Site updated: 2020-05-26 13:56:41

Author: Yu Xiong

2016/02/25/mathSymbol/index.html

@@ -302,10 +302,11 @@ <h1 class="card-title h3 mb-2">mathSymbol</h1>
                     <article id="post-content">
                         <p>Here I will test some math symbols that I just install MathJax plugin based hexo-math package.<br>I guess it shall be very similar to LaTeX format.</p>
 <p>This is an expression $ x + y = 5 $ which $ x = 2 $ and $ y =2 $.</p>
-<p>$$ (\sin 3 \psi)^2 + \frac{2}{3} $$</p>
-<p>let’s what will be generated! here.</p>
-<p>$$\frac{\partial u}{\partial t}<br>= h^2 \left( \frac{\partial^2 u}{\partial x^2} +<br>\frac{\partial^2 u}{\partial y^2} +<br>\frac{\partial^2 u}{\partial z^2}\right)$$</p>
-<p>This equation $ \cos 2\theta = \cos^2 \theta - \sin^2 \theta =  2 \cos^2 \theta - 1 $ is inline.</p>
+<script type="math/tex; mode=display">(\sin 3 \psi)^2 + \frac{2}{3}</script><p>let’s what will be generated! here.</p>
+<script type="math/tex; mode=display">\frac{\partial u}{\partial t}
+= h^2 \left( \frac{\partial^2 u}{\partial x^2} +
+\frac{\partial^2 u}{\partial y^2} +
+\frac{\partial^2 u}{\partial z^2}\right)</script><p>This equation $ \cos 2\theta = \cos^2 \theta - \sin^2 \theta =  2 \cos^2 \theta - 1 $ is inline.</p>
 
                     </article>
 
@@ -435,7 +436,7 @@ <h1 class="card-title h3 mb-2">mathSymbol</h1>
 
 <!-- ### Custom Footer ### --><!-- hexo-inject:begin --><!-- Begin: Injected MathJax -->
 <script type="text/x-mathjax-config">
-  MathJax.Hub.Config("");
+  MathJax.Hub.Config({"tex2jax":{"inlineMath":[["$","$"],["\\(","\\)"]],"skipTags":["script","noscript","style","textarea","pre","code"],"processEscapes":true},"TeX":{"equationNumbers":{"autoNumber":"AMS"}}});
 </script>
 
 <script type="text/x-mathjax-config">
@@ -447,7 +448,7 @@ <h1 class="card-title h3 mb-2">mathSymbol</h1>
   });
 </script>
 
-<script type="text/javascript" src="custom_mathjax_source">
+<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 <!-- End: Injected MathJax -->
 <!-- hexo-inject:end -->

2016/03/07/大学-注释译文及导读指南/index.html

@@ -441,7 +441,7 @@ <h2 id="挥舞-Flapping-和周期变矩-Feathering-相等性"><a href="#挥舞-F
 
 <!-- ### Custom Footer ### --><!-- hexo-inject:begin --><!-- Begin: Injected MathJax -->
 <script type="text/x-mathjax-config">
-  MathJax.Hub.Config("");
+  MathJax.Hub.Config({"tex2jax":{"inlineMath":[["$","$"],["\\(","\\)"]],"skipTags":["script","noscript","style","textarea","pre","code"],"processEscapes":true},"TeX":{"equationNumbers":{"autoNumber":"AMS"}}});
 </script>
 
 <script type="text/x-mathjax-config">
@@ -453,7 +453,7 @@ <h2 id="挥舞-Flapping-和周期变矩-Feathering-相等性"><a href="#挥舞-F
   });
 </script>
 
-<script type="text/javascript" src="custom_mathjax_source">
+<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 <!-- End: Injected MathJax -->
 <!-- hexo-inject:end -->

