Merge remote-tracking branch 'origin/master'

书籍/力学书籍/力学/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library)/auto/Chap 10 EVALUATION OF STRUCTURALPROPERTY MATRICES.md

@@ -384,7 +384,26 @@ $$
 The symmetric form of this equation shows that the mass matrix (like the stiffness matrix) is symmetric; that is, $m_{i j}=m_{j i}$ ; also it may be noted that this expression is equivalent to the corresponding term in the first of Eqs. (8-18) in the case where $i=j$ . When the mass coefficients are computed in this way, using the same interpolation functions which are used for calculating the stiffness coefficients, the result is called the consistent-mass matrix. In general, the cubic hermitian polynomials of Eqs. (10- 16) are used for evaluating the mass coefficients of any straight beam segment. In the special case of a beam with uniformly distributed mass the results are  
 该方程的对称形式表明质量矩阵（如刚度矩阵）是对称的；即，$m_{i j}=m_{j i}$；还可以注意到，当$i=j$时，该表达式等效于式(8-18)中第一个方程的相应项。当以这种方式计算质量系数时，使用与计算刚度系数相同的插值函数，结果称为一致质量矩阵。通常，式(10-16)中的三次Hermite多项式用于评估任何直梁段的质量系数。在质量均匀分布的梁的特殊情况下，结果为
 $$
-\left\{\begin{array}{c}{f_{I1}}\\ {f_{I2}}\\ {f_{I3}}\\ {f_{I4}}\end{array}\right\}=\frac{\overline{{m}}L}{420}\begin{array}{r l r l}{\mathrm{~156~}}&{54}&{22L}&{-13L}\\ {\mathrm{~54~}}&{156}&{13L}&{-22L}\\ {\mathrm{~22~}}&{13L}&{4L^{2}}&{-3L^{2}}\\ {\mathrm{~}}&{\mathrm{~-22~}}&{-3L^{2}}&{4L^{2}}\end{array}\right\}\begin{array}{c}{\langle\ddot{v}_{1}}\\ {\ddot{v}_{2}}\\ {\ddot{v}_{3}}\\ {\ddot{v}_{4}}\end{array}
+\begin{Bmatrix}
+f_{I1} \\
+f_{I2} \\
+f_{I3} \\
+f_{I4}
+\end{Bmatrix}
+= \frac{\bar{m}L}{420}
+\begin{bmatrix}
+156 & 54 & 22L & -13L \\
+54 & 156 & 13L & -22L \\
+22L & 13L & 4L^2 & -3L^2 \\
+-13L & -22L & -3L^2 & 4L^2
+\end{bmatrix}
+\begin{Bmatrix}
+\ddot{v}_1 \\
+\ddot{v}_2 \\
+\ddot{v}_3 \\
+\ddot{v}_4
+\end{Bmatrix}
+\tag{10-29}
 $$  
 
 When the mass coefficients of the elements of a structure have been evaluated, the mass matrix of the complete element assemblage can be developed by exactly the same type of superposition procedure as that described for developing the stiffness matrix from the element stiffness [Eq. (10-23)]. The resulting mass matrix in general will have the same configuration, that is, arrangement of nonzero terms, as the stiffness matrix.  
@@ -399,6 +418,8 @@ The dynamic analysis of a consistent-mass system generally requires considerably
 
 ![](e1d4ede24cd2bed83a4cc2626bf6bc2ee8f36d92f4f7fea958253348306f722f.jpg)  
 FIGURE E10-2  Analysis of lumped- and consistent-mass matrices: (a) uniform mass in members; (b) lumping of mass at member ends; (c) forces due to acceleration $\ddot{v}_{1}=1$ (consistent); $(d)$ forces due to acceleration $\ddot{v}_{2}=1$ (consistent).  
+图 E10-2 集中质量矩阵和一致质量矩阵分析：(a) 构件中质量均匀分布；(b) 质量集中在构件端部；(c) 由加速度 $\ddot{v}_{1}=1$ 引起的力（一致）；(d) 由加速度 $\ddot{v}_{2}=1$ 引起的力（一致）。
+
 Example E10-2. The structure of Example E10-1, shown again in Fig. E10-2a, will be used to illustrate the evaluation of the structural mass matrix. First the lumped-mass procedure is used: half the mass of each member is lumped at the ends of the members, as shown in Fig. E10-2b. The sum of the four contributions at the girder level then acts in the sidesway degree of freedom $m_{11}$ ; no mass coefficients are associated with the other degrees of freedom because these point masses have no rotational inertia.  
 
