Ukudlidliza komugqa: ukunwebeka kwezingxenye ohlelweni kungaphansi komthetho wehuku, futhi amandla okudambisa akhiqizwa ngesikhathi sokunyakaza alingana nesibalo sokuqala sesivinini esijwayelekile (okuphuma kokuphuma kwesikhathi kwezixhumanisi ezijwayelekile).
umqondo
Isistimu yomugqa ngokuvamile iyimodeli engabonakali yokudlidliza kwesistimu yangempela.Isistimu yokudlidliza engumugqa isebenzisa isimiso sokuma okuphezulu, okungukuthi, uma impendulo yesistimu ingu-y1 ngaphansi kwesenzo sokufaka x1, kanye no-y2 ngaphansi kwesenzo sokufaka x2, bese impendulo yesistimu ngaphansi kwesenzo sokufaka x1 kanye ne-x2 ithi y1+y2.
Ngokwesisekelo somgomo we-superposition, okokufaka okungenasizathu kungahlukaniswa kube isamba sochungechunge lwemiqondo engapheli, bese impendulo ephelele yesistimu ingatholwa.Isamba sezingxenye ze-harmonic ze-excitation yezikhathi ezithile singanwetshwa sibe yi-a. uchungechunge lwezingxenye ze-harmonic ngokuguqulwa kwe-Fourier, kanye nomphumela wengxenye ngayinye ye-harmonic ohlelweni ungaphenywa ngokuhlukana.Ngakho-ke, izici zokuphendula zamasistimu aqondile ahlala njalo. amapharamitha angachazwa ngokuphendula okuguquguqukayo noma impendulo yemvamisa.
Impendulo ye-Impulse ibhekisela ekuphenduleni kwesistimu ku-unit impulse, ebonisa izici zokuphendula zesistimu kusizinda sesikhathi.Impendulo ye-Frequency ibhekisela kusici sokuphendula sohlelo ekufakweni kweyunithi ye-harmonic.Ukuxhumana phakathi kwakho kokubili kunqunywa. nge-Fourier transform.
ukuhlukaniswa
Ukudlidliza komugqa kungahlukaniswa ngokudlidliza okuqondile kwesistimu ye-degree-of-freedom kanye nokudlidliza okuqondile kwesistimu ye-multi-degree-of-freedom.
(1) ukudlidliza komugqa kwesistimu yedigri eyodwa-yenkululeko ukudlidliza okuqondile ukuma kwakho kunganqunywa ngokuhlanganisa okujwayelekile.Kuwukudlidliza okulula okungatholakala kukho imiqondo eminingi eyisisekelo nezici zokudlidliza.Kuhlanganisa okulula ukudlidliza kwe-harmonic, ukudlidliza kwamahhala, ukudlidliza kokunciphisa nokudlidliza okuphoqelelwe.
Ukudlidliza okulula kwe-harmonic: ukunyakaza okuphindaphindayo kwento eseduze nendawo yayo yokulinganisa ngokomthetho we-sinusoidal ngaphansi kwesenzo samandla okubuyisela ngokulingana nokugudluzwa kwayo.
Ukudlidliza okudambisiwe: ukudlidliza okukhona ubude bawo buncishiswa ngokuqhubekayo ukuba khona kokungqubuzana nokumelana ne-dielectric noma okunye ukusetshenziswa kwamandla.
Ukudlidliza okuphoqelelwe: ukudlidliza kwesistimu ngaphansi kwesasasa eliqhubekayo.