2016/03/13/Helicopter-Rotor-Referece-Axes/index.html

@@ -335,10 +335,10 @@ <h2 id="旋翼系统的结构"><a href="#旋翼系统的结构" class="headerlin
 <ul>
 <li><p>水平铰的作用：在直升机前飞时，由于飞行速度的存在，使得旋翼前行桨叶的相对气流速度大于后行桨叶的相对气流速度，从而使前行桨叶产生的拉力大于后行桨叶的拉力。在没有水平铰时，两侧桨叶拉力大小不等将构成滚转力矩使直升机滚转。有<br>水平铰时，情况不同。前行桨叶拉力大，便绕水平铰向上挥舞；后行桨叶拉力小，便绕水平铰向下挥舞。这样不平衡的滚转力矩无法传到机身，从而避免了直升机前飞中产生滚转。</p>
 </li>
-<li><p>垂直铰（即垂直关节）的作用：直升机前飞时，桨叶在绕轴转动时要绕水平铰挥舞，这就造成桨叶重心距旋翼轴的距离不断变化，如图1-3（b）所示。从而引起周期交变的哥氏力。所谓哥氏力（也叫回转力）是物体在旋转系统中，一面旋转一面又有<br>相对于该系统运动时所出现的一种附加惯性力。其方向顺旋转方向。其矢量表达式为<br>$$ F = 2 m \Omega V $$<br>公式中 $m$ – 桨叶质量，$\Omega$ – 旋翼旋转角速度，$V$ – 桨叶重心对旋翼轴径向速度。<br>一片桨叶的哥氏力的最大值高达桨叶自重的七倍以上。巨大的哥氏力必然会在旋转面内造成很大的交变弯矩，如果无垂直铰，桨叶根部会材料疲劳而损坏，如果传到机身，将引起机体震动加剧。有了垂直铰，桨叶绕垂直铰摆动一个角度，从而使桨叶根部所受的沿旋转方向的交变弯矩大大减少。</p>
-</li>
-<li><p>轴向铰（轴向关节）的作用：通过操作机构，可使桨叶绕轴向铰偏转，以改变桨距角的大小，从而改变桨叶的拉力。桨距角大，拉力就大，反之则减小。</p>
+<li><p>垂直铰（即垂直关节）的作用：直升机前飞时，桨叶在绕轴转动时要绕水平铰挥舞，这就造成桨叶重心距旋翼轴的距离不断变化，如图1-3（b）所示。从而引起周期交变的哥氏力。所谓哥氏力（也叫回转力）是物体在旋转系统中，一面旋转一面又有<br>相对于该系统运动时所出现的一种附加惯性力。其方向顺旋转方向。其矢量表达式为</p>
+<script type="math/tex; mode=display">F = 2 m \Omega V</script><p>公式中 $m$ — 桨叶质量，$\Omega$ — 旋翼旋转角速度，$V$ — 桨叶重心对旋翼轴径向速度。<br>一片桨叶的哥氏力的最大值高达桨叶自重的七倍以上。巨大的哥氏力必然会在旋转面内造成很大的交变弯矩，如果无垂直铰，桨叶根部会材料疲劳而损坏，如果传到机身，将引起机体震动加剧。有了垂直铰，桨叶绕垂直铰摆动一个角度，从而使桨叶根部所受的沿旋转方向的交变弯矩大大减少。</p>
 </li>
+<li>轴向铰（轴向关节）的作用：通过操作机构，可使桨叶绕轴向铰偏转，以改变桨距角的大小，从而改变桨叶的拉力。桨距角大，拉力就大，反之则减小。</li>
 </ul>
 <h2 id="旋翼类型"><a href="#旋翼类型" class="headerlink" title="旋翼类型"></a>旋翼类型</h2><p>旋翼的类型大致分为四类：铰接式；跷跷板式；无铰接式；无轴承式。</p>
 <ul>
@@ -472,7 +472,7 @@ <h2 id="旋翼类型"><a href="#旋翼类型" class="headerlink" title="旋翼
 
