diff --git a/.obsidian/plugins/copilot/data.json b/.obsidian/plugins/copilot/data.json
index 87cb51e..9ee3207 100644
--- a/.obsidian/plugins/copilot/data.json
+++ b/.obsidian/plugins/copilot/data.json
@@ -144,8 +144,8 @@
       "provider": "google",
       "enabled": true,
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-      "baseUrl": "http://60.205.246.14:8000",
-      "apiKey": "gyz",
+      "baseUrl": "",
+      "apiKey": "AIzaSyAnULu8WrFeKeOpW2SoJdqXGu4FrDcyB2I",
       "isEmbeddingModel": false,
       "capabilities": [
         "reasoning",
@@ -153,7 +153,7 @@
         "websearch"
       ],
       "stream": true,
-      "displayName": "gemini-2.5-flash",
+      "displayName": "gemini-2.5-flash-gemini",
       "enableCors": true
     },
     {
@@ -172,6 +172,21 @@
       "stream": true,
       "displayName": "gemini-2.5-pro",
       "enableCors": true
+    },
+    {
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+      "provider": "ollama",
+      "enabled": true,
+      "isBuiltIn": false,
+      "baseUrl": "https://possibly-engaged-filly.ngrok-free.app/",
+      "apiKey": "",
+      "isEmbeddingModel": false,
+      "capabilities": [
+        "reasoning"
+      ],
+      "stream": true,
+      "displayName": "gpt-oss:20b",
+      "enableCors": true
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diff --git a/书籍/力学书籍/力学/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library)/auto/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library).md b/书籍/力学书籍/力学/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library)/auto/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library).md
index c34836b..50316fe 100644
--- a/书籍/力学书籍/力学/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library)/auto/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library).md	
+++ b/书籍/力学书籍/力学/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library)/auto/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library).md	
@@ -983,27 +983,26 @@ $$
 The response given by the first term of Eq. (2-29) is depicted in Fig. 2-5 as a vector representing the complex constant $G_{1}$ rotating in the counterclockwise direction with the angular velocity $\omega$ ; also shown are its real and imaginary constants. It will be noted that the resultant response vector $\left(G_{R}+i\,G_{I}\right)\exp(i\omega t)$ leads vector $G_{R}\exp(i\omega t)$ by the phase angle $\theta$ ; moreover it is evident that the response also can be expressed in terms of the absolute value, $\overline{G}$ , and the combined angle $(\omega t+\theta)$ . Examination of the second term of Eq. (2-29) shows that the response associated with it is entirely equivalent to that shown in Fig. 2-5 except that the resultant vector $\overline{{G}}\exp[-i(\omega t\!+\!\theta)]$ is rotating in the clockwise direction and the phase angle by which it leads the component $G_{R}\exp(-i\omega t)$ also is in the clockwise direction.  
 由方程 (2-29) 的第一项给出的响应在图 2-5 中描绘为一个向量，表示复常数 $G_{1}$ 以角速度 $\omega$ 沿逆时针方向旋转；图中还显示了它的实部和虚部常数。值得注意的是，合响应向量 $\left(G_{R}+i\,G_{I}\right)\exp(i\omega t)$ 以相位角 $\theta$ 超前向量 $G_{R}\exp(i\omega t)$ ；此外，显然响应也可以用绝对值 $\overline{G}$ 和组合角 $(\omega t+\theta)$ 来表示。检查方程 (2-29) 的第二项表明，与之相关的响应与图 2-5 中所示的响应完全等效，不同之处在于合向量 $\overline{{G}}\exp[-i(\omega t\!+\!\theta)]$ 沿顺时针方向旋转，并且它超前分量 $G_{R}\exp(-i\omega t)$ 的相位角也沿顺时针方向。
 
-The two counter-rotating vectors $\overline{{G}}\exp[i(\omega t+\theta)]$ and $\overline{{G}}\exp[-i(\omega t+\theta)]$ that represent the total free-vibration response given by Eq. (2-29) are shown in Fig. 2-6;  
-代表由式 (2-29) 给出的总自由振动响应的两个反向旋转向量 $\overline{{G}}\exp[i(\omega t+\theta)]$ 和 $\overline{{G}}\exp[-i(\omega t+\theta)]$ 如 图 2-6 所示；
+
 ![](971b6f64e38f1091af1b6e11ff5c9363f0593ab047d236d237211c3a358ccd87.jpg)  
 
 
 FIGURE 2-5 Portrayal of first term of Eq. (2-29).  
 
