Merge remote-tracking branch 'origin/master'

多体+耦合求解器/参考文献/Craig-Coupling of substructures for dynamic an/auto/Craig-Coupling of substructures for dynamic an.md

@@ -199,58 +199,60 @@ $$
 $$  
 
 Either the set of interface constraint modes $\Psi_{c}$ defined by Eq. (13), or the combined set $\left[\Psi_{r}\ \Psi_{e}\right]$ defined by Eqs. (16) and (19), spans the static response of the substructure to interface loading and allows for arbitrary interface displacements $\pmb{u}_{b}$ . Along with the interface displacement, there is accompanying displacement of the interior of the substructure, as determined by Eqs. (13), (16), and (19). Additional interior fexibility can be incorporated by including fixed-interface normal modes, fixed-interface Krylov vectors, or other fixed-interface assumed modes in the component mode matrix $\Psi[3,\,5,\,23]$  
+无论是由公式(13)定义的界面约束模态集合 $\Psi_{c}$，还是由公式(16)和(19)定义的组合集合 $\left[\Psi_{r}\ \Psi_{e}\right]$，都能覆盖次结构的静态响应，并允许任意界面位移 $\pmb{u}_{b}$。 伴随界面位移的是次结构内部的位移，其由公式(13)、(16)和(19)确定。 还可以通过在模态矩阵 $\Psi[3,\,5,\,23]$ 中包含固定界面简正模态、固定界面 Krylov 向量或其他固定界面假定模态来引入额外的内部柔度。
 
 ## 2.3. Attachment Modes  
 
 An attachment mode is defined as the component displacement vector due to a single unit force applied at one of the coordinates of a given set $\pmb{A}$ Consequently, attachment modes are just columns of the associated fexibility matrix. Attachment modes were defined by Bamford[4], and they get their name from their usefulness in representating the deformation of a structure to loading (e.g., an external force, an attached mass, or an attached fexible component) at the point where the attachment mode's unit force is applied. In this paper we are interested in defining attachment modes to represent the response of a component to forces at its interface with adjoining components. One diffculty encountered in using attachment modes is that many components have one to six rigid-body degrees of freedom, making it impossible to apply directly to the unrestrained component the necessary unit forces in order to compute the resulting attachment mode shapes. However, one option in this case is to select a set $\mathcal{R}$ of boundary rigid-body degrees of freedom, (mathematically) restrain the component at these DOFs, and then form cantilever attachment modes by applying unit loads at the redundant boundary coordinates, that is, for $\boldsymbol{A}=\boldsymbol{\mathcal{E}}$ .Then,  
 
+一种**附着模态被定义为由于在给定集合 $\pmb{A}$ 的一个坐标上施加一个单位力所引起的位移矢量**。因此，附着模态实际上是相关柔度矩阵的列。Bamford[4] 定义了附着模态，它们之所以得名，是因为它们在表示结构在载荷作用下的变形（例如，一个外部力、一个附加质量或一个附加柔性部件）时非常有用，变形发生在附着模态单位力作用点。在本文中，我们感兴趣的是定义附着模态来表示组件与其相邻组件在界面处对力的响应。使用附着模态时遇到的一个困难是，许多组件具有一个到六个刚体自由度，这使得无法直接将必要的单位力施加到未约束的组件上，以计算由此产生的附着模态形状。然而，在这种情况下，一种选择是选择一组边界刚体自由度 $\mathcal{R}$，（数学上）约束组件在这些自由度处，然后通过在冗余边界坐标上施加单位载荷来形成悬臂附着模态，即对于 $\boldsymbol{A}=\boldsymbol{\mathcal{E}}$ 。然后，
 $$
 \left[\begin{array}{l l l}{K_{i i}}&{K_{i e}}&{K_{i r}}\\ {K_{e i}}&{K_{e e}}&{K_{e r}}\\ {K_{r i}}&{K_{r e}}&{K_{r r}}\end{array}\right]\left[\begin{array}{l}{\Psi_{i e}}\\ {\Psi_{e e}}\\ {0_{r e}}\end{array}\right]=\left[\begin{array}{l}{0_{i e}}\\ {I_{e e}}\\ {R_{r e}}\end{array}\right]
 $$  
 