 <!-- ### Custom Footer ### --><!-- hexo-inject:begin --><!-- Begin: Injected MathJax -->
 <script type="text/x-mathjax-config">
-  MathJax.Hub.Config("");
+  MathJax.Hub.Config({"tex2jax":{"inlineMath":[["$","$"],["\\(","\\)"]],"skipTags":["script","noscript","style","textarea","pre","code"],"processEscapes":true},"TeX":{"equationNumbers":{"autoNumber":"AMS"}}});
 </script>
 
 <script type="text/x-mathjax-config">
@@ -484,7 +484,7 @@ <h2 id="旋翼类型"><a href="#旋翼类型" class="headerlink" title="旋翼
   });
 </script>
 
-<script type="text/javascript" src="custom_mathjax_source">
+<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 <!-- End: Injected MathJax -->
 <!-- hexo-inject:end -->

2016/03/24/Helicopter-intro/index.html

@@ -152,7 +152,7 @@
     <meta name="mobile-web-app-capable" content="yes"><meta name="application-name" content="Xiong Yu 熊宇"><meta name="msapplication-starturl" content="http://yoursite.com"><meta name="apple-mobile-web-app-capable" content="yes"><meta name="apple-mobile-web-app-title" content="Xiong Yu 熊宇"><meta name="apple-mobile-web-app-status-bar-style" content="black-translucent">
 
     <!-- ### The Open Graph & Twitter Card Protocol ### -->
-    <meta property="og:title" content="主要旋翼类型 | Xiong Yu 熊宇"><meta property="og:site_name" content="Xiong Yu 熊宇"><meta property="og:type" content="article"><meta property="og:url" content="http://yoursite.com/2016/08/09/typesofrotor/"><meta property="og:locale" content="en"><meta name="description" content="Teetering Rotor Teetering旋翼有变桨轴承(Pitch Bearing), 可以挥舞运动(Flapping), 但是是通过旋翼中轴实现, 所以一只桨叶向上挥舞时, 相对应另一头的桨叶将下挥舞. Teetering并没有震摆运动(Lead-Lag Motion). 此种旋翼较多使用在Bell直升机机型上.   Fully Articulated Rotor Fully Arti - Yu Xiong - Xiong Yu 熊宇"><meta name="keywords" content="Rotor"><meta property="og:image" content="http://yoursite.com/photos/teetering.jpg"><meta property="og:image" content="http://yoursite.com/photos/fullyarticulate.png"><meta property="og:image" content="http://yoursite.com/photos/hingeless.jpg"><meta property="og:image" content="http://yoursite.com/photos/bearingless.jpg"><meta property="article:published_time" content="2016-08-09T20:56:00.000Z"><meta property="article:modified_time" content="2016-08-09T21:20:36.000Z"><meta property="og:updated_time" content="2016-08-09T21:20:36.000Z"><meta property="article:author" content="Yu Xiong"><meta property="article:tag" content="Rotor"><meta name="twitter:card" content="summary">
+    <meta property="og:title" content="主要旋翼类型 | Xiong Yu 熊宇"><meta property="og:site_name" content="Xiong Yu 熊宇"><meta property="og:type" content="article"><meta property="og:url" content="http://yoursite.com/2016/08/09/typesofrotor/"><meta property="og:locale" content="en"><meta name="description" content="Teetering RotorTeetering旋翼有变桨轴承(Pitch Bearing), 可以挥舞运动(Flapping), 但是是通过旋翼中轴实现, 所以一只桨叶向上挥舞时, 相对应另一头的桨叶将下挥舞. Teetering并没有震摆运动(Lead-Lag Motion). 此种旋翼较多使用在Bell直升机机型上. Fully Articulated RotorFully Articula - Yu Xiong - Xiong Yu 熊宇"><meta name="keywords" content="Rotor"><meta property="og:image" content="http://yoursite.com/photos/teetering.jpg"><meta property="og:image" content="http://yoursite.com/photos/fullyarticulate.png"><meta property="og:image" content="http://yoursite.com/photos/hingeless.jpg"><meta property="og:image" content="http://yoursite.com/photos/bearingless.jpg"><meta property="article:published_time" content="2016-08-09T20:56:00.000Z"><meta property="article:modified_time" content="2016-08-09T21:20:36.000Z"><meta property="og:updated_time" content="2016-08-09T21:20:36.000Z"><meta property="article:author" content="Yu Xiong"><meta property="article:tag" content="Rotor"><meta name="twitter:card" content="summary">
 