-it is evident here that the imaginary components of the two vectors cancel each other leaving only the real vibratory motion  
-
+The two counter-rotating vectors $\overline{{G}}\exp[i(\omega t+\theta)]$ and $\overline{{G}}\exp[-i(\omega t+\theta)]$ that represent the total free-vibration response given by Eq. (2-29) are shown in Fig. 2-6;  it is evident here that the imaginary components of the two vectors cancel each other leaving only the real vibratory motion  
+代表由式 (2-29) 给出的总自由振动响应的两个反向旋转向量 $\overline{{G}}\exp[i(\omega t+\theta)]$ 和 $\overline{{G}}\exp[-i(\omega t+\theta)]$ 如 图 2-6 所示；此处显而易见，两个向量的虚部相互抵消，只留下真实的振动运动。
 $$
 v(t)=2\;\overline{{G}}\;\cos(\omega t+\theta)
 $$  
 
 An alternative for this real motion expression may be derived by applying the Euler transformation Eq. (2-23a) to Eq. (2-29), with the result  
-
+这种真实运动表达式的另一种形式可以通过将欧拉变换方程 Eq. (2-23a) 应用于方程 Eq. (2-29) 推导出来，结果是
 $$
 v(t)=A\,\cos\omega t+B\,\sin\omega t
 $$  
 
 in which $A\,=\,2G_{R}$ and $B\:=\:-2G_{I}$ . The values of these two constants may be determined from the initial conditions, that is, the displacement $v(0)$ and velocity $\dot{v}(0)$ at time $t=0$ when the free vibration was set in motion. Substituting these into Eq. (2-31) and its first time derivative, respectively, it is easy to show that  
-
+其中 $A\,=\,2G_{R}$ 且 $B\:=\:-2G_{I}$ 。这两个常数的值可以根据初始条件确定，即当自由振动开始时，在 $t=0$ 时刻的位移 $v(0)$ 和速度 $\dot{v}(0)$。将这些代入式 (2-31) 及其一阶时间导数，可以很容易地证明
 $$
 v(0)=A=2G_{R}\qquad\qquad{\frac{\dot{v}(0)}{\omega}}=B=-2G_{I}
 $$  
@@ -1015,12 +1014,12 @@ v(t)=v(0)\ \cos\omega t+{\frac{{\dot{v}}(0)}{\omega}}\ \sin\omega t
 $$  
 
 This solution represents a simple harmonic motion (SHM) and is portrayed graphically in Fig. 2-7. The quantity $\omega$ , which we have identified previously as the angular velocity (measured in radians per unit of time) of the vectors rotating in the complex plane, also is known as the circular frequency. The cyclic frequency, usually referred to as the frequency of motion, is given by  
-
+该解表示一个简谐运动 (SHM)，并在图 2-7 中以图形方式描绘。量 $\omega$，我们之前已将其识别为在复平面中旋转的向量的角速度（以弧度每单位时间测量），也称为圆频率。循环频率，通常被称为运动频率，由下式给出
 $$
 f={\frac{\omega}{2\pi}}
 $$  
 
-Its reciprocal  
+Its reciprocal  其倒数
 
 $$
 {\frac{1}{f}}={\frac{2\pi}{\omega}}=T
@@ -1031,8 +1030,13 @@ FIGURE 2-7 Undamped free-vibration response.
 
 is the time required to complete one cycle and is called the period of the motion. Usually for structural and mechanical systems the period $T$ is measured in seconds and the frequency is measured in cycles per second, commonly referred to as Hertz $(H z)$ .  
 
