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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>6 强迫振动（受迫振动）</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b><font color="#0000FF">一、模型</font></b></td> <td width="50%" rowspan="5"> <p align="center"><img border="0" src="pic2/3086.h76.gif" width="200" height="103"></td> </tr> <tr> <td width="50%">最简模型如图。 <font color="#800000">设简谐激励。</font></td> </tr> <tr> <td width="50%"><b><font color="#0000FF">二、振动方程</font></b></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic2/3086.h77.gif" width="171" height="22"></td> <td> <font color="#800000">非齐次方程</font></td> </tr> </table> </td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td> 或 </td> <td><img border="0" src="pic2/3086.h78.gif" width="183" height="31"></td> <td> </td> <td> （3）</td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td><b><font color="#0000FF">三、解</font></b></td> </tr> <tr> <td></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>由常微分方程理论知方程(3)的解： </td> <td></td> <td><img border="0" src="pic2/3086.h79.gif" width="84" height="28"></td> </tr> <tr> <td align="center">x1 对应齐次方程的通解：</td> <td align="center" rowspan="2"><font color="#FF0000" size="5">╋</font></td> <td align="center"> x2 该非齐次方程的特解：</td> </tr> <tr> <td align="center"><img border="0" src="pic2/3086.h80.gif" width="171" height="31"></td> <td align="center"><img border="0" src="pic2/3086.h81.gif" width="136" height="28"></td> </tr> <tr> <td align="center" colspan="2"><img border="0" src="pic2/3086.h82.gif" width="345" height="32"></td> <td align="center"><b>强迫振动通解</b></td> </tr> <tr> <td align="center" colspan="2"> <p align="left">当 t 足够大时，第一项趋于0</td> <td align="center"></td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic2/3086.h83.gif" width="40" height="24"></td> <td> <b>强迫振动稳态解</b> </td> <td><img border="0" src="pic2/3086.h84.gif" width="129" height="26"></td> <td> （4）</td> </tr> </table> </td> </tr> <tr> <td><b><font color="#0000FF">四、稳态解的幅频特性和相频特性</font></b></td> </tr> <tr> <td>将稳态解(4)代入方程(3) ，可求得稳态解的两个常数：</td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic2/3086.h85.gif" width="361" height="61"></td> <td>式中 <b>频率比</b></td> <td> <p align="center"><img border="0" src="pic2/3086.h86.gif" width="61" height="54"></td> </tr> <tr> <td> <p align="center"><img border="0" src="pic2/3086.h87.gif" width="258" height="54"></td> <td><b>静力偏移</b></td> <td><img border="0" src="pic2/3086.h88.gif" width="106" height="54"></td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%" valign="top">当系统一定时，ωd 、σ为常数。我们特别关心当激励幅值 f 一定时，外激励频率f的变化对振动的影响。因此<font color="#FF00FF">B和φ为ω的函数</font>，故称之为<b><font color="#FF0000">幅频特性</font></b>和<b><font color="#FF0000">相频特性</font></b>。其关于ω的曲线分别称为<b><font color="#FF0000">幅频(特性)曲线</font></b>和<b><font color="#FF0000">相频(特性)曲线</font></b>。如图。</td> <td width="50%"> <p align="center"><img border="0" src="pic2/3086.h89.gif" width="345" height="267"></td> </tr> </table> </td> </tr> <tr> <td></td> </tr> <tr> <td> <p align="center"> <a href="3085.htm"><font color="#FF6666">[ 上一节 ]</font></a> <a href="3087.htm"><font color="#00CC00">[ 下一节 ]</font></a> </td> </tr> </table> </BODY></HTML> ⌨️ 快捷键说明
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