模態(tài)分析的通俗解釋

-.z.MODALSPACE-INOUROWNLITTLEWORLD模態(tài)空間–在我們自己的小世界中PeteAvitabile著westrongmc譯Couldyoue*plainmodalanalysisforme"Well...itwilltakealittlebitbuthere'sonethatanyonecanunderstand.你能為我解釋模態(tài)分析嗎.嗯…說來有點(diǎn)話長(zhǎng)，但下面的解釋人人都可理解。You'renotthefirstonetoaskmetoe*plainmodalanalysisinsimpletermssoanyonecanunderstandit.Inanutshell,wecouldsaythatmodalanalysisisaprocesswherebywedescribeastructureintermsofitsnaturalcharacteristicswhicharethefrequency,dampingandmodeshapes-itsdynamicproperties.Wellthat'samouthfulsolet'se*plainwhatthatmeans.Withoutgettingtootechnical,Ioftene*plainmodalanalysisintermsofthemodesofvibrationofasimpleplate.Thise*planationisusuallyusefulforengineerswhoarenewtovibrationsandmodalanalysis.請(qǐng)我用簡(jiǎn)單的概念來解釋模態(tài)分析，以便任何人都可以理解它，你不是第一個(gè)人。簡(jiǎn)言之，模態(tài)分析是一種方法，籍此，可以根據(jù)構(gòu)造的頻率、阻尼和振型等固有屬性-其動(dòng)態(tài)特性-來描述構(gòu)造。這真夠拗口的，那我們來解釋這是什么意思。不鉆技術(shù)牛角尖，我經(jīng)常用一個(gè)簡(jiǎn)單平板的振動(dòng)模態(tài)來解釋模態(tài)分析。對(duì)于剛接觸振動(dòng)及模態(tài)分析的工程師們來講，這種解釋向來有益。Let’sconsiderafreelysupportedflatplate.Let'sapplyaconstantforcetoonecorneroftheplate.Weusuallythinkofaforceinastaticsensewhichwouldcausesomestaticdeformationintheplate.ButherewhatIwouldliketodoistoapplyaforcethatvariesinasinusoidalfashion.Let'sconsiderafi*edfrequencyofoscillationoftheconstantforce.Wewillchangetherateofoscillationofthefrequencybutthepeakforcewillalwaysbethesamevalue-onlytherateofoscillationoftheforcewillchange.Wewillalsomeasuretheresponseoftheplateduetothee*citationwithanaccelerometerattachedtoonecorneroftheplate.考慮一個(gè)自由支撐平板，施加常力于平板一角。我們通常從靜態(tài)的意義上來對(duì)待一個(gè)力，它在平板引起*種靜態(tài)變形。但這里我要做的是施加一個(gè)按正弦方式變化的力，振蕩頻率固定的常力。我們將改變振蕩頻率，但不改變力的峰值-僅是力的振蕩頻率改變。另在平板一角安裝一加速度計(jì)來測(cè)量鼓勵(lì)引起的平板響應(yīng)。Nowifwemeasuretheresponseontheplatewewillnoticethattheamplitudechangesaswechangetherateofoscillationoftheinputforce.Therewillbeincreasesaswellasdecreasesinamplitudeatdifferentpointsaswesweepupintime.Thisseemsveryoddsinceweareapplyingaconstantforcetothesystemyettheamplitudevariesdependingontherateofoscillationoftheinputforce.Butthisise*actlywhathappens-theresponseamplifiesasweapplyaforcewitharateofoscillationthatgetscloserandclosertothenaturalfrequency(orresonantfrequency)ofthesystemandreachesama*imumwhentherateofoscillationisattheresonantfrequencyofthesystem.Whenyouthinkaboutit,that'sprettyamazingsinceIamapplyingthesamepeakforceallthetime-onlytherateofoscillationischanging!如果現(xiàn)在測(cè)量平板響應(yīng)，注意到當(dāng)改變輸入力的振蕩頻率時(shí)，響應(yīng)幅值也發(fā)生變化。頻率升高過程中，不同時(shí)刻點(diǎn)上，幅值有增也有減。這好似很奇怪，因?yàn)槲覀兪┘映Ａτ谙到y(tǒng)，響應(yīng)幅值卻隨輸入力的振蕩速率而變化。但這確確實(shí)實(shí)發(fā)生了——當(dāng)施加的力的振蕩速率越來越接近于系統(tǒng)固有頻率〔或共振頻率〕時(shí)，響應(yīng)增大，當(dāng)振蕩速率為系統(tǒng)固有頻率時(shí)，響應(yīng)到達(dá)最大值。想想看，這真令人驚奇，因?yàn)槲颐繒r(shí)每刻都施加了一樣幅值的力-僅僅是振蕩速率改變而已！Thistimedataprovidesveryusefulinformation.ButifwetakethetimedataandtransformittothefrequencydomainusingtheFastFourierTransformthenwecanputesomethingcalledthefrequencyresponsefunction.Nowtherearesomeveryinterestingitemstonote.Weseethattherearepeaksinthisfunctionwhichoccurattheresonantfrequenciesofthesystem.Nowwenoticethatthesepeaksoccuratfrequencieswherethetimeresponsewasobservedtohavema*imumresponsecorrespondingtotherateofoscillationoftheinpute*citation.這個(gè)時(shí)域數(shù)據(jù)提供了非常有用的信息。但是如果采集到時(shí)域數(shù)據(jù)，并利用快速傅立葉變換將它變換到頻域，則可以求得所謂的頻響函數(shù)?，F(xiàn)在有幾點(diǎn)要關(guān)注：系統(tǒng)共振頻率處，這個(gè)函數(shù)上有峰值。輸入鼓勵(lì)的振蕩速率等于峰值頻率的位置，觀察到了時(shí)域最大響應(yīng)。