-The motion represented by Eq. (2-33) and depicted by Fig. 2-7 also may be interpreted in terms of a pair of vectors, v(0) and v˙(ω0) rotating counter-clockwise in the complex plane with angular velocity $\omega$ , as shown in Fig. 2-8. Using previously stated relations among the free-vibration constants and the initial conditions, it may be seen that Fig. 2-8 is equivalent to Fig. 2-5, but with double amplitude and with a negative phase angle to correspond with positive initial conditions. Accordingly, the amplitude $\rho=2\overline{{G}}$ , and as shown by Eq. (2-30) the free vibration may be expressed as  
+The motion represented by Eq. (2-33) and depicted by Fig. 2-7 also may be interpreted in terms of a pair of vectors, v(0) and ${\frac{{\dot{v}}(0)}{\omega}}$ rotating counter-clockwise in the complex plane with angular velocity $\omega$ , as shown in Fig. 2-8. Using previously stated relations among the free-vibration constants and the initial conditions, it may be seen that Fig. 2-8 is equivalent to Fig. 2-5, but with double amplitude and with a negative phase angle to correspond with positive initial conditions. Accordingly, the amplitude $\rho=2\overline{{G}}$ , and as shown by Eq. (2-30) the free vibration may be expressed as  
+是完成一个循环所需的时间，称为运动周期。通常，对于结构和机械系统，周期 $T$ 以秒为单位测量，频率以每秒循环次数测量，通常称为赫兹 $(H z)$。
 
+![](6a5d4f92e2ed963aed8ef60b2055c027587a098eaf7d50c3d4e1373e2bd35c6c.jpg)  
+FIGURE 2-8 Rotating vector representation of undamped free vibration.  
+
+由方程式 (2-33) 表示并由图 2-7 描绘的运动也可以根据一对向量 v(0) 和 ${\frac{{\dot{v}}(0)}{\omega}}$ 来解释，它们在复平面中以角速度 $\omega$ 逆时针旋转，如图 2-8 所示。使用先前陈述的自由振动常数和初始条件之间的关系，可以看出图 2-8 等效于图 2-5，但具有双倍振幅和负相位角以对应正初始条件。因此，振幅 $\rho=2\overline{{G}}$，并且如方程式 (2-30) 所示，自由振动可以表示为
 $$
 v(t)=\rho\,\cos(\omega t+\theta)
 $$  
@@ -1052,60 +1056,59 @@ $$
 # 2-6 DAMPED FREE VIBRATIONS  
 
 If damping is present in the system, the solution of Eq. (2-25) which defines the response is  
-
+如果系统存在阻尼，定义响应的式 (2-25) 的解是
 $$
 s_{1,2}=-\frac{c}{2m}\pm\sqrt{\left(\frac{c}{2m}\right)^{2}-\omega^{2}}
 $$  
 
-Three types of motion are represented by this expression, according to whether the quantity under the square-root sign is positive, negative, or zero. It is convenient to discuss first the case when the radical term vanishes, which is called the criticallydamped condition.  
+Three types of motion are represented by this expression, according to whether the quantity under the square-root sign is positive, negative, or zero. It is convenient to discuss first the case when the radical term vanishes, which is called the critically-damped condition.  
+此表达式表示三种运动，具体取决于根号下的量是正、负还是零。方便起见，我们首先讨论根式项消失的情况，这被称为临界阻尼条件。
 
-![](6a5d4f92e2ed963aed8ef60b2055c027587a098eaf7d50c3d4e1373e2bd35c6c.jpg)  
-FIGURE 2-8 Rotating vector representation of undamped free vibration.  
-
-# Critically-Damped Systems  
+## Critically-Damped Systems  
 
 If the radical term in Eq. (2-39) is set equal to zero, it is evident that $c/2m=\omega$ ; thus, the critical value of the damping coefficient, $c_{c}$ , is  
-
+如果式 (2-39) 中的根号项设为零，显然 $c/2m=\omega$；因此，阻尼系数的临界值 $c_{c}$ 是
 $$
 c_{c}=2\,m\,\omega
 $$  
 
