?? 3071_3.htm
字號(hào):
<HTML><HEAD><TITLE>new</TITLE><META content="text/html; charset=gb2312" http-equiv=Content-Type><LINK href="text.css" rel=stylesheet type=text/css><META content="Microsoft FrontPage 4.0" name=GENERATOR></HEAD><body leftmargin="15"><center><b><br>3 虛位移 虛功</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td width="20"><b><font color="#0000FF">一、</font></b></td> <td width="560"><b><font color="#0000FF">虛位移</font></b></td> </tr> <tr> <td width="20"></td> <td width="560">定義：在給定位置上，質(zhì)點(diǎn)或質(zhì)點(diǎn)系在<font color="#0000FF">約束所容許的條件下</font><font color="#008000">可能發(fā)生的</font><font color="#FF00FF">任何</font><font color="#800000">無(wú)限小</font>位移,稱為質(zhì)點(diǎn)或質(zhì)點(diǎn)系的<b>虛位移。</b></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>虛位移的數(shù)學(xué)意義</b>——廣義坐標(biāo)的變分<br> <b>虛位移有兩種情形</b>：<br> <b>質(zhì)點(diǎn)的虛位移</b>——線位移<br> <b>剛體的虛位移</b>——角位移<br> </td> <td width="50%" bgcolor="#0000FF"> <table border="0" cellspacing="1" width="100%"> <tr> <td width="100%" bgcolor="#FFFFFF">理解虛位移有4個(gè)要點(diǎn)：<br> ①為約束所容許，即不能破壞系統(tǒng)的約束<br> ②可能發(fā)生的，即假想的，與時(shí)間無(wú)關(guān)<br> ③所有的，可不止一種；<br> ④無(wú)限小，不改變系統(tǒng)位置。</td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><b>例子：</b></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellspacing="0" width="100%" cellpadding="0"> <tr> <td width="50%"><img border="0" src="pic2/3071_39.GIF" width="278" height="160"></td> <td width="50%" rowspan="2"> <p align="center"><img border="0" src="pic2/3071_310.GIF" width="271" height="196"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3071_311.GIF" width="345" height="99"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"> <p align="center">虛<br> 位<br> 移<br> 與<br> 實(shí)<br> 位<br> 移<br> 的<br> 比<br> 較<br> </td> <td width="50%"><img border="0" src="pic2/3071_312.GIF" width="503" height="240"></td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">二、</font></b></td> <td width="560"><b><font color="#0000FF">虛位移的求法——實(shí)際是求虛位移的關(guān)系</font></b></td> </tr> <tr> <td width="20"></td> <td width="560"><font color="#0000FF">1. 幾何法（運(yùn)動(dòng)分析法）</font></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="102%"> <tr> <td width="53%">假想系統(tǒng)運(yùn)動(dòng)，找該位置下各速度（角速度）的關(guān)系，即各虛位移的關(guān)系。通常將各有關(guān)虛位移用廣義坐標(biāo)的虛位移表示。</td> <td width="49%" rowspan="4"><img border="0" src="pic2/3071_313.GIF" width="271" height="196"></td> </tr> <tr> <td width="53%">例：曲柄連桿機(jī)構(gòu)</td> </tr> <tr> <td width="53%">選φ為廣義坐標(biāo)。</td> </tr> <tr> <td width="53%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>OA桿：</td> <td><img border="0" src="pic2/3071_314.GIF" width="113" height="29"></td> </tr> <tr> <td>AB瞬心在I：</td> <td><img border="0" src="pic2/3071_315.GIF" width="135" height="50"></td> </tr> <tr> <td>所以：</td> <td><img border="0" src="pic2/3071_316.GIF" width="217" height="50"></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><font color="#0000FF">2. 解析法（變分法）</font></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="28%">第 i 點(diǎn)：</td> <td width="72%"><img border="0" src="pic2/3071_317.GIF" width="269" height="27"></td> </tr> <tr> <td width="28%">虛位移：</td> <td width="72%"><img border="0" src="pic2/3071_318.GIF" width="252" height="58"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560">通常選直角坐標(biāo)系，直接寫各點(diǎn)直角坐標(biāo)的變分，且不在圖中畫出虛位移：</td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例</b>：曲柄連桿機(jī)構(gòu)</td> <td width="50%" rowspan="3"><img border="0" src="pic2/3071_319.GIF" width="235" height="108"></td> </tr> <tr> <td width="50%">選φ為廣義坐標(biāo)，考慮幾何關(guān)系：</td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3071_320.GIF" width="200" height="28"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_321.GIF" width="337" height="29"> <img border="0" src="pic2/3071_322.GIF" width="114" height="26"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_323.GIF" width="228" height="27"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_324.GIF" width="180" height="50"> <img border="0" src="pic2/3071_325.GIF" width="156" height="28"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_326.GIF" width="477" height="29"></td> </tr> <tr> <td width="20"></td> <td width="560">注：通常兩種方法各有側(cè)重，有些問(wèn)題用幾何法容易，有些問(wèn)題有解析法容易。