免了求解左特征向量，并在缩聚变换中增添速度约束模态以提高计算精度，加之充分利用管系的周期性，较大幅度地提高了输液螺旋管系振动分析的效率。     

汽车整车非线性动力计算

通过轿车副车架橡胶支承的动态特性试验和理论分析,实现橡胶支承迟滞特性的数学建模和参数识别。利用所建模型重构恢复力-位移迟滞回线,并与试验结果比较表明所建模型的正确性。介绍了具有线性和非线性连接子结构的自由界面模态综合法的基本原理,并采用该方法建立了考虑副车架橡胶支承迟滞特性的整车非线性动力学模型,用所建模型对汽车动力特性进行了数值仿真,并通过试验对仿真结果进行验证。     

Finite-Element Solution of Linear Nonstationary Dynamic Problems for Shell Structures

An analysis is made of the efficiency of applying a reduced basis of Lanczos vectors to the finite-element solution of nonstationary dynamic problems. The algorithm developed was implemented in a computer code, which is used here to perform the analysis. The numerical experiments demonstrate the rapid convergence and high efficiency of mixed reduced basis of vibration modes and Lanczos vectors in nonstationary dynamic problems for shell structures.     

大型结构特征值问题的Lanczos子结构并行算法

本文利用子结构和Lanczos方法,提出了大型结构固有频率与模态的并行解法。该方法在Lanczos方法的求解过程中,仅利用子结构刚度阵和质量阵并行进行凝聚,进而求得新的迭代矢量,最终求得三对角阵对应的特征值和特征向量。该算法在西安交通大学ELXSI-6400并行计算机上程序实现,计算结果表明能有效地节省计算时间和计算机的内存,为一种有效的大型工程结构动力问题的求解方法。     

有阻尼振动系统的自由界面子结构综合法

研究了阻尼振动系统的自由界面子结构综合法.为了在最终给出的系统综合方程中考虑剩余柔度矩阵的影响,本文利用质量矩阵、阻尼矩阵和结构保留模态矩阵构造了一种与保留模态矩阵加权正交的矩阵.在计算自由-自由结构的剩余柔度矩阵时,通过这种加权正交矩阵能够避免直接对子结构刚度矩阵的求逆运算.在此基础上提出了一种新的有阻尼振动系统的自由界面子结构综合法.算例分析表明,本文的方法具有很高的计算精度.     

Free vibration analyses by boundary element method using component mode synthesis

The boundary element method for dynamic analysis of two dimensional structures was developed by Nardini and Brebbia in 1983. Free vibration analysis of structures by BEM results in a generalized eigenproblem with coefficient matrices nonsymmetric and full. So, it costs a lot of CPU time to solve the eigenproblem. In order to reduce the cost the improved free interface coupling method has been adopted. By aid of lower eigenvectors and residual modes the degrees of freedom of substructure equaion of dynamic equilibrium can be reduced. By assembling the reduced substructure equations, the system of equations for the whole structure will be obtained. By using the traction and displacement compatibility conditions on the interface, the second transformation matrix has been developed for further reduction of system equations. The technique has been applied to some specific examples which give the evidence that the method is satisfactory and efficient.     

In-plane vibration analysis of plates in curvilinear domains by a differential quadrature hierarchical finite element method

Free in-plane vibration analysis of plates is carried out by a differential quadrature hierarchical finite element method (DQHFEM). The NURBS (Non-Uniform Rational B-Splines) patches of geometries were first transformed into differential quadrature hierarchical (DQH) patches, and then the elastic field was discretized by the same DQH basis. The DQHFEM solved the compatibility problem caused by different parametrization of neighbouring patches of isogeometric analysis using NURBS. And mesh refinement in DQHFEM does not propagate from patch to patch. The DQHFEM matrices also have the embedding property as the hierarchical finite element method (HFEM). In-plane vibration analyses of plates of several planforms showed that the DQHFEM is similar as the fixed interface mode synthesis method that can analyse a structure using a few nodes on the boundary of substructure elements and only several clamped modes inside each substructure element, but the DQHFEM does not need modal analysis and is of high accuracy. The accuracy and convergence of the DQHFEM were validated through comparison with exact and approximate results in literatures and computed by the authors.     