 It can be seen that these attachment modes are just an expanded form of the columns of the righthand partition of the Hexibility matrix $\bar{G}_{c}$ of Eq. (17) with $A=\mathcal{E}$ . That is,  
-
+可以看出，这些附着模态不过是方程 (17) 中 $\bar{G}_{c}$ 右侧分区的列的扩展形式，其中 $A=\mathcal{E}$ 。也就是说，
 $$
 \boldsymbol{\Psi}_{\boldsymbol{s}\,\boldsymbol{N}_{c}}\equiv\left[\begin{array}{l}{\Psi_{i e}}\\ {\Psi_{e e}}\\ {0_{r e}}\end{array}\right]=\left[\begin{array}{l}{G_{i e}}\\ {G_{e e}}\\ {0_{r e}}\end{array}\right]
 $$  
 
 Two important topics that arise when freeinterface normal modes are to be employed to represent the fexible behavior of unrestrained components are inertia relief and residual fezibility, both of which were discussed by MacNeal[6] and Rubin[7]. Sections 2.4 and 2.5 treat these two topics, and the related forms of attachment modes are defined.  
-
+当需要利用自由界面简正模态来表示不受约束构件的柔性行为时，惯性释放和残余柔性是两个重要的议题，这些议题均由 MacNeal[6] 和 Rubin[7] 讨论过。第 2.4 节和 2.5 节将分别讨论这两个议题，并定义相关的附着模态。
 ## 2.4. Inertia-Relief Attachment Modes  
 
 When a component has rigid-body freedom, it is appropriate to employ inertia-relief attachment modes[6, 7, 11]. The term inertia relief refers to the process of applying to the component an equilibrated load system $\pmb{f}_{f}$ , which consists of the original force vector $\pmb{f}$ equilibrated by the rigid-body d'Alembert force vector $M\ddot{\boldsymbol{u}}_{r}$ , where $\pmb{u}_{r}$ is the rigid-body motion due to $\pmb{f}$ .Starting with Eq. (1), let the displacement vector be separated into rigid-body displacement and fexible-body displacement, that is, let  
-
+当一个构件具有刚体自由度时，采用惯性释放连接模态[6, 7, 11]是合适的。惯性释放指的是将一个平衡载荷系统 $\pmb{f}_{f}$ 应用到构件上，该载荷系统由原始力矢量 $\pmb{f}$ 与刚体达朗贝尔力矢量 $M\ddot{\boldsymbol{u}}_{r}$ 平衡而成，其中 $\pmb{u}_{r}$ 是由 $\pmb{f}$ 引起的刚体运动。从公式(1)开始，将位移矢量分解为刚体位移和柔体位移，即，设
 $$
 \pmb{u}=\pmb{u}_{r}+\pmb{u}_{f}=\Psi_{r}\pmb{p}_{r}+\Phi_{f}\pmb{p}_{f}
 $$  
 
-whcrc all of thc $N_{f}$ fexiblc-body modes are included in $\Phi_{f}$ . Then, the equations  
+where all of the $N_{f}$ fexible-body modes are included in $\Phi_{f}$ . Then, the equations  
 
 $$
 \Psi_{r}^{T}M\Phi_{f}=0\ ,\ \ \bar{M}_{r r}=\Psi_{r}^{T}M\Psi_{r}
 $$  
 
 are the appropriate orthogonality equation and the definition of the rigid-body modal mass matrix, respectively. (It is not assumed that the rigid-body modes are orthonormalized.） Since $K\Psi_{r}~\,=\,\,0$ Eqs. (1) and (22) can be combined to give  
-
+分别是适当的正交方程和刚体模态质量矩阵的定义。（未假设刚体模态是正交归一化的。）由于 $K\Psi_{r}~\,=\,\,0$，可以将方程 (1) 和 (22) 结合起来得到
 $$
 M\Phi_{f}\ddot{p}_{f}+K\Phi_{f}p_{f}=f-M\Psi_{r}\ddot{p}_{r}
 $$  
 