 The consistent-mass matrix is obtained by applying unit accelerations to each degree of freedom in succession while constraining the others and determining the resulting inertial forces from the coefficients of Eq. (10-29). Considering first the sidesway acceleration, as shown in Fig. E10-2c, it must be noted that the coefficients of Eq. (10-29) account only for the transverse inertia of the columns. The inertia of the girder due to the acceleration parallel to its axis must be added as a rigid-body mass (3mL), as shown.  
@@ -406,33 +427,49 @@ The consistent-mass matrix is obtained by applying unit accelerations to each de
 The joint rotational acceleration induces only accelerations transverse to the members, and the resulting girder and column contributions are given by Eq. (10-29), as shown in Fig. E10-2d. The final mass matrices, from the lumpedand consistent-mass formulations, are  
 示例 E10-2。图 E10-2a 中再次显示的示例 E10-1 的结构将用于说明结构质量矩阵的评估。首先采用集中质量法：每个构件一半的质量集中在构件的两端，如图 E10-2b 所示。梁层面上四个贡献的总和然后作用于侧移自由度 $m_{11}$；没有质量系数与其它自由度相关联，因为这些质点没有转动惯量。通过依次对每个自由度施加单位加速度，同时约束其他自由度，并根据方程 (10-29) 的系数确定由此产生的惯性力，从而获得一致质量矩阵。首先考虑侧移加速度，如图 E10-2c 所示，必须指出方程 (10-29) 的系数仅考虑柱的横向惯性。由于平行于其轴线的加速度引起的梁的惯性必须作为刚体质量 (3mL) 添加，如图所示。节点转动加速度仅引起构件的横向加速度，由此产生的梁和柱的贡献由方程 (10-29) 给出，如图 E10-2d 所示。根据集中质量和一致质量公式得到的最终质量矩阵为
 $$
-\begin{array}{r}{\mathbf{m}=\frac{\overline{{m}}L}{210}\begin{array}{l}{\left[840\quad0\quad0\right]}\\ {\left[\begin{array}{l l l}{0}&{0}&{0}\\ {0}&{0}&{0}\\ {0}&{0}&{0}\end{array}\right]}\end{array}\quad\mathbf{m}=\frac{\overline{{m}}L}{210}\begin{array}{l}{\left[786\quad11L\quad11L\right]}\\ {11L\quad26L^{2}\quad-18L^{2}}\\ {\left[11L\quad-18L^{2}\quad26L^{2}\right]}\end{array}}\end{array}
+\mathbf{m} = \frac{\bar{m}L}{210}
+\begin{bmatrix}
+840 & 0 & 0 \\
+0 & 0 & 0 \\
+0 & 0 & 0
+\end{bmatrix}
+\quad \text{Lumped}
+$$
+
+$$
+\mathbf{m} = \frac{\bar{m}L}{210}
+\begin{bmatrix}
+786 & 11L & 11L \\
+11L & 26L^2 & -18L^2 \\
+11L & -18L^2 & 26L^2
+\end{bmatrix}
+\quad \text{Consistent}
 $$  
 
 # 10-3 DAMPING PROPERTIES  
 
 If the various damping forces acting on a structure could be determined quantitatively, the finite-element concept could be used again to define the damping coefficients of the system. For example, the coefficient for any element might be of the form [compare with the corresponding term in the second of Eqs. (8-18) for the case where $i=j]$  
-
+如果作用在结构上的各种阻尼力能够定量确定，有限元概念就可以再次用于定义系统的阻尼系数。例如，任何单元的系数可能具有以下形式 [与方程 (8-18) 的第二个式子中 $i=j$ 情况下的相应项进行比较]
 $$
 c_{i j}=\int_{0}^{L}c(x)\,\psi_{i}(x)\,\psi_{j}(x)\,d x
 $$  
 
 in which $c(x)$ represents a distributed viscous-damping property. After the element damping influence coefficients were determined, the damping matrix of the complete structure could be obtained by a superposition process equivalent to the direct stiffness method. In practice, however, evaluation of the damping property $c(x)$ (or any other specific damping property) is impracticable. For this reason, the damping is generally expressed in terms of damping ratios established from experiments on similar structures rather than by means of an explicit damping matrix c. If an explicit expression of the damping matrix is needed, it generally will be computed from the specified damping ratios, as described in Chapter 12.  
-
+其中 $c(x)$ 表示一种分布式的粘性阻尼特性。在单元阻尼影响系数确定后，完整结构的阻尼矩阵可以通过等效于直接刚度法的叠加过程获得。然而，在实践中，评估阻尼特性 $c(x)$（或任何其他特定的阻尼特性）是不可行的。因此，阻尼通常以根据对类似结构进行的实验确定的阻尼比的形式表示，而不是通过显式阻尼矩阵 c。如果需要阻尼矩阵的显式表达式，它通常将根据指定的阻尼比计算，如第12章所述。
 # 10-4 EXTERNAL LOADING  
 