块Lanczos法在大跨屋盖风致响应中的应用

提出块Lanczos向量直接叠加法分析大跨屋盖结构的风致响应.将适用于单个初始荷载向量的Lanczos方法推广到由多个初始荷载向量线性组合的一般动力荷载情况.由于不仅Lanczos块内的向量之间相互正交,而且Lanczos块之间也相互正交,屋盖结构的运动方程变换为块三对角矩阵的带状形式.这个途径不仅便于有效地应用时间域逐步积分解法,而且便于应用频率域解法.对脉动风荷载作用下的屋盖结构,多个初始荷载向量可应用本征正交分解得到.它将风压场分解为主坐标与协方差模态的组合,主坐标仅依赖时间而协方差模态仅依赖空间位置.根据圆拱顶屋盖模型风洞试验得到的风荷载,采用块Lanczos法、一般的Lanczos法以及传统的模态叠加法计算了屋盖竖向位移响应.对块Lanczos法的精度及效率作了讨论.     

Parametric aeroelastic modeling based on component modal synthesis and stability analysis for horizontally folding wing with hinge joints

To investigate the aeroelastic stability of a folding wing effectively, a parametric aeroelastic analysis approach is proposed. First, the fixed interface component modal synthesis is used to derive the structural dynamic equation for a folding wing, in which the elastic connection is considered. The unsteady aerodynamic model is established by the doublet lattice method (DLM), and the aeroelastic model is achieved from integration of the DLM with the component modal analysis. The generalized aerodynamic influence coefficient matrix is established by modes kept and constraint modes of each component. The aeroelastic stability of a folding wing is investigated based on the Gram matrix in control theory. The effectiveness of the proposed method is verified via comparison with traditional flutter eigenvalue analysis for both extended and folded configurations. The proposed method identifies coupled modes and improves computational efficiency when compared to classical aeroelastic stability analysis methods, such as the p–k method.     

Hybrid (numerical-experimental) modeling of complex structures with linear and nonlinear components

The present work investigates the performance of two systematic methodologies leading to hybrid modeling of complex mechanical systems. This is done by applying numerical methods in determining the equations of motion of some of the substructures of large order mechanical systems, while the dynamic characteristics of the remaining components are determined through the application of appropriate experimental procedures. In their simplest version, the models examined are assumed to possess linear characteristics. For such systems, it is possible to apply several hybrid methodologies. Here, the first of the methods selected is performed in the frequency domain, while the second method has its roots and foundation in time domain analysis. Originally, the accuracy and effectiveness of these methodologies is illustrated by numerical results obtained for two complex mechanical models, where the equations of motion of each substructure are first set up by applying the finite element method. Then, the equations of motion of the complete system are derived and their dimension is reduced substantially, so that the new model is sufficiently accurate up to a prespecified level of forcing frequencies. The formulation is developed in a general way, so that application of other methods, including experimental techniques, is equally valid. This is actually performed in the final part of this study, where experimental results are employed in conjunction with numerical results in order to predict the dynamic response of a mechanical structure possessing a linear substructure with high modal density, supported on four substructures with strongly nonlinear characteristics.     

杂交元本征应力模式和应力子空间的性质研究

详细讨论了有限元本征应力模式和应力子空间的性质，并着重讨论和进一步完善了与杂交应力有限元应力子空间有关的一些定理，为提出新方法提供了理论基础，主要包括：（1）证明了杂交元特征值不大于对应位移元的特征值；（2）证明了矩阵H非奇异的充分必要条件是假设应力模式线性无关；（3）证明了杂交元所对应位移元的本征应力模式形成的杂交元与该位移元相同；（4）证明了等价假设应力模式形成相同的杂交元；（5）证明了确定杂交元本征应力模式的充分必要条件是其范数平方等于所形成杂交元的变形模态特征值；（6）证明了杂交元假设应力模式与变形模态的能量一一对应的充分必要条件是假设应力模式彼此正交且与所对应位移元的本征应力模式除了一一对应者之外都正交。     

An iterative approach for nonproportionally damped systems

Modal analysis of nonproportionally damped linear dynamic systems is considered. Dynamic response of such systems can be expressed by a modal series in terms of complex modes. Normally state-space based methods or approximate perturbation methods are necessary for the computation of complex modes. In this paper, an iterative method to calculate complex modes from classical normal modes for general linear systems is proposed. A simple numerical algorithm is developed to implement the iterative method. The new method is illustrated using a numerical example.