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<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>5 虚位移原理</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>事实上，我们早已知道： </td> <td><img border="0" src="pic2/3071_549.GIF" width="84" height="28"> </td> <td>又称<b>虚功原理</b></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">有了上述各种概念，可严格叙述为：</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td bgcolor="#00CC99">具有完整、双面、定常、理想约束的质点系，在给定位置保持平衡的充要条件是，所有作用于质点系上的主动力在任何虚位移上所做的虚功之和为零。</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"><font color="#FF0000">用虚位移原理可求两类问题：</font></td> </tr> <tr> <td width="20"><b><font color="#0000FF">一、</font></b></td> <td width="540"><b><font color="#0000FF">求主动力或平衡条件（位置）——对几何可变体系</font></b></td> </tr> <tr> <td width="20"></td> <td width="540">解题步骤：</td> </tr> <tr> <td width="20"></td> <td width="540">(一)研究整体（不取分离体），并选广义坐标；<br> (二)（若用几何法）画出系统一组虚位移，并用广义坐标虚位移表示所有对应主动力的虚位移； <br> (若用解析法,不画虚位移)画出直角坐标系,并求所有对应主动力坐标的变分;<br> (三)列解方程。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例1</b>：<font color="#800000">本章开头例子</font></td> <td width="50%" rowspan="7"> <p align="center"><img border="0" src="pic2/3071_550.GIF" width="201" height="206"></td> </tr> <tr> <td width="50%">如图，系统平衡。已知Q、l、α，求P</td> </tr> <tr> <td width="50%">答案：</td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3071_551.GIF" width="106" height="49"></td> </tr> <tr> <td width="50%"><b>例2</b>：<font color="#800000">(例1变形) 或 书P294，例7-4</font></td> </tr> <tr> <td width="50%">已知Q、l、k,求平衡时θ(以方程给出)</td> </tr> <tr> <td width="50%"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="25%" rowspan="2"> <p align="center"><img border="0" src="pic2/3071_552.GIF" width="130" height="153"></td> <td width="25%" rowspan="2">注：<br> 弹簧处理方法：去之，代以弹簧力，为常主动力。</td> <td width="25%" rowspan="2"><img border="0" src="pic2/3071_553.GIF" width="153" height="159"></td> <td width="25%" valign="bottom">答案：</td> </tr> <tr> <td width="25%"><img border="0" src="pic2/3071_554.GIF" width="180" height="46"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"><b>例3</b>：<font color="#800000">（例7-2, P291）</font></td> </tr> <tr> <td width="20"></td> <td width="540">图示机构。<br> 已知OA = r，铅直杆O'E = l，O'B = BE，AB水平，φ。求图示位置时力偶M与力Q的关系。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"> <p align="center"><img border="0" src="pic2/3071_555.GIF" width="253" height="158"></td> <td width="50%"> <p align="center"><img border="0" src="pic2/3071_556.GIF" width="273" height="173"></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>答案： </td> <td><img border="0" src="pic2/3071_557.GIF" width="116" height="27"></td> </tr> </table> </td> <td width="50%"> <p align="center">D处滑块应画上。事实上,此图在原图上画</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="1" cellpadding="0" cellspacing="0" bordercolor="#008080"> <tr> <td>问题：用虚功方程可解几个代数未知量？</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">看例子——平面自由刚体</td> <td width="50%" rowspan="5"> <p align="center"><img border="0" src="pic2/3071_558.GIF" width="176" height="144"></td> </tr> <tr> <td width="50%">给刚体虚位移：</td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic2/3071_559.GIF" width="62" height="23"></td> <td> 对应平动 </td> </tr> <tr> <td> <p align="center"><img border="0" src="pic2/3071_560.GIF" width="24" height="22"></td> <td> 对应转动</td> </tr> </table> </td> </tr> <tr> <td width="50%"> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"><img border="0" src="pic2/3071_561.GIF" width="382" height="31"></td> </tr> <tr> <td width="20"></td> <td width="540"><img border="0" src="pic2/3071_562.GIF" width="285" height="31"></td> </tr> <tr> <td width="20"></td> <td width="540">变分方程对应独立代数方程数 ＝ 广义坐标数</td> </tr> <tr> <td width="20"><b><font color="#0000FF">二、</font></b></td> <td width="540"><b><font color="#0000FF">求约束力（或内力）——一般为几何不变体系</font></b></td> </tr> <tr> <td width="20"></td> <td width="540">处理方法：去掉约束，代之以约束力，转化为几何可变体系，同一。</td> </tr> <tr> <td width="20"></td> <td width="540">一般去掉1个约束，转化为1自由度的可变体系。</td> </tr> <tr> <td width="20"></td> <td width="540"><b>各种约束的解除方法：</b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="25%"></td> <td width="25%"><img border="0" src="pic2/3071_563.GIF" width="213" height="86"></td> <td width="25%"></td> <td width="25%"><img border="0" src="pic2/3071_564.GIF" width="214" height="71"></td> </tr> <tr> <td width="25%"><font color="#0000FF">去B铰链</font></td> <td width="25%"><img border="0" src="pic2/3071_565.GIF" width="225" height="97"></td> <td width="25%"><font color="#0000FF">去A处转动约束</font></td> <td width="25%"><img border="0" src="pic2/3071_566.GIF" width="224" height="81"></td> </tr> <tr> <td width="25%"><font color="#0000FF">去A铰链X方向约束</font></td> <td width="25%"><img border="0" src="pic2/3071_567.GIF" width="228" height="86"></td> <td width="25%"><font color="#0000FF">去A处x方向约束</font></td> <td width="25%"><img border="0" src="pic2/3071_568.GIF" width="231" height="68"></td> </tr> <tr> <td width="25%"><font color="#0000FF">去A铰链Y方向约束</font></td> <td width="25%"><img border="0" src="pic2/3071_569.GIF" width="224" height="79"></td> <td width="25%"><font color="#0000FF">去A处y方向约束</font></td> <td width="25%"><img border="0" src="pic2/3071_570.GIF" width="219" height="97"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="33%"><b>例4</b>：<br> 将本章开头例子改动</td> <td width="33%" rowspan="5"><img border="0" src="pic2/3071_571.GIF" width="191" height="196"></td> <td width="34%" rowspan="5"><img border="0" src="pic2/3071_572.GIF" width="196" height="201"></td> </tr> <tr> <td width="33%">已知Q、l、α，求C处水平反力。</td> </tr> <tr> <td width="33%">去掉C处水平约束，同例1。</td> </tr> <tr> <td width="33%"></td> </tr> <tr> <td width="33%"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例5</b>：书上 P295 例7-5</td> <td width="50%" rowspan="2"><img border="0" src="pic2/3071_573.GIF" width="290" height="133"></td> </tr> <tr> <td width="50%">已知：M = 5.0 kN· m，P1 = P2 = 4 kN，q = 2 kN/m，α= 30°，l = 2 m。求固定端A的反力。</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"></td> </tr> <tr> <td width="560" colspan="2" align="center"> <a href="3071_4.htm"><font color="#FF6666">[ 上一节 ]</font></a> <a href="3072_1.htm"><font color="#00CC00">[ 下一节 ]</font></a> </td> </tr></table></BODY></HTML> ⌨️ 快捷键说明
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