Yintoni intshukumo yomgca?

Ukungcangcazela komgca: i-elasticity yamacandelo kwinkqubo ixhomekeke kumthetho we-hooke, kwaye amandla okudambisa awenziwe ngexesha lokunyakaza alingana ne-equation yokuqala yesantya esiqhelekileyo (ixesha eliphuma kwi-generalized coordinates).

ingcamango

Inkqubo yomgca idla ngokuba yimodeli engabonakaliyo yentshukumo yokwenyani.Inkqubo yokungcangcazela kwemigca isebenzisa umgaqo-siseko we-superposition, oko kukuthi, ukuba impendulo yenkqubo ngu-y1 phantsi kwesenzo segalelo x1, kunye no-y2 phantsi kwesenzo segalelo x2, ke impendulo yenkqubo phantsi kwesenzo segalelo x1 kunye no-x2 ngu-y1+y2.

Ngokwesiseko somgaqo-siseko we-superposition, igalelo elingenasizathu lingachithwa libe sisimbuku soluhlu lweempembelelo ezingapheliyo, kwaye ke impendulo epheleleyo yenkqubo inokufumaneka.Isixa samacandelo e-harmonic we-excitation ye-periodic inokwandiswa ibe yi- uchungechunge lwamacandelo e-harmonic ngu-Fourier ukuguqula, kunye nesiphumo secandelo ngalinye le-harmonic kwinkqubo inokuphandwa ngokwahlukileyo.Ngoko ke, iimpawu zokuphendula zeenkqubo zomgca kunye nokuqhubekayo iiparamitha zinokuchazwa ngempendulo engxamisekileyo okanye ngokuphendula rhoqo.

Impendulo ye-impulse ibhekisela kwimpendulo yenkqubo kwi-unit impulse, ebonisa iimpawu zokuphendula zenkqubo kwixesha lexesha. ngotshintsho lweFourier.

ukuhlelwa

Ungcangcazelo lomgama lungohlulwa lube lungcangcazelo olulandelelanayo lwenkqubo yedigri enye yenkululeko kunye nokungcangcazela kwemigca yenkqubo yenkululeko.

(1) ungcangcazelo olulayini lwenkqubo yeqondo elinye lenkululeko lungcangcazelo olumda olumo lunokumiselwa lulungelelwaniso oluqhelekileyo.Yeyona ntshukumo ilula ekunokuvela kuyo iingqiqo ezininzi ezisisiseko kunye neempawu zokungcangcazela.Ibandakanya elula ukungcangcazela kwe-harmonic, ukungcangcazela kwasimahla, ukungcangcazela kunye nokungcangcazela ngenkani.

Ungcangcazelo olulula lwe-harmonic: intshukumo ebuyelanayo yento kwindawo ekufutshane nendawo yayo yokulinganisa ngokomthetho we-sinusoidal phantsi kwesenzo sokubuyisela amandla ngokomlinganiselo wokufuduswa kwayo.

Ukungcangcazela okudambisiweyo: Ukungcangcazela okuthe i-amplitude ithotywa ngokuqhubekayo kubukho be-friction kunye nokumelana ne-dielectric okanye okunye ukusetyenziswa kwamandla.

Ukungcangcazela okunyanzelekileyo: ukungcangcazela kwenkqubo phantsi kovuselelo oluqhubekayo.

(2) ukungcangcazela kwelayini kwenkqubo ye-multi-degree-of-freedom kukungcangcazela kwenkqubo yomgca ene-n≥2 degrees of freedom.Inkqubo ye-n degrees yenkululeko ine-frequencies zendalo kunye neendlela eziphambili.Naluphi na ulungelelwaniso lokungcangcazela. yenkqubo inokumelwa njengendibaniselwano yomgca yeendlela eziphambili.Ngoko ke, indlela engundoqo yendlela ye-superposition isetyenziswa ngokubanzi kuhlalutyo lokuphendula oluguquguqukayo lweenkqubo ezininzi ze-dof. ukulinganisa kunye nohlalutyo lweempawu zendalo zokungcangcazela kwenkqubo iba linyathelo lesiqhelo kuyilo oluguquguqukayo lwenkqubo.Iimpawu eziguquguqukayo zeenkqubo ezininzi ze-dof nazo zinokuchazwa ngeempawu zokuphindaphinda imveliso, uphawu lwematriksi luyakhiwa.Kukho unxulumano oluqinisekileyo phakathi kophawu oluphindaphindayo kunye nemowudi engundoqo.Ijiko lophawu lwe-amplitude-frequency yenkqubo yenkululeko emininzi yahlukile kuleyo inkqubo yenkululeko enye.