(2) ukudlidliza komugqa kwesistimu ye-degree-of-freedom ukudlidliza kwesistimu yomugqa enamadigri angu-n≥2 enkululeko.Isistimu yama-degree angu-n enkululeko inamaza emvelo n nezindlela eziyinhloko.Noma yikuphi ukumiswa kokudlidliza yesistimu ingamelwa njengenhlanganisela yomugqa yezindlela ezinkulu.Ngakho-ke, indlela eyinhloko ye-superposition isetshenziswa kabanzi ekuhlaziyweni okuguquguqukayo kwempendulo yezinhlelo ze-multi-dof.Ngale ndlela, i ukukala nokuhlaziya izici zemvelo zokudlidliza zohlelo kuba isinyathelo esivamile ekwakhiweni okuguquguqukayo kwesistimu.Izici eziguquguqukayo zezinhlelo ze-multi-dof nazo zingachazwa ngezici zemvamisa.Njengoba kunomsebenzi wesici semvamisa phakathi kokufaka ngakunye kanye okukhiphayo, kwakhiwa i-matrix ye-frequency character.Kunobudlelwane obuqondile phakathi kophawu lwemvamisa kanye nemodi eyinhloko.Ijika lesici se-amplitude-frequency yesistimu yenkululeko eminingi yehlukile kuleyo uhlelo lwenkululeko eyodwa.
Ukudlidliza komugqa wedigri eyodwa yesistimu yenkululeko
Ukudlidliza okuqondile lapho ukuma kwesistimu kunganqunywa khona ngokuhlanganisa okujwayelekile.Kuwukuvevezela okulula nokuyisisekelo kakhulu okungatholakala kukho imiqondo eminingi eyisisekelo nezici zokudlidliza.Kuhlanganisa ukudlidliza okulula kwe-harmonic, ukudlidliza okumanzi kanye nokudlidliza okuphoqelelwe. .
Ukudlidliza kwe-Harmonic
Ngaphansi kwesenzo sokubuyisela amandla ngokulingana nokufuduka, into iphindaphinda ngendlela ye-sinusoidal eduze nendawo yayo yokulinganisa (FIG. 1).X imele ukususwa futhi u-t umele isikhathi. Inkulumo yezibalo yalokhu kudlidliza ithi:
(1)Lapho u-A eyinani eliphakeme kakhulu lokugudluka x, elibizwa ngokuthi i-amplitude, futhi emele ubukhulu bokudlidliza;I-Omega n iwukukhuphuka kwe-engeli ye-amplitude yokudlidliza ngomzuzwana, okubizwa ngokuthi i-angular frequency, noma ifrikhwensi eyindilinga; ibizwa ngesigaba sokuqala.Ngokuya ku-f= n/2, inani lokuzungeza ngomzuzwana libizwa ngokuthi i-frequency;I-inverse yalokhu, T=1/f, isikhathi esisithathayo ukuze sinyakazise umjikelezo owodwa, futhi lokho kubizwa isikhathi.I-Amplitude A, i-frequency f (noma i-angular frequency n), isigaba sokuqala, esaziwa ngokuthi i-harmonic vibration izakhi ezintathu.
I-FIG. 1 ijika lokudlidliza elilula le-harmonic
Njengoba kuboniswe ku-FIG. 2, i-harmonic oscillator elula yenziwa isisindo esigxilile esingu-m esixhunywe isiphethu somugqa.Lapho ukususwa kokudlidliza kubalwa ukusuka endaweni yokulinganisa, isibalo sokudlidliza sithi:
Kuphi ukuqina kwentwasahlobo.Isixazululo esijwayelekile salesibalo esingenhla sithi (1).A futhi singanqunywa indawo yokuqala engu-x0 kanye nesivinini sokuqala kokuthi t=0:
Kodwa i-omega n inqunywa kuphela izici zesistimu ngokwayo m no-k, ngaphandle kwezimo zokuqala ezengeziwe, ngakho-ke i-omega n yaziwa nangokuthi imvamisa yemvelo.
I-FIG. 2 idigri eyodwa yesistimu yenkululeko
Ukuze uthole i-oscillator elula ye-harmonic, isamba samandla ayo e-kinetic namandla angaba khona ahlala njalo, okungukuthi, amandla aphelele emishini yesistimu ayagcinwa.Enqubweni yokudlidliza, amandla e-kinetic namandla angaba khona aguqulwa njalo abe komunye nomunye.