 Then both values of $s$ given by Eq. (2-39) are the same, i.e.,  
-
+那么，由式 (2-39) 给出的 $s$ 的两个值是相同的，即
 $$
 s_{1}=s_{2}=-\frac{c_{c}}{2m}=-\omega
 $$  
 
 The solution of Eq. (2-20) in this special case must now be of the form  
-
+方程 (2-20) 在这种特殊情况下的解现在必须是以下形式
 $$
 v(t)=(G_{1}+G_{2}\,t)\;\exp(-\omega t)
 $$  
 
 in which the second term must contain $t$ since the two roots of Eq. (2-25) are identical. Because the exponential term $\exp(-\omega t)$ is a real function, the constants $G_{1}$ and $G_{2}$ must also be real.  
+其中第二项必须包含 $t$，因为方程 (2-25) 的两个根是重合的。由于指数项 $\exp(-\omega t)$ 是一个实函数，因此常数 $G_{1}$ 和 $G_{2}$ 也必须是实数。
 
 Using the initial conditions $v(0)$ and $\dot{v}(0)$ , these constants can be evaluated leading to  
-
+利用初始条件 $v(0)$ 和 $\dot{v}(0)$，可以求出这些常数，从而得到
 $$
 v(t)=\big[v(0)\;(1-\omega t)+\dot{v}(0)\;t\big]\;\exp(-\omega t)
 $$  
 
 which is portrayed graphically in Fig. 2-9 for positive values of $v(0)$ and $\dot{v}(0)$ . Note that this free response of a critically-damped system does not include oscillation about the zero-deflection position; instead it simply returns to zero asymptotically in accordance with the exponential term of Eq. (2-43). However, a single zero-displacement crossing would occur if the signs of the initial velocity and displacement were different from each other. A very useful definition of the critically-damped condition described above is that it represents the smallest amount of damping for which no oscillation occurs in the free-vibration response.  
-
+其在图2-9中以图形方式描绘，适用于$v(0)$和$\dot{v}(0)$为正值的情况。注意，临界阻尼系统的这种自由响应不包括围绕零变形位置的振荡；相反，它根据式(2-43)的指数项渐近地返回到零。然而，如果初始速度和位移的符号彼此不同，则会发生单次零位移穿越。上述临界阻尼条件的一个非常有用的定义是，它代表了在自由振动响应中不发生振荡的最小阻尼量。
 ![](37469d268c30aa607f662652a1ace851e603e99b13ca0d2c5a2328e1308480ad.jpg)  
 
 FIGURE 2-9 Free-vibration response with critical damping.  
 
-# Undercritically-Damped Systems  
+## Undercritically-Damped Systems  
 
 If damping is less than critical, that is, if $c<c_{c}$ (i.e., $c<2m\omega_{\perp}$ ), it is apparent that the quantity under the radical sign in Eq. (2-39) is negative. To evaluate the free-vibration response in this case, it is convenient to express damping in terms of a damping ratio $\xi$ which is the ratio of the given damping to the critical value;  
-
+如果阻尼小于临界阻尼，即如果 $c<c_{c}$ (亦即 $c<2m\omega_{\perp}$ )，显然，式 (2-39) 中根号下的量为负值。为了评估这种情况下的自由振动响应，方便地用阻尼比 $\xi$ 来表示阻尼，阻尼比 $\xi$ 是给定阻尼与临界值之比；
 $$
 \xi\equiv\frac{c}{c_{c}}=\frac{c}{2m\omega}
 $$  
 
