vault backup: 2025-04-30 16:19:14

力学书籍/Kinematically nonlinear finite element model of a horizontal axis wind turbine/auto/Kinematically nonlinear finite element model of a horizontal axis wind turbine. Part 2.md

@@ -708,93 +708,194 @@ Shaft: Nodes are numbered from 1 to $m$.
 Blade: Nodes are numbered from 1 to ${n}$.
 	Blade node ${B1}$ is at the joint to the shaft, and common with shaft node ${Am}$.  
 
-The reference systems are right handed, rectangular coordinate systems (Cartesian). The axis indices are designated by the symbols $\pmb{x},\pmb{y}$ and $_z$ , or synonymously by 1, 2, and 3, respectively, throughout the thesis.  
+The reference systems are right handed, rectangular coordinate systems (Cartesian). The axis indices are designated by the symbols $\pmb{x},\pmb{y}$ and $\pmb{z}$ , or synonymously by 1, 2, and 3, respectively, throughout the thesis.  
 
 All the angles are defined relative to a coordinate axis, and are considered positive when a corresponding rotation of a right hand screw will move the screw in the positive direction of the axis. This definition is throughout the report referred to as e.g. the positive ${\boldsymbol{z}}{\boldsymbol{\mathbf{r}}}$ -sense,or just the positive angle, when it is clear from the context which axis is the actual one.  
 
 Not all the coordinate systems used in the transformations are shown in Fig. 4 to avoid overcrowding the figure, and others have been displaced parallel relative to the original location, in order to show how other systems move relative to them. All applied coordinate systems will be defined uniquely, when the tranformations are described in Sec. 2.4.  
 
-Tower support.  
+塔：节点编号从 1 到 $\ell$。
+塔节点 $T1$ 位于塔座处。
+塔节点 ${T\ell}$ 位于塔顶，且与轴节点 A1 共享。
 
-The tower substructure coordinate system (index $\pmb{T}$ ) has its origin at the tower support at node T1. The $\pmb{x_{T}}-$ and ${\pmb y}_{\pmb T}$ -axis are in a horizontal plane and the ${\pmb z}{\pmb T}$ -axis is vertical downward. The tower is assumed to be rigidly supported, and the displacements to be zero at the support.  
+轴：节点编号从 1 到 $m$。
+轴节点 ${A1}$ 位于与塔的连接处，且与塔节点 $T\ell$ 共享。轴节点 ${Am}$ 位于与叶片轮毂的连接处，且与叶片节点 $B1$ 共享。
 
-# Connection between tower and shaft-nacelle.  
+叶片：节点编号从 1 到 ${n}$。
+叶片节点 ${B1}$ 位于与轴的连接处，且与轴节点 ${Am}$ 共享。
 
-At the tower top, at the common node between the tower (node No. $\pmb{T\ell}$ ) and the shaft (node No. A1), several coordinate systems have their origo. The node is the coupling node between the two substructures.  
+参考坐标系为右手直角坐标系（笛卡尔坐标系）。坐标轴索引由符号 $\pmb{x},\pmb{y}$ 和 $\pmb{z}$ 表示，或分别同义地表示为 1, 2 和 3，贯穿于本论文中。
+
+所有角度均相对于坐标轴定义，当右手螺旋体的相应旋转使螺旋体沿坐标轴正向移动时，角度被认为是正向的。本报告中，此定义被称为例如正 ${\boldsymbol{z}}_{\boldsymbol{\mathbf{T}}}$ 方向，或仅仅是正角度，当上下文清楚地表明实际指的是哪个坐标轴时。
+
+为了避免图 4 过于拥挤，并非所有在变换中使用的坐标系都显示在图中，另一些坐标系则相对于原始位置平行移动，以显示它们如何相对于其他系统移动。所有应用的坐标系将在第 2.4 节描述变换时被唯一定义。
+
+## Tower support.  
+
+The tower substructure coordinate system (index $\pmb{T}$ ) has its origin at the tower support at node T1. The $\pmb{x_{T}}-$ and ${\pmb y}_{\pmb T}$ -axis are in a horizontal plane and the ${\pmb z}_{\pmb T}$ -axis is vertical downward. The tower is assumed to be rigidly supported, and the displacements to be zero at the support.  
+## 塔架支撑
+
+塔架子结构坐标系（记为 $\pmb{T}$）的坐标原点位于塔架支撑点T1。$\pmb{x}_{\pmb{T}}$ 轴和 ${\pmb y}_{\pmb{T}}$ 轴位于水平面内，而 ${\pmb z}_{\pmb{T}}$ 轴则垂直向下。假设塔架支撑刚性固定，支撑点的位移为零。
+
+## Connection between tower and shaft-nacelle.  
+
+At the tower top, at the common node between the tower (node No. ${T\ell}$ ) and the shaft (node No. A1), several coordinate systems have their origo. The node is the coupling node between the two substructures.  
 