Nowifweoverlaythetimetracewiththefrequencytracewhatwewillnoticeisthatthefrequencyofoscillationatthetimeatwhichthetimetracereachesitsma*imumvaluecorrespondstothefrequencywherepeaksinthefrequencyresponsefunctionreachama*imum.Soyoucanseethatwecanuseeitherthetimetracetodeterminethefrequencyatwhichma*imumamplitudeincreasesoccurorthefrequencyresponsefunctiontodeterminewherethesenaturalfrequenciesoccur.Clearlythefrequencyresponsefunctioniseasiertoevaluate.現(xiàn)在如果將時(shí)域波形跟頻響圖形疊加在一起，會(huì)注意到時(shí)域波形到達(dá)最大值時(shí)的振蕩頻率與頻響函數(shù)最大峰處的頻率相一致。所以，既可以利用時(shí)域波形來確定幅值到達(dá)最大值處的頻率，也可以用頻響函數(shù)來確定固有頻率何處發(fā)生。顯然，用頻響函數(shù)更容易求。Youthoughtitwasprettyamazinghowthestructurehasthesenaturalcharacteristics.Well,thedeformationpatternsatthesenaturalfrequenciesalsotakeonavarietyofdifferentshapesdependingonwhichfrequencyisusedforthee*citationforce.構(gòu)造為何具有這些固有屬性，你感到大為驚奇。對(duì)了，在這些固有頻率處，變形形式也大為不同，依賴于激振力用哪個(gè)頻率。Nowlet'sseewhathappenstothedeformationpatternonthestructureateachoneofthesenaturalfrequencies.Let'splace45evenlydistributedaccelerometersontheplateandmeasuretheamplitudeoftheresponseoftheplatewithdifferente*citationfrequencies.Ifweweretodwellateachoneofthefrequencies-eachoneofthenaturalfrequencies-wewouldseeadeformationpatternthate*istsinthestructure.Thefigureshowsthedeformationpatternsthatwillresultwhenthee*citationcoincideswithoneofthenaturalfrequenciesofthesystem.Weseethatwhenwedwellatthefirstnaturalfrequency,thereisafirstbendingdeformationpatternintheplateshowninblue.Whenwedwellatthesecondnaturalfrequency,thereisafirsttwistingdeformationpatternintheplateshowninred.Whenwedwellatthethirdandfourthnaturalfrequencies,thesecondbendingandsecondtwistingdeformationpatternsareseeningreenandmagenta,respectively.Thesedeformationpatternsarereferredtoasthemodeshapesofthestructure.(That'snotactuallyperfectlycorrectfromapuremathematicalstandpointbutforthesimplediscussionhere,thesedeformationpatternsareveryclosetothemodeshapes,forallpracticalpurposes.)好了，我們來看一看，在每個(gè)固有頻率處，構(gòu)造上的變形形式是怎樣的。在平板上均布45個(gè)加速度計(jì)，測(cè)量不同激振頻率的平板響應(yīng)幅值。如果在每個(gè)頻率處駐留——

每次一個(gè)固有頻率——可以觀察構(gòu)造上的變形形式。圖中顯示了按*一階系統(tǒng)固有頻率鼓勵(lì)時(shí)，得到的變形形式。在第一階固有頻率駐留時(shí)，平板具有第一階彎曲變形形式，如藍(lán)色所示。在第二階固有頻率駐留時(shí)，平板具有第一階扭轉(zhuǎn)變形形式，如紅色所示。在第三、四階固有頻率駐留時(shí)，第二階彎曲和第二階扭轉(zhuǎn)變形形式如綠色和紫紅色所示。這些變形形式稱為構(gòu)造的模態(tài)振型。〔從純粹數(shù)學(xué)角度講，這不完全正確。但事實(shí)上，此處簡(jiǎn)單討論起見，這些變形形式非常接近于模態(tài)振型?！砃owthesenaturalfrequenciesandmodeshapesoccurinallstructuresthatwedesign.Basically,therearecharacteristicsthatdependontheweightandstiffnessofmystructurewhichdeterminewherethesenaturalfrequenciesandmodeshapeswille*ist.Asadesignengineer,Ineedtoidentifythesefrequenciesandknowhowtheymightaffecttheresponseofmystructurewhenaforcee*citesthestructure.Understandingthemodeshapeandhowthestructurewillvibratewhene*citedhelpsthedesignengineertodesignbetterstructures.Nowthereismuchmoretoitallbutthisisjustaverysimplee*planationofmodalanalysis.你看，我們?cè)O(shè)計(jì)的所有構(gòu)造都具有這些固有頻率和模態(tài)振型。從本質(zhì)上講，這些特性依賴于構(gòu)造的質(zhì)量和剛度，它決定了固有頻率和模態(tài)振型存于何處。作為設(shè)計(jì)工程師，需要識(shí)別這些頻率，并且需要知道當(dāng)力鼓勵(lì)構(gòu)造時(shí)，它們是如何影響構(gòu)造響應(yīng)的。理解模態(tài)振型和受激構(gòu)造如何振動(dòng)，將有助于設(shè)計(jì)工程師設(shè)計(jì)出更優(yōu)的構(gòu)造。然而模態(tài)分析的容很多，這只是一個(gè)非常簡(jiǎn)單的解釋。Nowwecanbetterunderstandwhatmodalanalysisisallabout-itisthestudyofthenaturalcharacteristicsofstructures.Boththenaturalfrequencyandmodeshape(whichdependsonthemassandstiffnessdistributionsinmystructure)areusedtohelpdesignmystructuralsystemfornoiseandvibrationapplications.Weusemodalanalysistohelpdesignalltypesofstructuresincludingautomotivestructures,aircraftstructures,spacecraft,puter