 Introducing Eq. (2-44) into Eq. (2-39) leads to  
-
+将方程 (2-44) 代入方程 (2-39)，可得
 $$
 s_{1,2}=-\xi\omega\pm i\,\omega_{D}
 $$  
@@ -1117,23 +1120,26 @@ $$
 $$  
 
 is the free-vibration frequency of the damped system. Making use of Eq. (2-21) and the two values of $s$ given by Eq. (2-45), the free-vibration response becomes  
-
+是阻尼系统的自由振动频率。利用方程 (2-21) 和由方程 (2-45) 给出的 $s$ 的两个值，自由振动响应变为
 $$
 v(t)=\big[G_{1}\,\exp(i\omega_{D}t)+G_{2}\,\exp(-i\omega_{D}t)\big]\;\exp(-\xi\omega t)
 $$  
 
 in which the constants $G_{1}$ and $G_{2}$ must be complex conjugate pairs for the response $v(t)$ to be real, i.e., $G_{1}=G_{R}+i\,G_{I}$ and $G_{2}=G_{R}-i\,G_{I}$ similar to the undamped case shown by Eq. (2-27).  
+其中，常数 $G_{1}$ 和 $G_{2}$ 必须是复共轭对，以便响应 $v(t)$ 为实数，即 $G_{1}=G_{R}+i\,G_{I}$ 且 $G_{2}=G_{R}-i\,G_{I}$，这类似于公式 (2-27) 所示的无阻尼情况。
 
 The response given by Eq. (2-47) can be represented by vectors in the complex plane similar to those shown in Fig. 2-6 for the undamped case; the only difference is that the damped circular frequency $\omega_{D}$ must be substituted for the undamped circular frequency $\omega$ and the magnitudes of the vectors must be forced to decay exponentially with time in accordance with the term outside of the brackets, $\exp(-\xi\omega t)$ .  
 
 Following the same procedure used in arriving at Eq. (2-31), Eq. (2-47) also can be expressed in the equivalent trigonometric form  
+由式(2-47)给出的响应可以用复平面中的向量表示，类似于图2-6中所示的无阻尼情况；唯一的区别是，必须用阻尼圆频率$\omega_{D}$代替无阻尼圆频率$\omega$，并且向量的幅值必须根据括号外的项$\exp(-\xi\omega t)$随时间呈指数衰减。
 
+按照推导式(2-31)所用的相同步骤，式(2-47)也可以表示为等效的三角函数形式
 $$
 v(t)=\left[A\,\cos\omega_{D}t+B\,\sin\omega_{D}t\right]\,\exp(-\xi\omega t)
 $$  
 
 where $A=2G_{R}$ and $B=-2G_{I}$ . Using the initial conditions $v(0)$ and $\dot{v}(0)$ , constants $A$ and $B$ can be evaluated leading to  
-
+其中 $A=2G_{R}$ 且 $B=-2G_{I}$。利用初始条件 $v(0)$ 和 $\dot{v}(0)$，可以求出常数 $A$ 和 $B$，从而得到
 $$
 v(t)=\left[v(0)\,\cos\omega_{D}t+\left({\frac{{\dot{v}}(0)+v(0)\xi\omega}{\omega_{D}}}\right)\,\sin\omega_{D}t\right]\,\exp(-\xi\omega t)
 $$  
@@ -1153,7 +1159,9 @@ $$
 Note that for low damping values which are typical of most practical structures, $\xi<20\%$ , the frequency ratio $\omega_{D}/\omega$ as given by Eq. (2-46) is nearly equal to unity. The relation between damping ratio and frequency ratio may be depicted graphically as a circle of unit radius as shown in Fig. 2-10.  
 
 A plot of the response of an undercritically-damped system subjected to an initial displacement $v(0)$ but starting with zero velocity is shown in Fig. 2-11. It is of interest to note that the underdamped system oscillates about the neutral position, with a constant circular frequency $\omega_{D}$ . The rotating-vector representation of Eq. (2-47) is equivalent to Fig. 2-6 except that $\omega$ is replaced by $\omega_{D}$ and the lengths of the vectors diminish exponentially as the response damps out.  
+请注意，对于大多数实际结构中常见的低阻尼值（$\xi<20\%$），由式 (2-46) 给出的频率比 $\omega_{D}/\omega$ 几乎等于1。阻尼比与频率比之间的关系可以图形化地表示为单位半径的圆，如图 2-10 所示。
 