 The shaft substructure coordinate system (index $\pmb{A}$ ) has its origin here. It is rigidly connected to the shaft and corotates with the shaft. The $\pmb{\mathcal{x}}_{\pmb{A}^{\bullet}}$ and $\pmb{z}_{\pmb{A}}$ -axis are in a plane perpendicular to the shaft axis, and the $\pmb{y}_{A}$ -axis is coinciding with the shaft axis in the undeformed state and oriented in direction of the mean wind. This set of axes also define the azimuthal position of the rotor, $\theta_{2A}^{A}=\theta_{}$ which is zero when the $\pmb{z}_{A}$ -axis is in the vertical plane. The angle is positive in the positive $\pmb{y}_{A}$ -sense. Because the substructure coordinate system is rigidly attached to the shaft, the deformations of the shaft at this point are zero, measured relative to this reference system.  
 
-Further, at the tower top a coordinate system is rigidly attached (index $T^{\prime}$ ). In the undeformed state its axes are parallel to the tower substructure coordinate axes $(T)$ . It follows the tower top during elastic deformation, and its angular rotations are identical to the angular deformation at the tower top node, $\left\{\theta_{T\ell}^{\bar{T}}\right\}$  
+Further, at the tower top a coordinate system is rigidly attached (index $T^{\prime}$ ). In the undeformed state its axes are parallel to the tower substructure coordinate axes $(T)$ . It follows the tower top during elastic deformation, and its angular rotations are identical to the angular deformation at the tower top node, $\left\{\theta_{T\ell}^{{T}}\right\}$  
 
-An intermediate coordinate system (index $N$ ), serving to define the bearing controlled yaw rotation, is located at the same point. The coordinate system corotates with the nacelle. In the zero-yaw position and the undeformed state its axes are parallel to the tower substructure coordinate axes $(T)$ The yaw angle $\pmb{\theta}_{3N}^{N}$ is the positive rotation about the tower ${\pmb z}{\pmb T}$ -axis.  
+An intermediate coordinate system (index $N$ ), serving to define the bearing controlled yaw rotation, is located at the same point. The coordinate system corotates with the nacelle. In the zero-yaw position and the undeformed state its axes are parallel to the tower substructure coordinate axes $(T)$ The yaw angle $\pmb{\theta}_{3N}^{N}$ is the positive rotation about the tower ${\pmb z}_{\pmb T}$ -axis.  
 
-The last coordinate system (index $R$ ) with origo at the tower top, is a system which is stationary in the nacelle, and has its $\pmb{y}\pmb{R}$ -axis coinciding with the shaft axis in the undeformed state, i.e. it coincides with the $A$ -system, when the azimuthal position is zero. The coordinate system is rotated the positive angle $\pmb{\theta}_{1R}^{R}$ about the $\pmb{x}_{\pmb{R}}$ axis relaive to the $N\cdot$ system. $\pmb{\theta}_{1R}^{R}$ isthe tit angle. This coordinate system is not shown in Fig. 4 in its original position, but in a parallel displaced version at the shaft end, identified by the index $R^{*}$  
+The last coordinate system (index $R$ ) with origo at the tower top, is a system which is stationary in the nacelle, and has its $\pmb{y}_{\pmb{R}}$ -axis coinciding with the shaft axis in the undeformed state, i.e. it coincides with the $A$ -system, when the azimuthal position is zero. The coordinate system is rotated the positive angle $\pmb{\theta}_{1R}^{R}$ about the $\pmb{x}_{\pmb{R}}$ axis relaive to the $N\cdot$ system. $\pmb{\theta}_{1R}^{R}$ isthe tit angle. This coordinate system is not shown in Fig. 4 in its original position, but in a parallel displaced version at the shaft end, identified by the index $R^{*}$  
 
-# Connection between shaft and blade.  
+tower与轴-机舱连接。
 
-The shaft end node (No. Am) and the center rotor blade node (No. $_{B1}$ ) coincide, and the common node connects the two substructures.  
+在tower顶部，tower（节点号 ${T\ell}$）与轴（节点号 A1）的公共节点处，有几个坐标系的原点。该节点是两个子结构之间的耦合节点。
+
+主轴子结构坐标系（索引 $\pmb{A}$）在此处有其原点。它与轴刚性连接并随轴共转。$\pmb{\mathcal{x}}_{\pmb{A}^{\bullet}}$ 和 $\pmb{z}_{\pmb{A}}$ 轴位于与轴轴垂直的平面内，而 $\pmb{y}_{A}$ 轴在未变形状态下与轴轴重合，并指向平均风向。该坐标轴系还定义了转子的方位角位置，$\theta_{2A}^{A}=\theta_{}$，当 $\pmb{z}_{A}$ 轴位于垂直平面内时为零。角度以正 $\pmb{y}_{A}$ 意义为正。由于子结构坐标系与轴刚性连接，因此相对于此参考系统，该点处的轴的变形为零。
+
+此外，在塔楼顶部，有一个坐标系刚性连接（索引 $T^{\prime}$）。在未变形状态下，其轴与塔楼子结构坐标轴（$T$）平行。它跟随塔楼顶部进行弹性变形，其角旋转与塔楼顶部节点的角变形相同，即 $\left\{\theta_{T\ell}^{{T}}\right\}$。
+
+一个中间坐标系（索引 $N$），用于定义承载控制偏航旋转，位于同一位置。该坐标系随机舱共转。在零偏航位置和未变形状态下，其轴与塔楼子结构坐标轴（$T$）平行。偏航角 $\pmb{\theta}_{3N}^{N}$ 是关于塔楼 ${\pmb z}_{\pmb T}$ 轴的正向旋转。
+
+最后一个坐标系（索引 $R$），其原点位于塔楼顶部，是一个相对于机舱固定的系统，其 $\pmb{y}_{\pmb{R}}$ 轴在未变形状态下与轴轴重合，即与 $A$ 系统重合，当方位角位置为零时。该坐标系绕 $\pmb{x}_{\pmb{R}}$ 轴相对于 $N$ 系统旋转正角 $\pmb{\theta}_{1R}^{R}$。$\pmb{\theta}_{1R}^{R}$ 是tilt角。该坐标系在图 4 中未显示其原始位置，而是在轴端显示一个平行的位移版本，由索引 $R^{*}$ 标识。
+
+## Connection between shaft and blade.  
+
+The shaft end node (No. Am) and the center rotor blade node (No. ${B1}$ ) coincide, and the common node connects the two substructures.  
 