Ukudlidliza okudambisayo
Ukudlidliza obude bawo be-amplitude buncishiswa ngokuqhubekayo ukungqubuzana nokumelana ne-dielectric noma okunye ukusetshenziswa kwamandla.Ngokudlidliza okuncane, isivinini ngokuvamile asisikhulu kakhulu, futhi ukumelana okuphakathi kuhambisana nesivinini kumandla okuqala, okungabhalwa ngokuthi c. i-coefficient yokudambisa.Ngakho-ke, i-equation yokudlidliza yedigri eyodwa yenkululeko enomugqa wokudambisa ingabhalwa ngokuthi:
(2)Lapho, m =c/2m ebizwa ngokuthi ipharamitha yokudambisa, futhi.Isixazululo esijwayelekile sefomula (2) singabhalwa:
(3)Ubudlelwano bezinombolo phakathi kwe-omega n ne-PI bungahlukaniswa ngamacala amathathu alandelayo:
N > (esimeni sokudambisa okuncane) izinhlayiyana ezikhiqiza ukudlidliza kokunciphisa, isibalo sokudlidliza sithi:
Ubukhulu bayo buncipha ngokuhamba kwesikhathi ngokomthetho we-exponential oboniswe ku-equation, njengoba kuboniswe emugqeni wamachashazi ku-FIG. 3.Uma sikhuluma ngokuqinile, lokhu kudlidliza kuyenzeka ngezikhathi ezithile, kodwa ukuvama kokuphakama kwakho kungachazwa ngokuthi:
Ibizwa ngokuthi izinga lokunciphisa i-amplitude, sikuphi isikhathi sokudlidliza.I-logarithm yemvelo yezinga lokunciphisa i-amplitude ibizwa ngokuthi isilinganiso se-logarithm minus (amplitude). Ngokusobala, =, kulesi simo, ilingana no-2/1. Ngokuqondile i-delta yokuhlola yokuhlola futhi, ngokusebenzisa ifomula engenhla ingabalwa c.
Ngalesi sikhathi, isixazululo se-equation (2) singabhalwa:
Ngokuhambisana nesiqondiso sesivinini sokuqala, ingahlukaniswa ngamacala amathathu angadlidlizi njengoba kukhonjisiwe ku-FIG. 4.
N < (esimweni sokudambisa okukhulu), isixazululo se-equation (2) siboniswa kuzibalo (3).Kuleli qophelo, isistimu ayisadlidlizi.
Ukudlidliza okuphoqelelwe
Ukudlidliza kwesistimu ngaphansi kwesasasa eliqhubekayo.Ukuhlaziywa kokudlidliza kuphenya ngokuyinhloko ukusabela kwesistimu ekusaseni.Injabulo yesikhathi esithile iyinjabulo evamile evamile.Njengoba isasasa lezikhathi ezithile lingahlala liboliswa libe yisamba sokusatshalaliswa kwe-harmonic okuningana, ngokuvumelana nesimiso se-superposition, kuphela. impendulo yesistimu ekuvusweni ngakunye kwe-harmonic iyadingeka.Ngaphansi kwesenzo se-harmonic excitation, i-equation ehlukile yokunyakaza kwedigri eyodwa. of freedom damped system ingabhalwa:
Impendulo iyisamba sezingxenye ezimbili. Ingxenye eyodwa ukuphendula kokudlidliza okumanzi, okubola ngokushesha ngokuhamba kwesikhathi.Impendulo yenye ingxenye yokudlidliza okuphoqelelwe ingabhalwa:
I-FIG. 3 ijika lokudlidliza elimanzi
I-FIG. Amajika angu-4 ezimo ezintathu zokuqala ezinomswakama obalulekile
Thayipha i
I-H /F0= h (), isilinganiso se-amplitude yokuphendula engaguquki ukuya ku-amplitude yenjabulo, ebonisa izici ze-amplitude-frequency, noma umsebenzi ozuzayo;Amabhithi okuphendula isimo esizinzile nesisusa sesigaba, ukubonakaliswa kwezici zefrikhwensi yesigaba.Ubudlelwano phakathi kwabo kanye i-excitation frequency iboniswa ku-FIG. 5 kanye ne-FIG. 6.