 
 
@@ -219,7 +219,7 @@
     },
 
     "keywords": "Rotor",
-    "description": "Teetering Rotor Teetering旋翼有变桨轴承(Pitch Bearing), 可以挥舞运动(Flapping), 但是是通过旋翼中轴实现, 所以一只桨叶向上挥舞时, 相对应另一头的桨叶将下挥舞. Teetering并没有震摆运动(Lead-Lag Motion). 此种旋翼较多使用在Bell直升机机型上.   Fully Articulated Rotor Fully Arti - Yu Xiong - Xiong Yu 熊宇"
+    "description": "Teetering RotorTeetering旋翼有变桨轴承(Pitch Bearing), 可以挥舞运动(Flapping), 但是是通过旋翼中轴实现, 所以一只桨叶向上挥舞时, 相对应另一头的桨叶将下挥舞. Teetering并没有震摆运动(Lead-Lag Motion). 此种旋翼较多使用在Bell直升机机型上. Fully Articulated RotorFully Articula - Yu Xiong - Xiong Yu 熊宇"
 }
 </script>
 
@@ -302,22 +302,10 @@ <h1 class="card-title h3 mb-2">主要旋翼类型</h1>
 
 
                     <article id="post-content">
-                        <h2 id="Teetering-Rotor"><a href="#Teetering-Rotor" class="headerlink" title="Teetering Rotor"></a>Teetering Rotor</h2><img src="/photos/teetering.jpg" width="50%" height="50%">
-Teetering旋翼有变桨轴承(Pitch Bearing), 可以挥舞运动(Flapping), 但是是通过旋翼中轴实现, 所以一只桨叶向上挥舞时, 相对应另一头的桨叶将下挥舞. Teetering并没有震摆运动(Lead-Lag Motion). 此种旋翼较多使用在Bell直升机机型上.
-
-
-<h2 id="Fully-Articulated-Rotor"><a href="#Fully-Articulated-Rotor" class="headerlink" title="Fully Articulated Rotor"></a>Fully Articulated Rotor</h2><img src="/photos/fullyarticulate.png" width="50%" height="50%">
-Fully Articulated Rotor为全铰链型旋翼, 可以进行俯仰运动(Pitch Motion), 挥舞运动(Flapping Motion) 和 震摆运动(Lead-Lag Motion). 多数Sikorsky的直升机都是采用此类型旋翼.
-
-
-<h2 id="Hingeless-Rotor"><a href="#Hingeless-Rotor" class="headerlink" title="Hingeless Rotor"></a>Hingeless Rotor</h2><img src="/photos/hingeless.jpg" width="50%" height="50%">
-Hingeless Rotor更加复杂点, 其没有挥舞铰链(Flapping Hinge)和震摆铰链(Lag Hinge). 又叫 "Soft-inplane" 旋翼. X2型直升机采用的此种旋翼.
-
-
-<h2 id="Bearingless-Rotor"><a href="#Bearingless-Rotor" class="headerlink" title="Bearingless Rotor"></a>Bearingless Rotor</h2><img src="/photos/bearingless.jpg" width="60%" height="60%">
-Bearingless Rotor是没有任何铰链或者没有俯仰轴承(Pitch Bearing). Bell 429和EC-B5型直升机都是采用此种旋翼.
-
-
+                        <h2 id="Teetering-Rotor"><a href="#Teetering-Rotor" class="headerlink" title="Teetering Rotor"></a>Teetering Rotor</h2><p><img src="/photos/teetering.jpg" width="50%" height="50%"><br>Teetering旋翼有变桨轴承(Pitch Bearing), 可以挥舞运动(Flapping), 但是是通过旋翼中轴实现, 所以一只桨叶向上挥舞时, 相对应另一头的桨叶将下挥舞. Teetering并没有震摆运动(Lead-Lag Motion). 此种旋翼较多使用在Bell直升机机型上.</p>
+<h2 id="Fully-Articulated-Rotor"><a href="#Fully-Articulated-Rotor" class="headerlink" title="Fully Articulated Rotor"></a>Fully Articulated Rotor</h2><p><img src="/photos/fullyarticulate.png" width="50%" height="50%"><br>Fully Articulated Rotor为全铰链型旋翼, 可以进行俯仰运动(Pitch Motion), 挥舞运动(Flapping Motion) 和 震摆运动(Lead-Lag Motion). 多数Sikorsky的直升机都是采用此类型旋翼.</p>
+<h2 id="Hingeless-Rotor"><a href="#Hingeless-Rotor" class="headerlink" title="Hingeless Rotor"></a>Hingeless Rotor</h2><p><img src="/photos/hingeless.jpg" width="50%" height="50%"><br>Hingeless Rotor更加复杂点, 其没有挥舞铰链(Flapping Hinge)和震摆铰链(Lag Hinge). 又叫 “Soft-inplane” 旋翼. X2型直升机采用的此种旋翼.</p>
+<h2 id="Bearingless-Rotor"><a href="#Bearingless-Rotor" class="headerlink" title="Bearingless Rotor"></a>Bearingless Rotor</h2><p><img src="/photos/bearingless.jpg" width="60%" height="60%"><br>Bearingless Rotor是没有任何铰链或者没有俯仰轴承(Pitch Bearing). Bell 429和EC-B5型直升机都是采用此种旋翼.</p>
 