Ukungcangcazela komgca weqondo elinye lenkqubo yenkululeko

Ukungcangcazela kwelayini apho ubume benkqubo bunokumiselwa lulungelelwaniso oluqhelekileyo.Yeyona ntshukumo ilula kwaye isisiseko ekunokuvela kuyo iingqiqo ezininzi ezisisiseko kunye neempawu zokungcangcazela.Ibandakanya ukungcangcazela okulula okuhambelanayo, ukungcangcazela okumanzi kunye nokungcangcazela okunyanzelekileyo. .

Ukungcangcazela kweHarmonic

Ngaphantsi kwesenzo sokubuyisela amandla ngokulinganayo nokufuduka, into iphinda ibuyele ngendlela ye-sinusoidal kufuphi nendawo yayo yokulinganisa (FIG. 1) .X imele ukufuduka kwaye i-t imele ixesha. Inkcazo yemathematika yolu ngcangcazelo yile:

(1)Apho u-A elona xabiso liphezulu lokufuduswa x, elibizwa ngokuba yi-amplitude, kwaye imele ubunzulu bentshukumo;I-Omega n yi-amplitude ye-Angle yokunyuswa kwentshukumo ngomzuzwana, ebizwa ngokuba yi-angular frequency, okanye i-circular frequency; kubizwa ngokuba sisigaba sokuqala.Ngokubhekiselele ku-f= n/2, inani lokujikeleza ngesekhondi libizwa ngokuba si-frequency;Inguquko yale, T=1/f, ixesha elithathayo ukujikeleza umjikelo omnye, kwaye loo nto ibizwa ngokuba lixesha.I-Amplitude A, frequency f (okanye i-angular frequency n), isigaba sokuqala, esaziwa ngokuba yi-harmonic vibration elula izinto ezintathu.

IKHIWANE. I-1 ye-harmonic vibration curve elula

Njengoko kubonisiwe kwi-FIG. I-2, i-oscillator elula ye-harmonic yenziwe ngubunzima obugxininisiweyo m exhunywe ngumthombo we-linear.

Kuphi na ukuqina kwentwasahlobo.Isisombululo ngokubanzi kule nxaki ingentla ngu-(1) .A kwaye sinokumiselwa kwindawo yokuqala x0 kunye nesantya sokuqala ku-t=0:

Kodwa i-omega n imiselwa kuphela ziimpawu zenkqubo ngokwayo m kunye no-k, ezizimeleyo kwiimeko ezongezelelweyo zokuqala, ngoko i-omega n yaziwa ngokuba yi-frequency yendalo.

IKHIWANE. I-2 idigri enye yenkqubo yenkululeko

Kwi-oscillator elula ye-harmonic, isixa samandla e-kinetic kunye namandla anokubakho ahlala ehlala, oko kukuthi, amandla apheleleyo omatshini wenkqubo agciniwe.Kwinkqubo yokungcangcazela, amandla e-kinetic kunye namandla anokubakho aguqulwa rhoqo.

Ukungcangcazela okumanzi

I-vibration e-amplitude yayo iqhubeka igxininiswe yi-friction kunye nokumelana ne-dielectric okanye enye i-energy vibration. Kwi-micro vibration, isantya ngokuqhelekileyo asisikhulu kakhulu, kwaye ukuchasana okuphakathi kuhambelana nesantya ukuya kumandla okuqala, angabhalwa njenge-c. i-coefficient yokudambisisa

(2)Apho, m =c/2m ibizwa ngokuba yiparamitha yokudambisa, kwaye.Isisombululo ngokubanzi sefomula (2) singabhalwa:

(3)Ubudlelwane bamanani phakathi kwe-omega n kunye ne-PI bunokwahlulwa ngokwezi meko zintathu zilandelayo:

N > (kwimeko yokudambisa okuncinci) iqhekezana eliveliswe ukungcangcazela, i-vibration equation yile:

I-amplitude yayo iyancipha kunye nexesha ngokuhambelana nomthetho we-exponential oboniswe kwi-equation, njengoko kuboniswe kumgca onamachaphaza kwi-FIG. 3. Ukuthetha ngokuthe ngqo, oku kungcangcazela kuyenzeka ngamaxesha athile, kodwa ukuphindaphindwa kwencopho yayo kunokuchazwa ngolu hlobo:

Ibizwa ngokuba yireyithi yokunciphisa i-amplitude, liphi ixesha lokungcangcazela.I-logarithm yendalo yezinga lokunciphisa i-amplitude ibizwa ngokuba yi-logarithm minus (amplitude) rate.Ngokucacileyo, =, kule meko, ilingana no-2/1.Ngqo ngokusebenzisa idelta yovavanyo lovavanyo kwaye, ngokusebenzisa le fomula ingentla ingabalwa c.

Ngeli xesha, isisombululo se-equation (2) sinokubhalwa:

Kunye nesalathiso sesantya sokuqala, sinokwahlulwa sibe ngamatyala amathathu angashukumiyo njengoko kubonisiwe kwiFIG. 4.

N < (kwimeko yokudambisa okukhulu), isisombululo se-equation (2) siboniswe kwi-equation (3) .Ngeli nqanaba, inkqubo ayisayi kunyakaza.

Ukungcangcazela okunyanzelekileyo

Ukungcangcazela kwenkqubo phantsi kwe-excitation eqhubekayo.Uhlalutyo lwe-Vibration luphanda ngokuphendula kwenkqubo kwi-excitation.I-excitation ye-periodic yi-excitation eqhelekileyo. impendulo yenkqubo kwi-excitation ye-harmonic nganye iyafuneka.Ngaphantsi kwesenzo sokuvuselela i-harmonic, i-equation ye-equation yentshukumo yedigri enye. yenkululeko inkqubo damped kungabhalwa:

Impendulo sisimbuku samacandelo amabini. Enye inxalenye yimpendulo yokungcangcazela okumanzi, okubola ngokukhawuleza ngexesha.Impendulo yenye inxalenye yokungcangcazela ngenkani ingabhalwa:

IKHIWANE. 3 ijiko lokungcangcazela elimanzi

IKHIWANE. Iigophe ezi-4 zeemeko ezintathu zokuqala ezine-damping ebalulekileyo

Chwetheza kwi

H / F0 = h (), ngumlinganiselo wempendulo ezinzileyo yeamplitude ukuya kwi-excitation amplitude, ebonisa iimpawu ze-amplitude-frequency, okanye ukufumana umsebenzi; Uvuselelo oluphindaphindiweyo luboniswa kwi-FIG. 5 kunye neFIG. 6.

Njengoko kunokubonwa kwi-curve ye-amplitude-frequency curve (FIG. 5), kwimeko ye-damping encinci, i-curve ye-amplitude-frequency inencopho enye. ebizwa ngokuba yi-resonant frequency of the system.Kwimeko ye-damping encinci, i-resonance frequency ayihlukanga kakhulu kwi-frequency yendalo.Xa i-excitation frequency. isondele kwi-frequency yendalo, i-amplitude iyanda ngokukhawuleza. Lo mcimbi ubizwa ngokuba yi-resonance.Nge-resonance, inzuzo yenkqubo yandiswa kakhulu, oko kukuthi, ukungcangcazela okunyanzeliswayo kolona xinzelelo.Ngoko ke, ngokubanzi, soloko uzama ukuphepha i-resonance, ngaphandle kokuba ezinye izixhobo kunye nezixhobo zokusebenzisa i-resonance ukuphumeza enkulu. ukungcangcazela.

IKHIWANE. I-5 amplitude frequency curve

Inokubonwa kwi-curve ye-frequency curve (umzobo 6), kungakhathaliseki ukuba ubungakanani be-damping, kwi-omega zero phase umahluko bits = PI / 2, olu phawu lunokusetyenziswa ngokufanelekileyo kumlinganiselo we-resonance.

Ukongeza kwi-excitation eqhubekayo, iinkqubo ngamanye amaxesha zidibana ne-excitation engazinzanga.Inokwahlulwa ngokungqongqo ibe ziindidi ezimbini: enye yimpembelelo yequbuliso.Okwesibini yimpembelelo ehlala ixesha elide yokuzikhethela.Phantsi kovuselelo olungazinzanga, impendulo yenkqubo nayo ayizinzanga.