 In order to support the definition of the coordinate systems at this node, the stationary Rsystem has been parallel displaced to the node, indicated with an upper star on the axis index, $R^{\ast}$  
 
-At the shaft end a coordinate system (index $S^{\prime}$ ) is rigidly attached to the node. In the undeformed state its axes are parallel with the axes of the $\pmb{A}_{\operatorname{\textbf{\em{\~}}}}$ -coordinate system. The system follows the shaft end during elastic deformation, and its angular rotations are identical to the angular deformation at the shaft end $\left\{\theta_{A m}^{A}\right\}$ ,measured relative to the $A\!\!\!$ -system.  
+At the shaft end a coordinate system (index $S^{\prime}$ ) is rigidly attached to the node. In the undeformed state its axes are parallel with the axes of the $\pmb{A}$ -coordinate system. The system follows the shaft end during elastic deformation, and its angular rotations are identical to the angular deformation at the shaft end $\left\{\theta_{A m}^{A}\right\}$ ,measured relative to the $A\!\!\!$ -system.  
 
 The blade substructure coordinate system (index $B$ ) has its origo at this node. It is corotating with the rotor blades and is rigidly attached to the blades. Its neutral position is coinciding with the $S^{\prime}$ -system. The $B$ -system can rotate about its $\pmb{x}_{\pmb{B}}$ -axis. The rotation corresponds to the bearing controlled teeter rotation $\theta_{1H}^{H}$ , which is zero when the two coordinate systems are coincident, and positive in the positive $\pmb{x}_{\pmb{B}}$ -sense. For a planar rotor, the $\pmb{z}_{\pmb{B}}$ -axis can be chosen coincident with a blade axis. The actual choice is however not important for a symmetrical non-teetering rotor. Any rotor configuration can be modelled within the blade substructure coordinate system.  
 
 Because the substructure coordinate system is rigidly attached to the center blade node, the deformation of the blades at this point are zero, measured relative to this reference system.  
 
+主轴与叶片之间的连接。
+
+主轴端节点（编号 Am）和中心转子叶片节点（编号 ${B1}$）重合，共同节点连接两个次结构。
+
+为了支持在此节点的坐标系定义，固定 R 系已被平行移动到该节点，并在轴索引上标有上标星号，表示为 $R^{\ast}$。
+
+在主轴端，一个坐标系（索引 $S^{\prime}$）被刚性地固定到该节点。在未变形状态下，其轴线与 A 坐标系的轴线平行。该系统在弹性变形过程中跟随主轴端运动，其角旋转与主轴端处的角变形 $\left\{\theta_{A m}^{A}\right\}$ 相同，相对于 A 系统测量。
+
+叶片次结构坐标系（索引 B）的原点位于该节点。它与转子叶片共转，并被刚性地固定到叶片上。其中性位置与 S' 系重合。B 系可以绕其 $\pmb{x}_{\pmb{B}}$ 轴旋转。该旋转对应于轴承控制的倾斜旋转 $\theta_{1H}^{H}$，当两个坐标系重合时为零，并且在正 $\pmb{x}_{\pmb{B}}$ 方向上为正。对于平面转子，$\pmb{z}_{\pmb{B}}$ 轴可以选择与叶片轴重合。然而，实际选择对于对称非倾斜转子并不重要。任何转子配置都可以建模在叶片次结构坐标系中。
+
+由于次结构坐标系被刚性地固定到中心叶片节点，因此相对于此参考系统测量，该点的叶片变形为零。
 # 2.3 Degrees of freedom.  
 
 According to the definitions above, a final summary of the degrees of freedom can be given.  
 
-The boundary conditions at the tower support, and the definitions of the substructure coordinate systems for the shaft and the blades, as rigidly attached to the respective substructures, imply that the degrees of freedom for the first node on all three substructures can be eliminated from the equations of motion. The kinematic analysis carried out according to these definitions will ensure that the displacement compatibility at the coupling nodes is fulfilled. The displacement vector at a node is defined by three translations and three rotations, for example for node No. $_i$ on the biade substructure $(B)$ as  
+The boundary conditions at the tower support, and the definitions of the substructure coordinate systems for the shaft and the blades, as rigidly attached to the respective substructures, imply that the degrees of freedom for the first node on all three substructures can be eliminated from the equations of motion. The kinematic analysis carried out according to these definitions will ensure that the displacement compatibility at the coupling nodes is fulfilled. The displacement vector at a node is defined by three translations and three rotations, for example for node No. $i$ on the blade substructure $(B)$ as  
 