                     </article>
 

2016/08/09/typesofrotor/index.html

@@ -308,8 +308,7 @@ <h1 id="直升机向前飞行"><a href="#直升机向前飞行" class="headerlin
 <p>挥舞铰链 (Flap Hinge) (Renard - 1904) 的发明缓解了桨叶根处的弯矩 (Bending Moment)。周期桨矩 (Cyclic Pitch) (Pescare - 1924) 的发明可以帮助控制旋翼所产生的推力矢量，也同时缓解了旋翼旋转时前进侧与后退侧产生的滚转力矩 (Rolling Moment)。</p>
 <p>桨叶的挥舞运动将会在桨叶旋转时滞后方向产生科里奥利力矩 (Coriolis Moment)。为了缓解这个在旋翼根部的滞后力矩，滞后铰链将会启用。</p>
 <p>对于一个无铰链的旋翼，挥舞和滞后铰链将不会启用。但是桨叶靠近跟部处结构上将会非常灵活从而一定程度上代替挥舞和滞后铰链。</p>
-<img src="/photos/-helicopterforwardflightrotor.png" width="80%" height="80%">
-
+<p><img src="/photos/-helicopterforwardflightrotor.png" width="80%" height="80%"></p>
 <p>Figure above. As each blade passes the 90° position on the left in a counterclockwise main rotor blade rotation, the maximum increase in angle of incidence occurs. As each blade passes the 90° position to the right, the maximum decrease in angle of incidence occurs. Maximum deflection takes place 90° later—maximum upward deflection at the rear and maximum downward deflection at the front—and the tip-path plane tips forward.</p>
 