+图 2-11 显示了欠阻尼系统在受到初始位移 $v(0)$ 但以零速度开始时的响应曲线。值得注意的是，欠阻尼系统以恒定的圆频率 $\omega_{D}$ 围绕中性位置振荡。式 (2-47) 的旋转矢量表示等效于图 2-6，不同之处在于 $\omega$ 被 $\omega_{D}$ 替换，并且随着响应的衰减，矢量的长度呈指数衰减。
 ![](2d37b0079cbf4769d4ea85693785a1f053205cdee3f60dd11567b89bead35dd1.jpg)  
 
 ![](5527ad04f088bf9f0312e85221e194eabecae071bcbbb37c38bb49acf51a9e14.jpg)  
@@ -1162,19 +1170,21 @@ FIGURE 2-11 Free-vibration response of undercritically-damped system.
 The true damping characteristics of typical structural systems are very complex and difficult to define. However, it is common practice to express the damping of such real systems in terms of equivalent viscous-damping ratios $\xi$ which show similar decay rates under free-vibration conditions. Therefore, let us now relate more fully the viscous-damping ratio $\xi$ to the free-vibration response shown in Fig. 2-11.  
 
 Consider any two successive positive peaks such as $v_{n}$ and $v_{n+1}$ which occur at times $\textstyle n\big(\frac{2\pi}{\omega_{D}}\big)$ and $\begin{array}{r}{(n+1)\frac{2\pi}{\omega_{D}}}\end{array}$ , respectively. Using Eq. (2-50), the ratio of these two successive values is given by  
+典型结构系统的真实阻尼特性非常复杂且难以定义。然而，通常的做法是将此类真实系统的阻尼用等效黏性阻尼比 $\xi$ 来表示，它们在自由振动条件下表现出相似的衰减率。因此，现在让我们更充分地将黏性阻尼比 $\xi$ 与图 2-11 所示的自由振动响应关联起来。
 
+考虑任意两个连续的正峰值，例如 $v_{n}$ 和 $v_{n+1}$，它们分别发生在时间 $\textstyle n\big(\frac{2\pi}{\omega_{D}}\big)$ 和 $\begin{array}{r}{(n+1)\frac{2\pi}{\omega_{D}}}\end{array}$。使用公式 (2-50)，这两个连续值的比率由下式给出
 $$
 v_{n}/v_{n+1}=\exp(2\pi\xi\omega/\omega_{D})
 $$  
 
 Taking the natural logarithm (ln) of both sides of this equation and substituting $\omega_{D}=$ $\omega\sqrt{1-\xi^{2}}$ , one obtains the so-called logarithmic decrement of damping, $\delta$ , defined by  
-
+对该方程两边取自然对数 (ln) 并代入 $\omega_{D}=$ $\omega\sqrt{1-\xi^{2}}$，得到所谓的阻尼对数衰减率 $\delta$，其定义为
 $$
 \delta\equiv\ln{\frac{v_{n}}{v_{n+1}}}=\frac{2\pi\xi}{\sqrt{1-\xi^{2}}}
 $$  
 
 For low values of damping, Eq. (2-54) can be approximated by  
-
+对于低阻尼值，方程 (2-54) 可以近似为
 $$
 \delta\doteq2\pi\xi
 $$  
@@ -1186,25 +1196,25 @@ $$
 $$  
 
 Sufficient accuracy is obtained by retaining only the first two terms in the Taylor’s series expansion on the right hand side, in which case  
-
+在右侧泰勒级数展开式中，仅保留前两项即可获得足够的精度，此时
 $$
 \xi\doteq\frac{v_{n}-v_{n+1}}{2\pi\,v_{n+1}}
 $$  
 