Isixhobo esinamandla sokuhlalutya ukungcangcazela okungazinzanga yindlela yokusabela kwempembelelo.Ichaza iimpawu eziguquguqukayo zenkqubo kunye nempendulo yethutyana yegalelo leyunithi yempembelelo yenkqubo.Impembelelo yeyunithi ingabonakaliswa njengomsebenzi wedelta.Kwinjineli, idelta umsebenzi uhlala uchazwa ngolu hlobo:

Apho u-0- emele inqaku ku-t-axis esondela ku-zero ukusuka ekhohlo;0 dibanisa yingongoma eya ku-0 ukusuka ekunene.

IKHIWANE. 6 isigaba frequency ijika

IKHIWANE. 7 naliphi na igalelo linokuthi lithathwe njenge sum of series of impulse elements

Inkqubo ihambelana nempendulo h (t) eyenziwa yiyunithi yempembelelo ku-t=0, ebizwa ngokuba ngumsebenzi wempendulo yempembelelo.Kucingelwa ukuba inkqubo imile phambi kokubetha, h(t)=0 ye-t<0.Ukwazi Umsebenzi wempendulo yempembelelo yendlela, singafumana impendulo yesixokelelwano kulo naliphi na igalelo x(t). Kweli nqanaba, ungacinga nge x(t) njengesiphumo sothotho lwempembelelo. izinto (FIG. 7).Impendulo yenkqubo yile:

Ngokusekwe kumgaqo-siseko wesikhundla esiphezulu, impendulo iyonke yenkqubo ehambelana no-x(t) yile:

Esi sidibanisi sibizwa ngokuba yi-convolution integral okanye i-superposition integral.

Ukungcangcazela komgca wenkqubo ye-multi-degree-of-freedom

Ukungcangcazela kwenkqubo yomgca ene-n≥2 degrees yenkululeko.

Umzobo we-8 ubonisa ii-subsystems ezimbini ezilula ze-resonant ezidityaniswe yi-coupling spring.Ngenxa yokuba yinkqubo ye-degree-degree-of-freedom, i-coordinates ezimbini ezizimeleyo ziyafuneka ukumisela indawo yayo.Kukho iifrikhwensi ezimbini zendalo kule nkqubo:

I-frequency nganye ihambelana nemo ye-vibration.I-oscillators ye-harmonic iqhuba i-harmonic oscillations ye-frequency efanayo, idlula ngokuhambelanayo kwindawo yokulinganisa kwaye ifikelele ngokuhambelanayo kwindawo egqithiseleyo.Kwi-vibration engundoqo ehambelana ne-omega enye, x1 ilingana no-x2; eyona ntshukumo iphambili ehambelana ne-omega omega ezimbini, i-omega omega enye.Kwintshukumo engundoqo, umlinganiselo wokufuduswa kobunzima obunye bugcina Unxulumano oluthile kwaye lwenza indlela ethile, ebizwa ngokuba yimowudi engundoqo okanye imo yendalo.I-orthogonality yobunzima kunye nokuqina ikhona phakathi kweendlela eziphambili, ezibonisa ukuzimela kokungcangcazela ngalunye. yenkqubo yamanqanaba amaninzi enkululeko.

IKHIWANE. 8 inkqubo enamanqanaba amaninzi enkululeko

Inkqubo ye-n degrees yenkululeko ine-frequencies zendalo kunye neendlela eziphambili.Naluphi na ulungelelwaniso lwe-vibration yenkqubo inokumelwa njengendibaniselwano yomgca yeendlela eziphambili.Ke ngoko, indlela engundoqo yendlela yokubekwa phezulu isetyenziswa ngokubanzi kuhlalutyo lwempendulo eguquguqukayo yobuninzi. -dof systems.Ngale ndlela, umlinganiselo kunye nohlalutyo lweempawu zendalo zokungcangcazela kwenkqubo iba linyathelo lesiqhelo kuyilo oluguquguqukayo lwenkqubo.

Iimpawu eziguquguqukayo zenkqubo ye-multi-dof nazo zingachazwa ngeempawu zefrikhwensi.Njengoko kukho umsebenzi weempawu eziphindaphindiweyo phakathi kwegalelo kunye nemveliso nganye, i-matrix ye-frequency characterism iyakhiwa.Ijiko leempawu ze-amplitude-frequency ye-multi-freedom system yahlukile. ukusuka kuleyo yenkqubo yenkululeko enye.