+根据上述定义，可以给出自由度的一个最终总结。
+
+ tower support处的边界条件，以及用于轴和叶片的子结构坐标系定义，它们被严格地附加到各自的子结构上，这意味着所有三个子结构上的第一个节点可以从运动方程中消除其自由度。根据这些定义进行的运动学分析将确保耦合节点处的位移相容性得以满足。一个节点的位移矢量由三个平移和三个旋转定义，例如对于叶片子结构 (B) 上的节点 No. $i$。
 $$
-\left\{q_{B i}^{B}\left(t\right)\right\}=\left\{\begin{array}{c}{\left\{u_{x B i}^{B}\left(t\right)}\\ {u_{y B i}^{B}\left(t\right)}\\ {\left\{\theta_{B i}^{B}\left(t\right)\right\}}\end{array}\right\}=\left\{\begin{array}{c}{u_{x B i}^{B}\left(t\right)}\\ {u_{y B i}^{B}\left(t\right)}\\ {u_{z B i}^{B}\left(t\right)}\\ {\theta_{x B i}^{B}\left(t\right)}\\ {\theta_{y B i}^{B}\left(t\right)}\\ {\theta_{y B i}^{B}\left(t\right)}\\ {\theta_{z B i}^{B}\left(t\right)}\end{array}\right\}
+\left\{ q_{B i}^{B}(t) \right\} = 
+\left\{\begin{array}{c}
+\{{u_{ B i}^{B}(t)}\} \\
+\{\theta_{ B i}^{B}(t)\} \\
+\end{array}\right\}=
+\left\{\begin{array}{c}
+u_{x B i}^{B}(t) \\
+u_{y B i}^{B}(t) \\
+u_{z B i}^{B}(t) \\
+\theta_{x B i}^{B}(t) \\
+\theta_{y B i}^{B}(t) \\
+\theta_{z B i}^{B}(t)
+\end{array}\right\}
 $$  
 
 where  
 
-$\begin{array}{r l}&{u_{x B i}^{B},\,u_{y B i}^{B},\,u_{z B i}^{B}}\\ &{\theta_{x B i}^{B},\,\theta_{y B i}^{B},\,\theta_{z B i}^{B}}\end{array}$ are translations at the node. are rotations at the node.  
+${u_{x B i}^{B},\,u_{y B i}^{B},\,u_{z B i}^{B}}$are translations at the node.
+$\theta_{x B i}^{B},\,\theta_{y B i}^{B},\,\theta_{z B i}^{B}$ are rotations at the node.  
 
 Generally, the time dependency is not stated explicitly below, unless it is found that it helps in clarifying the context.  
 
 For the substructures, the internal node degrees of freedom are expressed by the vectors  
+通常，时间依赖性在下文不会明确指出，除非发现明确指出有助于澄清上下文。
 
+对于子结构，内部节点的自由度由向量表达。
 $$
 \left\{q_{B B}^{B}\right\}=\left\{\begin{array}{c}{{\left\{q_{B2}^{B}\right\}}}\\ {{\left\{q_{B3}^{B}\right\}}}\\ {{\vdots}}\\ {{\left\{q_{B n}^{B}\right\}}}\end{array}\right\},\;\left\{q_{A A}^{A}\right\}=\left\{\begin{array}{c}{{\left\{q_{A2}^{A}\right\}}}\\ {{\left\{q_{A3}^{A}\right\}}}\\ {{\vdots}}\\ {{\left\{q_{A(m-1)}^{A}\right\}}}\end{array}\right\},\;\;\mathsf{a n d}\;\;\left\{q_{T T}^{T}\right\}=\left\{\begin{array}{c}{{\left\{q_{T2}^{T}\right\}}}\\ {{\left\{q_{T3}^{T}\right\}}}\\ {{\vdots}}\\ {{\left\{q_{T(\ell-1)}^{T}\right\}}}\end{array}\right\}
 $$  
 
-The coupling degrees of freedom are not included in these vectors, because they will appear separately in the equations of motion due to the kinematic coupling between the substructures. The couplingDOFs are  
-
+The coupling degrees of freedom are not included in these vectors, because they will appear separately in the equations of motion due to the kinematic coupling between the substructures. The coupling DOFs are  
+这些向量中不包含连接自由度，因为它们会在次结构的运动方程中单独出现，这是由于运动学耦合造成的。连接自由度是…
 $$
-\left\{q_{T\ell}^{T}\right\}=\left\{\begin{array}{l}{\left\{u_{T\ell}^{T}\right\}}\\ {\left\{\begin{array}{l}{\left\{u_{T\ell}^{T}}\\ {\ell\left\}}\\ {\left\{\theta_{T\ell}^{T}\right\}}\end{array}\right\}=\left\{\begin{array}{l}{u_{x T\ell}^{T}}\\ {u_{y T\ell}^{T}}\\ {u_{z T\ell}^{T}}\\ {\theta_{x T\ell}^{T}}\\ {\theta_{y T\ell}^{T}}\\ {\theta_{y T\ell}^{T}}\\ {\theta_{z T\ell}^{T}}\end{array}\right\}
+\left\{ q_{T\ell}^{T} \right\} = 
+\left\{\begin{array}{c}
+\{{u_{T\ell}^{T}}\} \\
+\{\theta_{T\ell}^{T}\} \\
+\end{array}\right\}=
+\left\{\begin{array}{c}
+u_{x T\ell}^{T} \\
+u_{y T\ell}^{T} \\
+u_{z T\ell}^{T} \\
+\theta_{x T\ell}^{T} \\
+\theta_{y T\ell}^{T} \\
+\theta_{z T\ell}^{T}
+\end{array}\right\}
+
 $$  
 