一般容易作運(yùn)動(dòng)學(xué)分析的問(wèn)題宜選用幾何法。</td> </tr> <tr> <td width="20"><b><font color="#0000FF">三、</font></b></td> <td width="560"><b><font color="#0000FF">虛功</font></b></td> </tr> <tr> <td width="20"></td> <td width="560">力在虛位移上所做的功稱為<b>虛功</b>。</td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力： </td> <td><img border="0" src="pic2/3071_327.GIF" width="350" height="31"></td> </tr> <tr> <td> <p align="center">或</td> <td><img border="0" src="pic2/3071_328.GIF" width="134" height="31"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic2/3071_329.GIF" width="61" height="31"></td> <td>指力</td> <td><img border="0" src="pic2/3071_330.GIF" width="22" height="26"></td> <td>對(duì)軸或瞬心P之矩，</td> </tr> </table> </td> <td width="50%" rowspan="6"><img border="0" src="pic2/3071_331.GIF" width="251" height="199"></td> </tr> <tr> <td width="50%">特別對(duì)剛體此式常用</td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力偶： </td> <td><img border="0" src="pic2/3071_332.GIF" width="93" height="28"></td> </tr> </table> </td> </tr> <tr> <td width="50%"><b>例</b> 曲柄連桿機(jī)構(gòu)，求各主動(dòng)力之虛功。</td> </tr> <tr> <td width="50%"><b>解1</b>：<font color="#800000">幾何法</font></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力偶M： </td> <td><img border="0" src="pic2/3071_333.GIF" width="100" height="26"></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力F： </td> <td><img border="0" src="pic2/3071_334.GIF" width="106" height="26"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力G： </td> <td>直接求C點(diǎn)虛位移不易，故不用下式求虛功： </td> <td><img border="0" src="pic2/3071_335.GIF" width="105" height="29"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>而用G對(duì)瞬心的力矩求： </td> <td><img border="0" src="pic2/3071_336.GIF" width="249" height="45"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>解2：</b><font color="#800000">變分法</font></td> <td width="50%" rowspan="5"><img border="0" src="pic2/3071_337.GIF" width="235" height="109"></td> </tr> <tr> <td width="50%">建立圖示坐標(biāo)系。選φ為廣義坐標(biāo)。</td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力偶M： </td> <td><img border="0" src="pic2/3071_338.GIF" width="100" height="26"></td> </tr> </table> </td> </tr> <tr> <td width="50%">力F：</td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3071_339.GIF" width="114" height="26"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_340.GIF" width="228" height="27"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_341.GIF" width="180" height="50"> <img border="0" src="pic2/3071_342.GIF" width="156" height="28"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_343.GIF" width="477" height="29"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_344.GIF" width="366" height="32"></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="228"> <tr> <td width="64">力G：</td> <td width="160"><img border="0" src="pic2/3071_345.GIF" width="160" height="49"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_346.GIF" width="391" height="50"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_347.GIF" width="292" height="46"></td> </tr> <tr> <td width="20"></td> <td width="560"></td> </tr> <tr> <td width="20"></td> <td width="560"></td> </tr> <tr> <td width="580" colspan="2"> <p align="center"> <a href="3071_2.htm"><font color="#FF6666">[ 上一節(jié) ]</font></a> <a href="3071_4.htm"><font color="#00CC00">[ 下一節(jié) ]</font></a> </td> </tr> </table> </BODY></HTML> ?? 快捷鍵說(shuō)明
復(fù)制代碼
Ctrl + C
搜索代碼
Ctrl + F
全屏模式
F11
切換主題
Ctrl + Shift + D
顯示快捷鍵
?
增大字號(hào)
Ctrl + =
減小字號(hào)
Ctrl + -