Njengoba kungabonwa kwijika le-amplitude-frequency curve (FIG. 5), esimweni sokumanzisa okuncane, ijika le-amplitude-frequency linokuphakama okukodwa.I-damping encane, ikhuphuka isiqongo;Imvamisa ehambisana nesiqongo ebizwa ngokuthi i-resonant frequency of the system.Endabeni yokumanzisa okuncane, i-resonance frequency ayihluke kakhulu kunemvamisa yemvelo.Lapho i-excitation frequency. iseduze nemvamisa yemvelo, i-amplitude iyanda kakhulu. Lesi simo sibizwa ngokuthi i-resonance.Nge-resonance, inzuzo yesistimu iyanda, okungukuthi, ukudlidliza okuphoqelekile kunamandla kakhulu. ukudlidliza.
I-FIG. 5 amplitude frequency curve
Ingabonwa kusukela kujika lemvamisa yesigaba (umfanekiso 6), kungakhathaliseki ukuthi ungakanani umswakama, kumabhithi omehluko wesigaba se-omega zero = PI / 2, lesi sici singasetshenziswa ngempumelelo ekulinganiseni ukuzwakala kwe-resonance.
Ngaphezu kwesasasa eliqhubekayo, amasistimu ngezinye izikhathi ahlangabezana nenjabulo engazinzile.Ingase ihlukaniswe cishe ibe izinhlobo ezimbili: eyodwa umthelela ongazelelwe.Okwesibili umphumela ohlala njalo wokuzenzela.Ngaphansi kwesasasa elingazinzile, ukusabela kwesistimu nakho akuzinzile.
Ithuluzi elinamandla lokuhlaziya ukudlidliza okungagxilile indlela yokuphendula umfutho.Ichaza izici eziguqukayo zesistimu nempendulo yesikhashana yokokufaka kweyunithi yomfutho wesistimu.I-unit impulse ingavezwa njengomsebenzi we-delta.Kubunjiniyela, i-delta umsebenzi uvame ukuchazwa ngokuthi:
Lapho u-0- emele iphuzu ku-axis ka-t esondela ku-zero ukusuka kwesokunxele; u-0 plus uyiphoyinti eliya ku-0 ukusuka kwesokudla.
I-FIG. 6 isigaba ijika imvamisa
I-FIG. 7 noma yikuphi okokufaka kungabhekwa njengesamba sochungechunge lwezakhi zomfutho
Isistimu ihambisana nempendulo h(t) ekhiqizwe i-unit impulse ku-t=0, ebizwa ngokuthi umsebenzi we-impulse response.Kuthatha ngokuthi isistimu imile ngaphambi kwe-pulse, h(t)=0 kokuthi t<0.Ukwazi umsebenzi wokuphendula umfutho wesistimu, singathola impendulo yesistimu kunoma yikuphi okokufaka x(t).Kuleli qophelo, ungacabanga ngo-x(t) njengesamba sochungechunge lomfutho. izakhi (FIG. 7).Impendulo yohlelo ithi:
Ngokusekelwe kumgomo we-Superposition, impendulo ephelele yesistimu ehambisana no-x(t) ithi:
Lokhu okubalulekile kubizwa ngokuthi i-convolution integral noma i-superposition integral.
Ukudlidliza okuqondile kwesistimu ye-multi-degree-of-freedom
Ukudlidliza kwesistimu yomugqa enamadigri angu-n≥2 enkululeko.