 To illustrate the accuracy of Eq. (2-57), the ratio of the exact value of $\xi$ as given by Eq. (2-54) to the approximate value as given by Eq. (2-57) is plotted against the approximate value in Fig. 2-12. This graph permits one to correct the damping ratio obtained by the approximate method.  
-
+为了说明方程 (2-57) 的准确性，图 2-12 绘制了由方程 (2-54) 给出的 $\xi$ 的精确值与由方程 (2-57) 给出的近似值之比随近似值的变化曲线。该图可以修正通过近似方法获得的阻尼比。
 ![](5e00bdf43f079f1d9ddf10a69422338d565d9365da0468795c008c234550d70b.jpg)  
 
 ![](933dae84b2047fceb9b09e403e5f728975fb944adcc1d2af94ee1ac85cc7393b.jpg)  
 
 For lightly damped systems, greater accuracy in evaluating the damping ratio can be obtained by considering response peaks which are several cycles apart, say $m$ cycles; then  
-
+对于轻阻尼系统，通过考虑相隔若干周期（例如 $m$ 个周期）的响应峰值，可以获得更高的阻尼比评估精度；则
 $$
 \ln{\frac{v_{n}}{v_{n+m}}}={\frac{2m\pi\xi}{\sqrt{1-\xi^{2}}}}
 $$  
 
 which can be simplified for low damping to an approximate relation equivalent to Eq. (2-57):  
-
+其对于低阻尼可简化为一个近似关系，等同于公式 (2-57)：
 $$
 \xi\doteq\frac{v_{n}-v_{n+m}}{2\,m\,\pi\,v_{n+m}}
 $$  
@@ -1215,6 +1225,11 @@ Example E2-1. A one-story building is idealized as a rigid girder supported by w
 
 From these data, the following dynamic behavioral properties are determined:  
 
+当实验观测到阻尼自由振动时，估算阻尼比的一个方便方法是计算振幅减小50%所需的循环次数。在这种情况下使用的关系以图2-13的形式给出。作为一条快速经验法则，方便记住的是，对于临界阻尼百分比等于10%、5%和2.5%的情况，相应的振幅分别在大约一、二和四个循环中减小50%。
+
+例 E2-1。一层建筑被理想化为由无质量柱支撑的刚性大梁，如图E2-1所示。为了评估该结构的动力特性，进行了一项自由振动试验，其中屋顶系统（刚性大梁）通过液压千斤顶横向位移，然后突然释放。在千斤顶操作过程中，观察到需要20 kips [9,072 kg] 的力才能使大梁位移0.20 in [0.508 cm]。在瞬时释放此初始位移后，第一次回摆时的最大位移仅为0.16 in [0.406 cm]，并且此位移循环的周期为 $T=1.40\ s e c$。
+
+根据这些数据，确定以下动力行为特性：
 ![](6c0607d3d603e35fcc3bd969fdd7c78fc66b1cb85bfc5ddf6f876718fdc6d87e.jpg)  
 
 (1) Effective weight of the girder:  
@@ -1254,7 +1269,7 @@ $$
 v_{6}=\left({\frac{v_{1}}{v_{0}}}\right)^{6}\,v_{0}=\left({\frac{4}{5}}\right)^{6}\,(0.20)=0.0524\,i n\quad[0.1331\;c m]
 $$  
 
-# Overcritically-Damped Systems  
+## Overcritically-Damped Systems  
 
 Although it is very unusual under normal conditions to have overcriticallydamped structural systems, they do sometimes occur as mechanical systems; therefore, it is useful to carry out the response analysis of an overcritically-damped system to make this presentation complete. In this case having $\xi\equiv c/c_{c}>1$ , it is convenient to write Eq. (2-39) in the form  
 