 and  
 
 $$
-\left\{q_{A m}^{A}\right\}=\left\{\begin{array}{l}{{\left\{u_{A m}^{A}\right\}}}\\ {{\left\{\begin{array}{l}{{\left\{u_{A m}^{A}\right\}}}\\ {{\left\{\theta_{A m}^{A}\right\}}}\end{array}\right\}}=\left\{\begin{array}{l}{{u_{{A m}}^{A}}}\\ {{u_{{y A m}}^{A}}}\\ {{u_{{z A m}}^{A}}}\\ {{\theta_{x A m}^{A}}}\\ {{\theta_{y A m}^{A}}}\\ {{\theta_{y A m}^{A}}}\\ {{\theta_{z A m}^{A}}}\end{array}\right\}}\end{array}\right.
+\left\{ q_{Am}^A \right\} = 
+\left\{\begin{array}{c}
+\left\{ u_{Am}^A \right\} \\ 
+\left\{ \theta_{Am}^A \right\}
+\end{array}\right\}=
+\left\{\begin{array}{c}
+u_{xAm}^A \\
+u_{y Am}^A \\
+u_{z Am}^A \\
+\theta_{x Am}^A \\
+\theta_{y Am}^A \\
+\theta_{z Am}^A
+\end{array}\right\}
 $$  
 
-The remaining degrees of freedom, appearing as scalars in the equations of motion, are  
-
+The remaining degrees of freedom, appearing as scalars in the equations of motion, are 
+$\theta_{3N}^{N}(t)$ the yaw angle
+$\theta_{1H}^{H}(t)$ the teeter angle
+$\theta_{2A}^{A}(t)$ the azimuthal position
 The tilt angle $\theta_{1R}^{R}$ is constant.  
+剩余的自由度，在运动方程中表现为标量，分别是：
+$\theta_{3N}^{N}(t)$ 偏航角
+$\theta_{1H}^{H}(t)$ 倾覆角
+$\theta_{2A}^{A}(t)$ 方位角
+倾斜角 $\theta_{1R}^{R}$ 为常数。
 
-Important implications of the substructuring.  
+## Important implications of the substructuring.  
 
 In Sec. 2.1 it was mentioned that the substructuring had other important implications than the appropriate incorporation of the elastic rotations in the kinematic analysis. One implication is that the limitations on the allowable rotations at the nodes on the shaft and the blade substructures are extended, compared to the limitations that had to be imposed, if the structure was described within a common coordinate system, for example the tower system. The reason is that the rigid body rotations, resulting from the rotations at the coupling nodes, are eliminated from the local substructure rotations, and relative to the common coordinates they can be larger than otherwise, and still be expressed as a vector.  
 
 Another implication is that the equations of motion can be easily updated during the solution, with respect to the change in geometry resulting from the coupling rotations, because the updating requires only a limited number of numerical operations. Thus, only the geometric nonlinearities within a substructure need to be considered when the structure is deformed.  
+在第2.1节中提到，子结构划分除了在运动学分析中恰当地包含弹性转动之外，还有其他重要的影响。其中一个影响是，与如果在公共坐标系（例如塔架系统）中描述整个结构时必须施加的限制相比，在轴和叶片子结构节点的允许转动受到更宽松的限制。其原因是，来自联接节点转动产生的刚体转动被从局部子结构转动中消除，相对于公共坐标，它们可以更大，并且仍然可以表示为向量。
 
+另一个影响是，由于更新只需要有限数量的数值运算，因此在联接转动引起的几何变化的情况下，运动方程可以很容易地在求解过程中进行更新。因此，在结构变形时，只需要考虑子结构内部的几何非线性。
 # 2.4  Transformation matrices.  
 
-The purpose of this section is to derive the transformation matrices which change the vector components in accordance with change of reference system. Further, the angular velocities of the coordiante systems are introduced.  
+The purpose of this section is to derive the transformation matrices which change the vector components in accordance with change of reference system. Further, the angular velocities of the coordinate systems are introduced.  
 
 The components of the three dimensional vectors used to describe positions and deformations and their time derivatives can be referenced to any set of coordinate axes. Throughout the analysis it will be necessary frequently to change the basis for the vectors. The vector notation is explained at the beginning of the symbol list in App. A, and shall not be repeated here. Only, it is important to stress one feature of the notation. The upper right index of a vector indicates what coordinate system its components are referenced to. Only in cases when it is unimportant or when the context makes it clear, what coordinate system is actually used as reference, this identification shall be omitted. Allthough the notation, now and then, may seem to be a little inelegant, it has throughout the derivations proven to be a valuable help, in this way to make it clear, what coordinate system the actual vector is referenced to. Especially when vectors of different origin are combined in an expression. The notation can often serve as a means for control of a vector expression.  
 
 When the basis for a vector is changed, the appropriate transformations must be applied. Only when position vectors are dealt with, the actual spatial position of the vector must be taken into account. All other vectors are uniquely defined by their orientation and size, and they can be moved by a parallel displacement to an appropriate position before transformation. This is equivalent to consider the coordinate systems involved in a transformation as having common origin and the vector to start at this origin.  
 