Umfanekiso wesi-8 ubonisa amasistimu angaphansi amabili alula axhunywe isiphethu esihlanganisayo.Ngenxa yokuthi iyisistimu yenkululeko eneziqu ezimbili, izixhumanisi ezimbili ezizimele ziyadingeka ukuze kunqunywe indawo yazo.Kunamafrikhwensi amabili emvelo kulolu hlelo:
Ifrikhwensi ngayinye ihambisana nemodi yokudlidliza.Ama-oscillator e-harmonic enza ama-oscillations e-harmonic of frequency efanayo, edlula ngendlela efanayo endaweni yokulinganisa futhi afinyelele ngokuhambisanayo endaweni eyeqisayo.Ekudlidlizeni okuyinhloko okuhambisana ne-omega eyodwa, x1 ilingana no-x2; ukudlidliza okuyinhloko okuhambisana ne-omega omega two, i-omega omega eyodwa.Ekudlidlizeni okuyinhloko, isilinganiso sokususwa kwesisindo ngasinye sigcina ukuhlobana okuthile futhi kwakha imodi ethile, ebizwa ngokuthi imodi eyinhloko noma imodi yemvelo.I-orthogonality yesisindo nokuqina ikhona phakathi kwezindlela eziyinhloko, ezibonisa ukuzimela kokudlidliza ngakunye.Imvamisa yemvelo kanye nemodi eyinhloko imelela izici zokudlidliza ezingokwemvelo. yohlelo lwenkululeko olunamazinga amaningi.
I-FIG. 8 uhlelo olunamadigri amaningi enkululeko
Isistimu ye-n degrees yenkululeko ine-n frequencies yemvelo kanye nezindlela eziyinhloko.Noma yikuphi ukumiswa kokudlidliza kwesistimu kungamelwa njengenhlanganisela yomugqa yezindlela ezinkulu.Ngakho-ke, indlela yokubeka phezulu yemodi eyinhloko isetshenziswa kakhulu ekuhlaziyweni okuguquguqukayo kwempendulo yeningi. -dof systems.Ngale ndlela, ukukala nokuhlaziywa kwezici zemvelo zokudlidliza kohlelo kuba yisinyathelo esijwayelekile ekwakhiweni okuguquguqukayo kwesistimu.
Izici eziguqukayo zamasistimu e-multi-dof nazo zingachazwa ngezici zemvamisa.Njengoba kunomsebenzi wesici semvamisa phakathi kokufaka nokuphuma ngakunye, kwakhiwa i-matrix yesici se-frequency.Ijika lesici se-amplitude-frequency yesistimu yenkululeko eminingi ihlukile. kusukela kuleso sohlelo lwenkululeko eyodwa.
I-elastomer iyandindizela
Isistimu ye-multi - degree of freedom engenhla iyimodeli elinganiselwe yemishini ye-elastomer.I-elastomer inenani elingapheli lamadigri enkululeko.Kunomehluko wobuningi kodwa awukho umehluko obalulekile phakathi kwakho kokubili.Noma iyiphi i-elastomer inenombolo engapheli yamafrikhwensi emvelo futhi inombolo engapheli yezindlela ezihambisanayo, futhi kukhona i-orthogonality phakathi kwezinhlobo zesisindo nokuqina.Noma yikuphi ukumiswa kokudlidliza kwe-elastomer ingase futhi imelelwe njengokuphezulu komugqa wezindlela ezinkulu.Ngakho-ke, ukuze kuhlaziywe impendulo eguquguqukayo ye-elastomer, indlela yokubeka phezulu yemodi eyinhloko isasebenza (bheka ukudlidliza komugqa kwe-elastomer).
Thatha ukudlidliza kweyunithi yezinhlamvu.Masisho ukuthi iyunithi yezinhlamvu encane yesisindo m ubude beyunithi ngayinye, ubude l, igxiliwe kuzo zombili iziphetho, futhi ukuqina ngu-T.Kulesi sikhathi, imvamisa yendalo yentambo inqunywa yilokhu okulandelayo. isibalo:
F =na/2l (n= 1,2,3…).