 When this equation is premultiplied by $\Psi_{r}^{T}$ and orthogonality is invoked, the result is the selfequilibrated force  
-
+当该方程被 $\Psi_{r}^{T}$ 前乘，并应用正交性时，结果是自平衡力。
 $$
 \pmb{f}_{f}=\pmb{f}-M\ddot{\pmb{u}}_{r}=P_{r}\pmb{f}
 $$  
 
 where $P_{r}$ is the inertia-relief projection matriz, de fined by  
+其中，$P_{r}$ 为惯性释放投影矩阵，定义如下：
 
 $$
 P_{r}=I-M\Psi_{r}\bar{M}_{r r}^{-1}\Psi_{r}^{T}
 $$  
 
-When any force vector is premultiplied by this inertia-relief projection matrix, the corresponding  
+When any force vector is premultiplied by this inertia-relief projection matrix, the corresponding force system is self-equilibrated. Also, from Eq. (26) it can easily be verified that $P_{r}^{T}$ is mass-orthogonal to the rigid-body modes, that is,  
-
+当任何力矢量被此惯性释放投影矩阵预乘时，对应的力系统会自平衡。 此外，从公式 (26) 可以很容易地验证，$P_{r}^{T}$ 与刚体模态正交，即，
-force system is self-equilibrated. Also, from Eq. (26) it can easily be verified that $P_{r}^{T}$ is mass-orthogonal to the rigid-body modes, that is,  
 
 $$
 \Psi_{r}{}^{T}M P_{r}^{T}=0
@@ -298,7 +300,9 @@ Figure 6: Elastic Flexibility Shapes
 The complete set of component normal modes $\Phi_{n}$ and the corresponding set of eigenvalues $\Lambda_{n n}$ are identified by the subscript $n$ , whether these are the $N_{i}$ fixed-interface modes, the $N_{f}$ free-free flexible (fex) modes, or some other form of component normal modes.  
 
 Let the (diagonal) modal mass matrix and modal stiffness matrix for modes $\Phi_{n}$ be  
+下标 $n$ 用于标识完整的组分正交模态集 $\Phi_{n}$ 及其对应的特征值集 $\Lambda_{n n}$，无论这些是 $N_{i}$ 个固定-固定界面模态，是 $N_{f}$ 个自由-自由柔性 (fex) 模态，还是其他形式的组分正交模态。
 
+设模态质量矩阵和模态刚度矩阵（均为对角矩阵）对于模态 $\Phi_{n}$ 为：
 $$
 {\bar{M}}=\Phi_{n}^{T}M\Phi_{n}\ ,\ \ {\bar{K}}=\Phi_{n}^{T}K\Phi_{n}
 $$  
@@ -313,11 +317,13 @@ Note that each column of the $j$ th mode's contribution to the elastic fexibilit
 
 $G$ is singular or not, from Eqs. (33b) and (34) it can be shown that  
 
+请注意，第 $j$ 个模态对弹性柔度矩阵的每一列都呈现出模态 $\phi_{j}$ 的形状。虽然弹性柔度矩阵 $G$ (如公式(34)) 和矩阵 $G_{f}$ (如公式(32)) 以及图6所示的矩阵，是采用不同的方式形成的，但它们在数值上是相同的。在本节中，我们将关注具有刚体自由度的分量，在这种情况下，$G$ 是奇异的，其秩为 $N_{f}$。无论弹性柔度矩阵 $G$ 是否为奇异，从公式(33b)和(34)可以看出，
 $$
 G^{T}K G=G
 $$  
 
 Since model reduction is one of the major objectives in CMS, the normal mode set is usually reduced to a smaller set of kept normal modes, denoted by $\Phi_{k}$ ，where $\Phi_{n}~\equiv~\left[\Phi_{k}~\Phi_{d}\right]$ .\*The deleted normal modes, $\Phi_{d}$ , are generally all of the modes above some specified cutof frequency. The portion of the fexibility matrix contributed by modes $\Phi_{d}$ is called the residual feribility matrir. It is given by  
+由于模型降阶是 CMS 中的一个主要目标，简正模态集通常会被降阶到较小的保留简正模态集合，记为 $\Phi_{k}$ ，其中 $\Phi_{n}~\equiv~\left[\Phi_{k}~\Phi_{d}\right]$ 。* 被删除的简正模态，$\Phi_{d}$ ，通常是某个指定截止频率以上的全部模态。由 $\Phi_{d}$ 模态贡献的柔度矩阵部分被称为残余柔度矩阵。其表达式为：
 
