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id="tpnrxl7j" class="title"> <h3><a>試驗模態分析技術<small></small></a></h3> </div> <!-- 頁面標題結束 --> <hr class="featurette-divider"> <!-- 中部開始 --> <div id="tpnrxl7j" class="container"> <!-- 正文 --> <div id="tpnrxl7j" class="lead" id="print"> <p> <span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;">實驗模態分析方法可以分為頻響函數法（簡稱測力法</span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;">）</span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;">和環境激勵法（簡稱 不測力法）兩種，所謂測力法就是在試驗過程中需要同時測量激勵力和響應的方 法。經典的測力法是利用頻域的頻響函數</span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;">（</span><span id="tpnrxl7j" class="211pt5" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;"><span lang="EN-US" style="font-size: 11pt;">FRF</span></span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;"><span style="font-family: SimSun;">)</span></span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;">或時域的脈沖響應函數</span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;">（</span><span id="tpnrxl7j" class="211pt5" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;"><span lang="EN-US" style="font-size: 11pt;">IRF</span></span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;"><span style="font-family: SimSun;">) </span></span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;">對模態參數進行估計。頻響函數是響應和力的傅里葉變換之比，而脈沖響應函數 也要先測得頻響函數然后經傅里葉逆變換</span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;">（</span><span id="tpnrxl7j" class="211pt5" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;"><span lang="EN-US" style="font-size: 11pt;">IFFT</span></span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;"><span style="font-family: SimSun;">)</span></span><span id="tpnrxl7j" class="2" style="line-height: 21.85pt; text-indent: 27pt; background-color: transparent;">獲得。因此，測力法必須利用 帶測力計的激振器或力錘施加可測量的激勵力。測力法可以估計所有的模態參數， 包括固有頻率、模態振型、模態阻尼或阻尼比、模態質量和模態剛度，而且精度 較高。</span></p> <p class="21" style="margin:0cm;margin-bottom:.0001pt;text-indent:27.0pt; line-height:21.85pt;mso-line-height-rule:exactly;background:transparent"><span id="tpnrxl7j" class="2">常用軟件中頻域測力法分圖解法和解析法兩種，圖解法較適合于阻尼小模態 不密集系統，如鋼結構。圖解法可選用峰值拾取法或圓擬合法。解析法常用于大 阻尼或模態密集系統。時域測力法普遍采用脈沖響應函數的最小二乘復指數法 </span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">LSCE</span></span><span id="tpnrxl7j" class="2"><span style="font-family: SimSun;"> (</span></span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">LeastSquareComplexExponential</span></span><span id="tpnrxl7j" class="2"><span style="font-family: SimSun;">)</span></span><span id="tpnrxl7j" class="2">進行計算，頻域解析法[<sup>43</sup>][<sup>44</sup>]可選用正 交多項式法。</span></p> <p class="21" style="margin:0cm;margin-bottom:.0001pt;text-indent:27.0pt; line-height:21.85pt;mso-line-height-rule:exactly;background:transparent"><span id="tpnrxl7j" class="2">所謂不測力法就是在試驗過程中不需要測量激勵力的方法。工程中的大量結 構和機器（如大型建筑，大型橋梁，汽輪發電機組等）都是很難人工施加激勵力 的，其結構的響應主要由環境激勵引起，如機器運行時由質量不平衡產生的慣性 力，車輛行駛時的振動以及微地震產生的地脈動等各種環境激勵，而這些環境激 勵是既不可控制又難以測量的。</span></p> <p class="21" align="left" style="margin: 0cm 0cm 0.0001pt; text-indent: 27pt; line-height: 21.85pt; background: transparent;"><span id="tpnrxl7j" class="2">不測力法只能利用系統的響應數據對固有頻率、模態振型、模態阻尼或阻尼 比這三個模態參數進行估計，但是這三個模態參數已經能夠滿足絕大多數工程中 結構動力特性分析的要求。軟件會利用測量得到的響應的自功率譜、互功率譜、 傳遞率和相干函數進行模態參數的估計。</span></p> <p class="21" style="margin:0cm;margin-bottom:.0001pt;text-indent:27.0pt; line-height:21.85pt;mso-line-height-rule:exactly;background:transparent"><span id="tpnrxl7j" class="2">不測力法也可分為解析法和圖解法兩種類型。使用范圍與測力法一致。圖解 法可選用自互功率譜綜合法或傳遞率法，解析法可選用隨機子空間法</span><span id="tpnrxl7j" class="2">（</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">SSI</span></span><span id="tpnrxl7j" class="2"><span style="font-family: SimSun;">)</span></span><span id="tpnrxl7j" class="2">。</span></p> <p class="21" style="margin:0cm;margin-bottom:.0001pt;text-indent:27.0pt; line-height:21.85pt;mso-line-height-rule:exactly;background:transparent"><span id="tpnrxl7j" class="2">另外利用軟件還可以通過時域和頻域的</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">ODS</span></span><span id="tpnrxl7j" class="2">動畫顯示更形象地模擬被測結 構或機械零件的振動。所謂時域的</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">ODS</span></span><span id="tpnrxl7j" class="2">動畫顯示，其原理類似于錄像機快錄慢放。 常用于機器起動或停止時的動響應</span><span id="tpnrxl7j" class="2">（</span><span id="tpnrxl7j" class="2">如位移、速度或加速度）相對于時間變量的 觀測。頻域的</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">ODS</span></span><span id="tpnrxl7j" class="2">動畫顯示，其原理類似于數字閃頻儀，用于動變形相對于頻率</span><span style="line-height: 22.3pt; background-color: transparent;">變量的觀測。當觀測到的頻率接近或等于共振頻率時，動變形可近似的作為結構 的振型。</span></p> <p class="21" style="margin-top:0cm;margin-right:0cm;margin-bottom:21.3pt; margin-left:0cm;text-indent:28.0pt;line-height:21.85pt;mso-line-height-rule: exactly;background:transparent"><span id="tpnrxl7j" class="2">試驗模態分析的過程如圖</span><span id="tpnrxl7j" class="2"><span style="font-family: SimSun;">3.1</span></span><span id="tpnrxl7j" class="2">所示。對被測試件上的各點施加激振力，同時 測出其響應；接著用信號分析設備求出激振點與響應點之間的傳遞函數，如果要 求振動模態，尚需對試件上的各點反復地求出傳遞函數；然后進行曲線擬合，識別 得出固有頻率、模態剛度、模態阻尼、模態質量和模態振型等參數；最后根據所 得到的模態參數，在顯示屏幕上將振動模態的動態過程顯示出來。</span></p> <p class="21" style="margin-top:0cm;margin-right:0cm;margin-bottom:21.3pt; 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