Ikuphi, isivinini sokusabalala segagasi eliguquguqukayo eduze kochungechunge lwentambo.Amafrikhwensi emvelo eyunithi yezinhlamvu ayenzeka kube ukuphindaphinda kwemvamisa eyisisekelo ngaphezu kuka-2l.Lokhu kuphindaphindeka kwenombolo kuholela esakhiweni esivumelanayo esijabulisayo.Ngokujwayelekile, akukho ubudlelwano obunjalo obuphelele phakathi kwamafrikhwensi emvelo we-elastomer.
Izindlela ezintathu zokuqala zeyunithi yezinhlamvu eziqinile ziboniswa ku-FIG. 9. Kunama-node athile ejikeni lemodi eyinhloko.Ekudlidlizeni okukhulu, ama-node awadlidlizi.FIG. 10 ikhombisa izindlela ezimbalwa ezijwayelekile zepuleti eliyindilinga elisekelwa ukuzungeza elinemigqa eyisiyingi eyakhiwe yimibuthano namadayamitha.
Ukwakhiwa okuqondile kwenkinga yokudlidliza kwe-elastomer kungaphethwa njengenkinga yenani lomngcele wezibalo ezihlukanisayo eziyingxenye. Nokho, isisombululo esiqondile singatholakala kuphela kwezinye zezimo ezilula kakhulu, ngakho-ke kufanele siphendukele kusixazululo esilinganiselwe se-elastomer eyinkimbinkimbi. inkinga yokudlidliza.Ingqikithi yezixazululo ezihlukahlukene ezilinganiselwe ukuguqula okungapheli kuya kwesiphetho, okungukuthi, ukuhlukanisa i-multi-degree-less yesistimu yenkululeko (isistimu eqhubekayo) ibe yisistimu yenkululeko eneziqu eziningi (i-discrete system) .Kunezinhlobo ezimbili zezindlela zokuhlukanisa ezisetshenziswa kabanzi ekuhlaziyeni ubunjiniyela: indlela yesici esinqunyelwe kanye nendlela yokuhlanganisa ye-modal.
I-FIG. 9 imodi yentambo
I-FIG. Imodi eyi-10 yepuleti eliyindilinga
Indlela yesici esiqediwe iyisakhiwo esiyinhlanganisela esifinyeza isakhiwo esiyinkimbinkimbi sibe inani elilinganiselwe lezinto futhi sizixhuma ngenani elilinganiselwe lamanodi.Iyunithi ngayinye iyi-elastomer;Ukugudluka kokusabalalisa kwesici kuvezwa umsebenzi wokuhumusha wokugudluka kwenodi.Bese amapharamitha wokusabalalisa we-elementi ngayinye agxilwe ku-node ngayinye ngefomethi ethile, futhi imodeli yomshini wesistimu ehlukene iyatholakala.
I-Modal synthesis iwukubola kwesakhiwo esiyinkimbinkimbi sibe izingxenye ezimbalwa ezilula.Ngesisekelo sokuqonda izici zokudlidliza zesakhiwo ngasinye esingaphansi, isakhi esingaphansi sihlanganiswa sibe isakhiwo esijwayelekile ngokuya ngezimo zokuxhumanisa kusixhumi esibonakalayo, kanye ne-morphology yokudlidliza ye-general. isakhiwo sitholakala ngokusebenzisa i-vibration morphology yesakhiwo ngasinye esingaphansi.
Lezi zindlela ezimbili zihlukile futhi zihlobene, futhi zingasetshenziswa njengereferensi.Indlela ye-modal synthesis ingabuye ihlanganiswe ngokuphumelelayo nesilinganiso sokuhlola ukwakha indlela yokuhlaziya yethiyori neyokuhlola yokudlidliza kwamasistimu amakhulu.
Isikhathi sokuthumela: Apr-03-2020