diff --git a/工作OKRs/25.9-11 OKR.canvas b/工作OKRs/25.9-11 OKR.canvas
index 8ca8f15..7102e61 100644
--- a/工作OKRs/25.9-11 OKR.canvas	
+++ b/工作OKRs/25.9-11 OKR.canvas	
@@ -6,7 +6,7 @@
 		{"id":"82708a439812fdc7","type":"text","text":"# 10月已完成\n\n","x":-220,"y":134,"width":440,"height":560},
 		{"id":"505acb3e6b119076","type":"text","text":"# 9月已完成\n\nP1 湍流 气动 多体 控制联调  done\n- 5mw 通了\n\t- 纯叶片变形\n\t- 纯塔架变形\n\t- 叶片+塔架变形 ","x":-700,"y":134,"width":440,"height":560},
 		{"id":"30cb7486dc4e224c","type":"text","text":"# 11月已完成\n\n\n\n","x":260,"y":134,"width":440,"height":560},
-		{"id":"c18d25521d773705","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\nP2 柔性部件 叶片、塔架变形算法 主线\n- 变形体动力学 简略看看ing\n- 柔性梁弯曲变形振动学习，主线 \n\t- 广义质量 刚度矩阵及含义\n\t\n- 梳理bladed动力学框架\n\t- 子结构文献阅读\n\t- 叶片模型建模 done\n- 共旋方法学习\n- DTU 变形量计算方法学习\n\n\nP1 线性化方法编写 搁置\n\nP1 气动、多体、控制、水动联调\nP2 湍流 气动 多体 控制联调 \n- 15mw呢  yaml多个模块都需要支持\n- 更换湍流风\n- dll 32位兼容 - 江\n\nP2 停机工况等调试\n\nP1 bladed对比--稳态，产出报告\n- 模态对比   两种描述方法不同，bladed方向更多，x y z deflection, x y z rotation，不好对比\n- 气动对比 aerodynamic info 轴向切向诱导因子，根部，尖部差距较大\n- 稳态变形量对比\n- 稳态变形量对比 -- steady power production loading、steady parked loading\n\nP1 稳态工况前端对接\n- 是否拆分成单独的bin，等待气动完成后开始\n- 如何接收参数  配置文件 \n\n\nP2 如何优雅的存储、输出结果。\nP2 yaw 自由度再bug确认 已知原理了\n","x":-597,"y":-803,"width":453,"height":457},
+		{"id":"c18d25521d773705","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\nP2 柔性部件 叶片、塔架变形算法 主线\n- 变形体动力学 简略看看ing\n- 柔性梁弯曲变形振动学习，主线 \n\t- 广义质量 刚度矩阵及含义\n\t\n- 梳理bladed动力学框架\n\t- 子结构文献阅读\n\t- 叶片模型建模 done\n- 共旋方法学习\n- DTU 变形量计算方法学习\n\n\nP1 线性化方法编写 搁置\n\nP1 气动、多体、控制、水动联调\nP2 湍流 气动 多体 控制联调 \n- 15mw呢  yaml多个模块都需要支持\n- 更换湍流风\n- dll 32位兼容 - 江\n\nP2 停机工况等调试\n\nP1 bladed对比--稳态运行载荷，产出报告\n- 模态对比   两种描述方法不同，bladed方向更多，x y z deflection, x y z rotation，不好对比\n- 气动对比 aerodynamic info 轴向切向诱导因子，根部，尖部差距较大\n- 气动新版本稳态跑通 done\n- 如何输出\n- 稳态变形量对比\n- 所有输出量\n\nP1 稳态工况前端对接\n- 是否拆分成单独的bin，等待气动完成后开始\n- 如何接收参数  配置文件 \n\nP1 专利\n\nP2 如何优雅的存储、输出结果。\nP2 yaw 自由度再bug确认 已知原理了\n","x":-597,"y":-803,"width":453,"height":457},
 		{"id":"86ab96a25a3bf82e","type":"text","text":" 湍流风+ 控制的联调，bladed也算一个算例\n- 加水动的联调\n- 8月份底完成这两个\n- 9月份完成停机等工况测试\n- 10月份明阳实际机型测试","x":580,"y":-803,"width":480,"height":220},
 		{"id":"e355f33c92cf18ea","type":"text","text":"9月份定常计算对接前端\n非定常测试完也对接前端","x":580,"y":-500,"width":480,"height":100},
 		{"id":"859e6853b7f1b92b","type":"text","text":"年底考核：\n专利\n线性化模块","x":1200,"y":-803,"width":320,"height":110}