-The transformation of such a three dimensional vector from, for example, the tower coordinate system $(T)$ to the shaft coordinate system $(A)$ is expressedby  
+The transformation of such a three dimensional vector from, for example, the tower coordinate system $(T)$ to the shaft coordinate system $(A)$ is expressed by  
+本节的目的是推导变换矩阵，这些矩阵能够根据参考系的变化来改变向量的分量。此外，还将介绍坐标系的角速度。
+
+用于描述位置和变形的三维向量的分量及其时间导数，可以参考任意一组坐标轴。在整个分析过程中，经常需要改变向量的基。向量符号的解释见符号列表附录A的开头，此处不再赘述。不过，必须强调一种符号的特征：向量右上角的索引表示其分量参考的坐标系。只有当参考坐标系不重要或上下文明确时，才可省略此标识。虽然这种符号有时可能显得有些不优雅，但在推导过程中，它始终被证明是一种宝贵的帮助，从而明确了实际向量参考的坐标系。尤其是在组合来自不同坐标系的向量时。这种符号通常可以作为控制向量表达式的一种手段。
+
+当向量的基发生变化时，必须应用适当的变换。仅在处理位置向量时，必须考虑向量的实际空间位置。其他所有向量由其方向和大小唯一定义，可以在变换之前通过平行移动将其移动到适当的位置。这等效于将参与变换的坐标系视为具有共同原点，并且向量从该原点开始。
+
+例如，将一个三维向量从塔坐标系 $(T)$ 变换到轴坐标系 $(A)$，用以下方式表示：
 
 $$
 \left\{u^{A}\right\}=\left[T_{T A}\right]\left\{u^{T}\right\}
@@ -803,7 +904,9 @@ $$
 where the matrix has dimension $\mathbf{3}\times\mathbf{3}$ The columns of the matrix are the components of the projections of the axis unit vectors of the $\pmb{T}$ -system on the axes of the $A\!\!\!/$ -system. These components are often denoted the direction cosines of the unit vectors. The lower matrix index $_{T A}$ carries the information that the transformation is from the $\pmb{T}\cdot\$ to the $\pmb{A}$ -system. This meaning of the sequence of the indices is adhered to throughout the thesis.  
 
 When dealing with Cartesian coordinate systems, the linear transformation expressed by $[T_{T A}]$ is called an orthonormal transformation, because the column vectors of the matrix $\{e_{i}\}$ have the following properties  
+其中矩阵的维度为 $\mathbf{3}\times\mathbf{3}$。矩阵的列向量是 $\pmb{T}$ 坐标系中轴向单位向量在 $A$ 坐标系上投影的各分量。这些分量通常被称为单位向量的方向余弦。下标矩阵 ${TA}$ 携带了变换是从 $\pmb{T}$ 系到 $\pmb{A}$ 系的信息。本论文始终遵循这种索引序列的含义。
 
+在处理笛卡尔坐标系时，由 $[T_{TA}]$ 表示的线性变换被称为正交变换，因为矩阵 $\{e_{i}\}$ 的列向量具有以下性质。
 $$
 \{e_{i}\}^{T}\,\{e_{j}\}=\left\{\begin{array}{l l}{{1\quad}}&{{{\mathrm{for~}}i=j}}\\ {{0\quad}}&{{{\mathrm{for~}}i\not=j}}\end{array}\right.
 $$  
@@ -817,12 +920,20 @@ $$
 $$  
 
 where the upper index $T$ denotes the transpose, and the index $-1$ the inverse of the matrix. The involved transformation matrices and the corresponding angular velocities are derived next.  
+其中 $\pmb{i}$ 和 $j$ 分别为实际的列数。
 
-# Tower - elastic tower, $\underline{{[T_{T T^{\prime}}]}}$  
+这些性质进一步推导出：
 
-In Fig. 5 the involved rotations are shown. The double arrows are not vectors. They only serve to show the actual rotation axis. The rotations are the elastic deformations at the tower top. The coordinate system with index $\scriptstyle{T_{0}^{\prime}}$ corresponds to the undeformed state. The $x^{\prime}-,y^{\prime}-$ , and $z^{\prime}.$ -axes show intermediate positions, and the $T^{\prime}\!.$ -axes correspond to the deformed state. During derivationfthetransfomatonatrixthrdftherotationssauedtobe $\theta_{1T\ell}^{T},\,\theta_{2T\ell}^{T},$ and $\theta_{3T\ell}^{T}$ . In order to avoid the problem of managing the order of the rotations in the final expressions, they are assumed small $\left(\cos\left(\theta\right)\simeq1\right.$ $\sin\left(\theta\right)\simeq\theta\rangle$ , and the relation to the vector representation of the deformations is kept unique.  
+$$
+\left[T_{T A}\right]^{T}=\left[T_{T A}\right]^{-1}=\left[T_{A T}\right]
+$$
 