                     </article>

2016/08/10/forwardflighthelicopter/index.html

@@ -310,9 +310,8 @@ <h2 id="Mobility-灵敏度-and-Impedance-阻抗"><a href="#Mobility-灵敏度-an
 <p>结构灵敏度(Mobility)可描述为受力物体或结构受到外力 (Fluctuating Force) 作用下所产生的振动量.</p>
 <p>实验中测量结构灵敏度(Mobility)是通过安装三个加速感应器在测量结构板上, 并由锤子作为外力使测试结构产生振动, 得到的加速数值做时间积分可得到速度. 最后, 速度除以外力可以得到导纳值. 当激发点和采集点重合时称为一个激发点导纳(Drive Point Mobility), 不重合时为交叉导纳(Cross-Mobility).</p>
 <p>激发点灵敏度(Drive Point Mobility)和交叉灵敏度(Cross-Mobility)组成的矩阵(Matrices)可用来计算此结构的共振(Resonances).</p>
-<p>灵敏度(Mobility)计算公式解析:<br>$$ Mobility = \frac{v(x,y)}{F(x_{o},y_{o})} = \frac{i\omega}{\frac{\rho h a b}{4}} \times \sum_{m=1}^\infty \sum_{n=1}^{\infty} (\frac{1}{\omega^{2}_{mn} - \omega^{2}} \times [\sin \frac{m\pi x}{a} \sin \frac{n\pi y}{b}]) $$</p>
-<p>$$ Mobility = \frac{v(x,y)}{F(x_{o},y_{o})} = \frac{i\omega}{\frac{\rho h a b}{4}} \times \sum_{m=1}^\infty \sum_{n=1}^{\infty} (\frac{1}{\omega^{2}_{mn} - \omega^{2}} \times [\sin \frac{m\pi x_{o}}{a} \sin \frac{n\pi y_{o}}{b}]) $$</p>
-<ul>
+<p>灵敏度(Mobility)计算公式解析:</p>
+<script type="math/tex; mode=display">Mobility = \frac{v(x,y)}{F(x\_{o},y\_{o})} = \frac{i\omega}{\frac{\rho h a b}{4}} \times \sum\_{m=1}^\infty \sum\_{n=1}^{\infty} (\frac{1}{\omega^{2}\_{mn} - \omega^{2}} \times [\sin \frac{m\pi x}{a} \sin \frac{n\pi y}{b}])</script><script type="math/tex; mode=display">Mobility = \frac{v(x,y)}{F(x\_{o},y\_{o})} = \frac{i\omega}{\frac{\rho h a b}{4}} \times \sum\_{m=1}^\infty \sum\_{n=1}^{\infty} (\frac{1}{\omega^{2}\_{mn} - \omega^{2}} \times [\sin \frac{m\pi x\_{o}}{a} \sin \frac{n\pi y\_{o}}{b}])</script><ul>
 <li>$(x,y)$ 为灵敏度值所在的位置; $(x_{o},y_{o})$ 为外力施加所在位置.</li>
 <li>$v$ 为速度(Velocity); $F$ 为外力 (Drive Force).</li>
 <li>结构质量 $m=\rho v = \rho h A = \rho h a b$; 模态质量 (Modal Mass) 是每一个模态的质量为$\frac{1}{4}$的总结构质量, $\frac{\rho h a b}{4}$.</li>
@@ -460,7 +459,7 @@ <h2 id="References"><a href="#References" class="headerlink" title="References">
 
 <!-- ### Custom Footer ### --><!-- hexo-inject:begin --><!-- Begin: Injected MathJax -->
 <script type="text/x-mathjax-config">
-  MathJax.Hub.Config("");
+  MathJax.Hub.Config({"tex2jax":{"inlineMath":[["$","$"],["\\(","\\)"]],"skipTags":["script","noscript","style","textarea","pre","code"],"processEscapes":true},"TeX":{"equationNumbers":{"autoNumber":"AMS"}}});
 </script>
 
 <script type="text/x-mathjax-config">
@@ -472,7 +471,7 @@ <h2 id="References"><a href="#References" class="headerlink" title="References">
   });
 </script>
 
-<script type="text/javascript" src="custom_mathjax_source">
+<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
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