 If the dynamic loading acting on a structure consists of concentrated forces corresponding with the displacement coordinates, the load vector of Eq. (9-2) can be written directly. In general, however, the load is applied at other points as well as the nodes and may include distributed loadings. In this case, the load terms in Eq. (9-2) are generalized forces associated with the corresponding displacement components.  
-
+如果作用在结构上的动载荷由与位移坐标相对应的集中力组成，则式(9-2)的载荷向量可以直接写出。然而，通常情况下，载荷除了作用在节点上，也作用在其他点上，并且可能包括分布载荷。在这种情况下，式(9-2)中的载荷项是与相应的位移分量相关联的广义力。
 Two procedures which can be applied in the evaluation of these generalized forces are described in the following paragraphs.  
-
-# Static Resultants  
+以下段落描述了两种可用于评估这些广义力的方法。
+## Static Resultants静态合力
 
 The most direct means of determining the effective nodal forces generated by loads distributed between the nodes is by application of the principles of simple statics; in other words, the nodal forces are defined as a set of concentrated loads which are statically equivalent to the distributed loading. In effect, the analysis is made as though the actual loading were applied to the structure through a series of simple beams supported at the nodal points. The reactive forces developed at the supports then become the concentrated nodal forces acting on the structure. In this type of analysis it is evident that generalized forces will be developed corresponding only to the translational degrees of freedom; the rotational nodal forces will be zero unless external moments are applied directly to the joints.  
-
-# Consistent Nodal Loads  
+确定由节点之间分布载荷产生的有效节点力最直接的方法是应用简单静力学原理；换句话说，节点力被定义为一组与分布载荷静力等效的集中载荷。实际上，分析是这样进行的，就好像实际载荷是通过一系列支撑在节点处的简支梁施加到结构上一样。在支座处产生的反作用力随后成为作用在结构上的集中节点力。在这种类型的分析中，显而易见的是，产生的广义力将仅对应于平移自由度；除非外部力矩直接施加到节点上，否则旋转节点力将为零。
+## Consistent Nodal Loads一致的节点载荷  
 
 A second procedure which can be used to evaluate nodal forces corresponding to all nodal degrees of freedom can be developed from the finite-element concept. This procedure employs the principle of virtual displacements in the same way as in evaluating the consistent-mass matrix, and the generalized nodal forces which are derived are called the consistent nodal loads. Consider the same beam segment as in the consistent-mass analysis but subjected to the externally applied dynamic loading shown in Fig. 10-8. When a virtual displacement $\delta v_{1}$ is applied, as shown in the sketch, and external and internal work are equated, the generalized force corresponding to $v_{1}$ is  
-
+从有限元概念中可以推导出第二种方法，用于评估对应于所有节点自由度的节点力。该方法采用虚位移原理，其方式与评估一致质量矩阵时相同，并且推导出的广义节点力被称为一致节点载荷。考虑与一致质量分析中相同的梁段，但其受到图10-8所示的外部施加的动态载荷。当施加虚位移 $\delta v_{1}$（如草图所示），并且外部功和内部功相等时，对应于 $v_{1}$ 的广义力为
 $$
 p_{1}(t)=\int_{0}^{L}p(x,t)\,\psi_{1}(x)\,d x
 $$  
@@ -441,7 +478,7 @@ $$
 FIGURE 10-8 Virtual nodal translation of a laterally loaded beam.  
 
 Thus, the element generalized loads can be expressed in general as  
-
+因此，单元广义载荷一般可以表示为
 $$
 p_{i}(t)=\int_{0}^{L}p(x,t)\,\psi_{i}(x)\,d x
 $$  
@@ -449,21 +486,23 @@ $$
 The generalized load $p_{3}$ corresponding to $v_{3}\,=\,\theta_{a}$ is an external moment applied at point $a$ . The positive sense of the generalized loads corresponds to the positive coordinate axes. The equivalence of Eq. (10-32) to the corresponding term in the fourth of Eqs. (8-18) should be noted.  
 