 $$
 G_{d}=\Phi_{d}\bar{K}_{d d}^{-1}\Phi_{d}^{T}=G-\Phi_{k}\bar{K}_{k k}^{-1}\Phi_{k}^{T}
@@ -326,25 +332,28 @@ $$
 where $G$ is the total fexibility matrix. Since it is not usually feasible to compute or measure the $\Phi_{d}$ modes, Eq. (36) is useful only because Eq. (32) exists as an alternative to Eq. (34) for determining the elastic fexibility matrix $G$  
 
 The matrix $G_{d}$ will always be a singular matrix because of the modes deleted in Eq. (36). Also, because of the mass- and stiffness-orthogonality of the kept modes to the deleted modes,  
+其中，$G$ 为总挠度矩阵。由于通常难以计算或测量 $\Phi_{d}$ 模态，方程 (36) 仅因为方程 (32) 作为确定挠度矩阵 $G$ 的替代方案而存在才有用。
 
+由于方程 (36) 中删除的模态，矩阵 $G_{d}$ 始终是一个奇异矩阵。此外，由于保留模态与删除模态的正交性（关于质量和刚度），
 $$
 \Phi_{k}^{T}M G_{d}=0,\ \mathrm{and}\ \ \Phi_{k}^{T}K G_{d}=0
 $$  
 
 and because of the orthogonality between all rigidbody modes and all fexible-body modes,  
-
+并且由于所有刚体模态与所有柔体模态之间具有正交性，
 $$
 \Psi_{r}^{T}M G_{d}=0,\ \mathrm{and}\ \ \Psi_{r}^{T}K G_{d}=0
 $$  
 
 Residual-fleribility attachment modes maybe de fined for forces applied at the interface coordinates, that is, for $\boldsymbol{A}=\boldsymbol{B}$ , by the following equation:  
+残余挠性连接模态可针对作用于界面坐标的力进行定义，即对于 $\boldsymbol{A}=\boldsymbol{B}$ ，通过以下方程：
 
 $$
 \begin{array}{r c l}{{\Psi_{d}}}&{{\equiv}}&{{\left[\begin{array}{c}{{\Psi_{i b}}}\\ {{\Psi_{b b}}}\end{array}\right]=G_{d}F_{b}}}\\ {{}}&{{=}}&{{[G_{f}-\Phi_{k}\bar{K}_{k k}^{-1}\Phi_{k}^{T}]\left[\begin{array}{c}{{0_{i b}}}\\ {{I_{b b}}}\end{array}\right]}}\end{array}
 $$  
 
 Figure 7 shows the attachment mode shape for the component with a unit force at DOF7; the top figure includes all six flex modes, the middle figure is the contribution of two “kept" modes, and the bottom figure is the corresponding residual fexibility attachment mode shape. It is clear that the order of magnitude of the residual fexibility is smaller than that of the fexibility of the kept modes. Figure 8 shows the residual-Hexibility attachmentmode shapes $({\bf k}{=}2)$ for the component with unit forces at DOFs 7 and 5 (left and right ends). The top two figure are the attachment-mode shapes for the individual unit forces; the middle figure is the shape produces by symmetric loading by two unit forces, and the bottom figure is the corresponding residual-fexibility attachment-mode shape for antisymmetric loading. It can easily be seen that these residual-fexibility shapes are free of the first two (kept) normal-mode contributions.  
-
+图 7 显示了该部件在第 7 自由度（DOF7）受单位力作用时的附着模态振型；顶图包含全部六种挠曲模态，中间图显示了两个“保留”模态的贡献，底图是对应的残余挠曲附着模态振型。 可以清楚地看出，残余挠曲的量级小于保留模态的挠曲量级。 图 8 显示了该部件在第 7 和第 5 自由度（分别对应左右端）受单位力作用时的残余挠曲附着模态振型（${\bf k}{=}2$）。 顶两张图是单个单位力作用下的附着模态振型；中间图是两个单位力对称加载产生的振型，底图是对应于反对称加载的残余挠曲附着模态振型。 可以很容易地看出，这些残余挠曲振型不包含前两个（保留）简正模态的贡献。
 ![](88ff35243039fc2e46d94f50e1031720e313dca7bbafb0eba9b0054bc93ed7b5.jpg)  
 Figure 7: An Illustration of Residual Flexibility.  
 