-The derivation of the transformation matrix and the angular velocity of the $T^{\prime}$ -systemis addressed in App. C, where the linearization is introduced in the final expressions.  
+其中上标 $T$ 表示转置，而 $-1$ 表示矩阵的逆。接下来推导涉及的变换矩阵和对应的角速度。
+## Tower - elastic tower, ${{[T_{T T^{\prime}}]}}$  
+
+In Fig. 5 the involved rotations are shown. The double arrows are not vectors. They only serve to show the actual rotation axis. The rotations are the elastic deformations at the tower top. The coordinate system with index $\scriptstyle{T_{0}^{\prime}}$ corresponds to the undeformed state. The $x^{\prime}-,y^{\prime}-$ , and $z^{\prime}.$ -axes show intermediate positions, and the $T^{\prime}\!.$ -axes correspond to the deformed state. During derivation of the transformation matrix the order of the rotation is assumed to be $\theta_{1T\ell}^{T},\,\theta_{2T\ell}^{T},$ and $\theta_{3T\ell}^{T}$ . In order to avoid the problem of managing the order of the rotations in the final expressions, they are assumed small $\left(\cos\left(\theta\right)\simeq1\right.,$ $\sin\left(\theta\right)\simeq\theta\rangle$ , and the relation to the vector representation of the deformations is kept unique.  
+
+The derivation of the transformation matrix and the angular velocity of the $T^{\prime}$ -system is addressed in App. C, where the linearization is introduced in the final expressions.  
 
 The resulting transformation matrix is  
 
@@ -836,7 +947,7 @@ $$
 \left\{\omega_{T^{\prime}T}^{T}\left(t\right)\right\}=\left\{\begin{array}{l}{\dot{\theta}_{1T\ell}^{T}}\\ {\dot{\theta}_{2T\ell}^{T}}\\ {\dot{\theta}_{3T\ell}^{T}}\end{array}\right\}=\left\{\dot{\theta}_{T\ell}^{T}\right\}
 $$  
 
-Elastic tower - nacelle, $[T_{T^{\prime}N}]$ yaw rotation.  
+## Elastic tower - nacelle, $[T_{T^{\prime}N}]$ yaw rotation.  
 
 The axes involved in the transformation are shown in Fig. 6  
 
@@ -855,7 +966,7 @@ $$
 \left\{\omega_{N T^{\prime}}^{N}\left(t\right)\right\}=\left\{\begin{array}{c}{{0}}\\ {{0}}\\ {{\dot{\theta}_{3N}^{N}}}\end{array}\right\}
 $$  
 
-Nacelle - shaft tilted, $[\underline{{T_{N R}}}]$ , tilt angle.  
+## Nacelle - shaft tilted, $[{{T_{N R}}}]$ , tilt angle.  
 
 The axes involved in the transformation are shown in Fig. 7  
 
@@ -874,7 +985,7 @@ $$
 \left\{\omega_{R N}^{R}\right\}=\left\{0\right\}
 $$  
 
-Shaft tilted -- shaft substructure, $[T_{R A}]$ azimuthal rotation.  
+## Shaft tilted -- shaft substructure, $[T_{R A}]$ azimuthal rotation.  
 
 The axes involved in the transformation are shown in Fig. 8  
 
@@ -888,13 +999,13 @@ and the angular velocity of the $\pmb{A}$ -system relative to the $\pmb{R}$ -sys
 
 ![](ef8dad763b486102f3a874043e90ab3c5ed7c77ef5f34fd4e4bbfed5ab7203a8.jpg)  
 
-# Figure 8: Azimuthal rotation, $\pmb{\theta_{2A}^{A}}=\pmb{\theta}.$  
+ Figure 8: Azimuthal rotation, $\pmb{\theta_{2A}^{A}}=\pmb{\theta}.$  
 
 $$
 \left\{\omega_{A R}^{A}\left(t\right)\right\}=\left\{\begin{array}{c}{{0}}\\ {{\dot{\theta}_{2A}^{A}}}\\ {{0}}\end{array}\right\}=\left\{\begin{array}{c}{{0}}\\ {{\omega}}\\ {{0}}\end{array}\right\}
 $$  
 
-Shaft substructure - elastic shaft, $\underline{{[T_{A S^{\prime}}]}}.$  
+Shaft substructure - elastic shaft, ${{[T_{A S^{\prime}}]}}.$  
 
 This transformation is equivalent to the transformation between the tower substructure $\pmb{T}.$ system and the coordinate system following the tower top $(T^{\prime})$ , in that the rotations represent elastic deformations,hereathe shaft end, $\left\{\theta_{A m}^{A}\right\}$  
 
@@ -910,7 +1021,7 @@ $$
 \left\{\omega_{S^{\prime}A}^{A}\left(t\right)\right\}=\left\{\begin{array}{l}{\dot{\theta}_{1A m}^{A}}\\ {\dot{\theta}_{2A m}^{A}}\\ {\dot{\theta}_{3A m}^{A}}\end{array}\right\}=\left\{\dot{\theta}_{A m}^{A}\right\}
 $$  
 
-Elastic shaft -- blade substructure, $\left[\pmb{T_{S^{\prime}B}}\right]$ , teeter angle.  
+## Elastic shaft -- blade substructure, $\left[\pmb{T_{S^{\prime}B}}\right]$ , teeter angle.  
 
 The axes involved in the transformation are shown in Fig. 9  
 
@@ -929,11 +1040,11 @@ $$
 \left\{\omega_{B S^{\prime}}^{B}(t)\right\}=\left\{\begin{array}{c}{{\dot{\theta}_{1H}^{H}}}\\ {{0}}\\ {{0}}\end{array}\right\}
 $$  
 
-Transformation between finite element- and substructure-coordinate system.  
+## Transformation between finite element- and substructure-coordinate system.  
 