 For the loads to be properly called consistent, the interpolation functions $\psi_{i}(x)$ used in Eq. (10-32) must be the same as those used to define the element stiffness coefficients. If linear interpolation functions  
+对应于 $v_{3}\,=\,\theta_{a}$ 的广义载荷 $p_{3}$ 是施加在点 $a$ 上的一个外力矩。广义载荷的正方向对应于正坐标轴。应该注意式 (10-32) 与式 (8-18) 中第四个方程的对应项的等效性。
 
+为了使载荷能够被恰当地称为协调载荷，式 (10-32) 中使用的插值函数 $\psi_{i}(x)$ 必须与用于定义单元刚度系数的插值函数相同。如果线性插值函数
 $$
 \psi_{1}(x)=1-\frac{x}{L}\qquad\qquad\psi_{2}(x)=\frac{x}{L}
 $$  
 
 were used instead, Eq. (10-32) would provide the static nodal resultants; in general this is the easiest way to compute the statically equivalent loads.  
-
+如果改为使用，方程 (10-32) 将提供静力节点合力；通常这是计算静力等效载荷最简单的方法。
 In some cases, the applied loading may have the special form  
-
+在某些情况下，施加的载荷可能具有特殊形式
 $$
 p(x,t)=\chi(x)\,f(t)
 $$  
 
 that is, the form of load distribution $\chi(x)$ does not change with time; only its amplitude changes. In this case the generalized force becomes  
-
+也就是说，载荷分布形式 $\chi(x)$ 不随时间变化；只有其幅值发生变化。在这种情况下，广义力变为
 $$
 p_{i}(t)=f(t)\,\int_{0}^{L}\chi(x)\,\psi_{i}(x)\,d x
 $$  
@@ -471,12 +510,16 @@ $$
 which shows that the generalized force has the same time variation as the applied loading; the integral indicates the extent to which the load participates in developing the generalized force.  
 
 When the generalized forces acting on each element have been evaluated by Eq. (10-32), the total effective load acting at the nodes of the assembled structure can be obtained by a superposition procedure equivalent to the direct stiffness process.  
+这表明广义力具有与施加载荷相同的时间变化；积分表示载荷参与产生广义力的程度。
 
-# 10-5 GEOMETRIC STIFFNESS  
+当通过式(10-32)评估了作用在每个单元上的广义力后，作用在组装结构节点上的总有效载荷可以通过等效于直接刚度法的叠加过程获得。
 
-# Linear Approximation  
+# 10-5 GEOMETRIC STIFFNESS几何刚度  
+
+## Linear Approximation线性近似  
 
 The geometric-stiffness property represents the tendency toward buckling induced in a structure by axially directed load components; thus it depends not only on the configuration of the structure but also on its condition of loading. In this discussion, it is assumed that the forces tending to cause buckling are constant during the dynamic loading; thus they are assumed to result from an independent static loading and are not significantly affected by the dynamic response of the structure. (When these forces do vary significantly with time, they result in a time-varying stiffness property, and analysis procedures based on superposition are not valid for such a nonlinear system.)  
+几何刚度特性代表了由轴向载荷分量在结构中引起的屈曲趋势；因此，它不仅取决于结构的构型，还取决于其载荷条件。在本次讨论中，假设趋于引起屈曲的力在动态载荷作用期间是恒定的；因此，它们被假定为由独立的静态载荷产生，并且不受结构动态响应的显著影响。（当这些力确实随时间显著变化时，它们会导致时变刚度特性，并且基于叠加原理的分析程序对于此类非线性系统无效。）
 
 ![](47aa4205d48fcfb427ce6b396eecce81e7f8722fa9c4e4b0280d5bda4ea881c5.jpg)  
 

学术讲座-交流-面试/2025.11.04 胡志强教授交流.md

@@ -0,0 +1,22 @@
+
+
+整体动力响应 数值编程
+
+人工智能技术的应用
+
+如何实现数字孪生
+
+
+雷诺数和弗劳德数相似，现在如何平衡
+牺牲气动力，用风扇替代，可以模拟推力，忽略叶片惯性力
+
+水平漫漂 算不准，比模型试验小20%
+动态电缆对水平位移敏感
+
+波浪二阶漫漂，风也有低频效应，漂得更远了
+
+SADA具体流程？
+
+如何训练得到？darwind plus
+
+电缆 系泊缆老坏

学术讲座-交流-面试/2025.11.7 陈哲院士交流.md

@@ -0,0 +1,6 @@
+
+丹麦奥尔堡能源技术系教授
+
+
+能源转型中的电力系统
+