@@ -352,22 +361,25 @@ Figure 7: An Illustration of Residual Flexibility.
 Figure 8: More Residual-Flexibility Shapes.  
 
 Incorporation of $\Psi_{d}$ into the component mode set ensures complete representation of static defection of the component due to forces applied at interface DOFs. In this sense, it is closely related to the mode-acceleration method for incorporating static completeness in dynamic-response computations[1, 7, 11]. Hintz has given an extensive discussion of the need for statically complete component mode sets in Ref. [25]. We will return to the topic of residual flexibility later in Section 4.2.  
+将 $\Psi_{d}$ 纳入模态集，可确保对由于界面自由度作用力引起的构件静态变形的完全表示。从这个意义上讲，它与用于在动态响应计算中实现静态完整性的模态加速法密切相关[1, 7, 11]。Hintz 在参考文献 [25] 中对使用静态完整的模态集的需求进行了详细讨论。我们将在第 4.2 节中再次回到残余柔性的主题。
+# 3. A Generalized Component Coupling Procedure for Undamped Structures 一种用于无阻尼结构的通用组件耦合程序
+
  
-# 3. A Generalized Component Coupling Procedure for Undamped Structures  
 
 In this section a generalized substructure coupling procedure that employs Lagrange multipliers to enforce  inter-component  displacement compatibility equations (and other constraint equations, if applicable) is presented. Let the system be composed of two components, labeled $_\alpha$ and $\beta$ , that have a common (generally redundant) interface. The physical displacements at the interface are constrained by the displacement compatibility equation  
-
+本节介绍一种通用的子结构耦合程序，该程序采用拉格朗日乘子来强制执行各组件位移相容方程（以及其他适用的约束方程）。假设系统由两个组件组成，分别标记为 $_\alpha$ 和 $\beta$，它们具有一个共同的（通常是冗余的）界面。该界面的物理位移受到位移相容方程的约束。
 $$
 \pmb{u}_{b}^{\alpha}=\pmb{u}_{b}^{\beta}
 $$  
 
 and the mutually reactive interface forces (i.e., not including external forces applied at the interface) are related by  
-
+并且相互作用的界面力（即不包括施加在界面上的外力）由以下关系关联：
 $$
 \hat{\pmb f}_{b}^{\alpha}+\hat{\pmb f}_{b}^{\beta}=\mathbf{0}
 $$  
 
 Constraint equations, such as Eq. (40) and any other constraint equations that are to be imposed (say $N_{C}$ equations in all), can be written in terms of the generalized coordinates $\pmb{p}$ and combined to form a matrix constraint equation of the form  
+约束方程，例如公式(40)以及任何其他需要施加的约束方程（总共设为 $N_{C}$ 个方程），可以表示为广义坐标 $\pmb{p}$ 的函数，并组合成如下形式的矩阵约束方程：
 
 $$
 C{\pmb p}={\bf0}

学术讲座-交流-面试/2025.7.7 李博面试.md

@@ -0,0 +1,14 @@
+
+
+南航 本硕博 
+米兰理工 双学位博士
+
+一直从事飞行器设计方向
+
+多体动力学传递矩阵法  transfer matrix
+
+
+使用什么工具 mbdyn？
+考虑柔性吗
+
+长柔叶片弯扭耦合 旋转 有什么想法

软件组工作讨论/2025.7.11 个人责任状讨论.md

@@ -0,0 +1,22 @@
+
+提交文稿是否是必须要写的
+开发者手册 理论手册 测试手册
+
+科研任务细化一下
+
+
+科研成果
+专利 改成 软件著作权 
+著作权，有没有互斥的问题，
+
+引才工作 参与面试
+
+手册 写0.几版
+
+steady calc 细化到哪块
+多体这块的开发 
+测试
+
+
+
+