-The derivation of the matrix which transforms between the local element coordinate system and the substructure coordinate system is described in Sec. 4.8. This matrix is especially actual when the element equations are assembled to the substructure equations of motion, and when deriving the node inertia loads.  
+The derivation of the matrix which transforms between the local element coordinate system and the substructure coordinate system is described in Sec. 4.8. This matrix is especially actual when the element equations are assembled to the substructure equations of motion, and when deriving the node inertia loads. 
 
-# Contraction of matrix products.  
+## Contraction of matrix products.  
 
 In the kinematic analysis in Sec. 3, products of transformation matrices appear, representing a chain of successive transformations. In order to simplify the expressions, these products have been contracted, so that the resulting transformation matrix only refers to the first and the last coordinate system in the chain of transformations. But when differentiation with respect to time is carried out, the origin of these contracted matrix products must be remembered in order to differentiate the time dependent matrices correctly.  
 

学术讲座-交流-面试/2025.4.30刘沛野面试.md

@@ -0,0 +1,24 @@
+
+问题：
+云服务器的访问量
+
+计算机硕士的课题，主要工作
+AWS开发模式，做技术支持？ 如何开发软件
+前后端最擅长什么，用什么框架
+
+软件界面开发有没有经验
+
+并行计算、异构计算
+
+
+
+
+回国的原因？
+
+化学转计算机的考虑？
+
+后续想做计算机还是做化学？
+
+化学本科 化学博士
+计算机硕士
+

工作OKRs/25.2-5 OKR.canvas

@@ -1,10 +1,10 @@
 {
 	"nodes":[
 		{"id":"b698e88ca5fb9c51","type":"text","text":"状态指标：\n推进OKR的时候也要关注这些事情，它们是完成OKR的保障。\n\n\n效率状态  green","x":-96,"y":80,"width":456,"height":347},
-		{"id":"2b068bfe5df15a72","type":"text","text":"# 目标：多体动力学模块完善\n### 每周盘点一下它们\n\n\n关键结果：建模原理、建模方法掌握    （7.5/10）\n\n关键结果：对标Bladed模块完成  （7.2/10）\n\n关键结果：风机多体动力学文献调研情况完成 （5/10）","x":-96,"y":-307,"width":456,"height":347},
+		{"id":"2b068bfe5df15a72","type":"text","text":"# 目标：多体动力学模块完善\n### 每周盘点一下它们\n\n\n关键结果：建模原理、建模方法掌握    （7.5/10）\n\n关键结果：对标Bladed模块完成  （8/10）\n\n关键结果：风机多体动力学文献调研情况完成 （5.5/10）","x":-96,"y":-307,"width":456,"height":347},
 		{"id":"01ee5c157d0deeae","type":"text","text":"# 推进计划\n未来四周计划推进的重要事情\n\n文献调研启动\n\n建模重新推导\n\n\n","x":-620,"y":80,"width":456,"height":347},
-		{"id":"1ebeabaf5c73ddbb","type":"text","text":"# 本月已完成\n\n多体原理学习 YouTube课程 018\n气动模块联合调试，跑通\n使用python搭建风电机组多体模型  刚性部件主动力、惯性力计算 ","x":-440,"y":520,"width":440,"height":340},
-		{"id":"58be7961ae7275a7","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\nP1 稳态工况多体动力学求解方法 --龙格库塔+ed_caloutput 初步方案完成\nP1 柔性部件 叶片、塔架主动力惯性力算法\n- 变形体动力学 简略看看ing\n- 浮动坐标系方法 如何用与梁模型\n\nP1 编写Steady Operational Loads求解器\n- 框架 完成\n- 多体设置参数 完成\n- 每个风速直接是否需要重新初始化 需要 根据参数重建坐标系和网格 \n\nP1 Steady Operational Loads求解器测试\nP1 yaw 自由度再bug确认 已知原理了\nP1 generator torque计算\n","x":-614,"y":-307,"width":450,"height":347}
+		{"id":"1ebeabaf5c73ddbb","type":"text","text":"# 4月已完成\n\n多体原理学习 YouTube课程 018\n\n气动模块联合调试，跑通\n\n使用python搭建风电机组多体模型  刚性部件主动力、惯性力计算 \n\n编写Steady Operational Loads求解器\n- 稳态工况多体动力学求解方法 --龙格库塔+ed_caloutput 初步方案完成\n- 遍历风速框架 完成\n- 不同风速下转速、变桨角度算法 完成\n- 多体设置参数 完成\n- 每个风速直接是否需要重新初始化 需要 完成\n\n\n\ngenerator torque计算 简单了解，确定方案","x":-440,"y":520,"width":440,"height":560},
+		{"id":"58be7961ae7275a7","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\n\nP1 柔性部件 叶片、塔架主动力惯性力算法\n- 变形体动力学 简略看看ing\n- 浮动坐标系方法 如何用于梁模型\n\nP1 Steady Operational Loads求解器测试 \nP1 yaw 自由度再bug确认 已知原理了\n\n","x":-614,"y":-307,"width":450,"height":347}
 	],
 	"edges":[]
 }