I-elastomer iyangcangcazela

Le multi-degree of freedom system ingentla yimodeli eqikelelwayo yomatshini weelastomer.Ielastomer inenani elingenasiphelo ledegrees zenkululeko.Kukho umahluko wobungakanani kodwa akukho mahluko ubalulekileyo phakathi kwezi zimbini.Nayiphi na elastomer inenani elingenasiphelo leefrikhwekhweni zendalo kwaye inani elingenasiphelo leendlela ezihambelanayo, kwaye kukho i-orthogonality phakathi kweendlela zobunzima kunye nokuqina.Naluphi na ulungelelwaniso lokungcangcazela kweelastomer. inokubonakaliswa kwakhona njengomgca ophezulu weendlela eziphambili.Ngoko ke, kuhlalutyo lwempendulo eguquguqukayo ye-elastomer, indlela ye-superposition yemowudi engundoqo isasebenza (jonga ukungcangcazela komgca we-elastomer).

Thatha ukungcangcazela komtya. Masithi umtya obhityileyo wobunzima m ngeyunithi ubude, ubude l, ucinezelekile kuzo zozibini iziphelo, kwaye uxinzelelo yi T.Ngeli xesha, ukuphindaphindeka kwendalo komtya kumiselwa ngoku kulandelayo. Inxaki:

F =na/2l (n= 1,2,3…).

Apho, siphi isantya sosasazo lwamaza amaza anqamlezayo kwicala lomtya.Izandi zendalo zemitya ziyenzeka ukuba ziziphindaphindo zesiseko esiphindaphindwayo ngaphezulu kwe-2l.Olu phinda-phiko ludityanisiweyo lukhokelela kulwakhiwo olumnandi lwe-harmonic. Ngokubanzi, akukho Unxulumano olupheleleyo olunjalo phakathi kwamaza endalo e-elastomer.

Iimowudi ezintathu zokuqala zomtya woxinzelelo zibonisiwe kwi-FIG. 9. Kukho ezinye iinqununu kwi-curve yemowudi ephambili.Kwi-vibration enkulu, ii-nodes azidlidlizi.FIG. I-10 ibonisa iindlela ezininzi eziqhelekileyo zepleyiti ejikelezayo exhaswa ngokujikelezayo kunye nemigca ye-nodal eyenziwe ngezangqa kunye nobubanzi.

Uqulunqo oluchanekileyo lwengxaki ye-elastomer vibration inokuqukunjelwa njengengxaki yexabiso lomda we-equations zokwahluka kwenxalenye. Nangona kunjalo, isisombululo esichanekileyo sinokufumaneka kuphela kwezinye iimeko ezilula, ngoko kufuneka sibhenele kwisisombululo esiqikelelweyo se-elastomer eyinkimbinkimbi. Ingxaki yokungcangcazela. Undoqo wezisombululo eziqikelelweyo ezahlukeneyo kukutshintsha okungapheliyo ukuya kwisiphelo, oko kukuthi, ukucalula imilenze-engaphantsi kwamaqondo amaninzi. yenkqubo yenkululeko (inkqubo eqhubekayo) kwi-multi-degree degree of freedom system (discrete system) .Zimbini iindidi zeendlela zokudiscretization ezisetyenziswa ngokubanzi kuhlalutyo lobunjineli: i-finite element method kunye ne-modal synthesis method.

IKHIWANE. 9 imowudi yomtya

IKHIWANE. Imodi ye-10 yepleyiti esetyhula

Indlela yesiqalelo esipheleleyo sisakhiwo esidityanisiweyo esitsala ulwakhiwo oluntsonkothileyo lube kwinani eliqingqiweyo lezinto kwaye lizidibanise kwinani eliqingqiweyo leendawo. iiparamitha zokusasazwa kwento nganye zigxininiswe kwi-node nganye kwifomathi ethile, kwaye imodeli yomatshini yenkqubo edibeneyo ifunyenwe.

I-Modal synthesis kukubola kolwakhiwo oluntsonkothileyo lube ngamacandelwana alula aliqela.Ngokwesiseko sokuqonda iimpawu zokungcangcazela kwesakhelo ngasinye, isakhelo sidityaniswa sibe sisakhiwo ngokubanzi ngokweemeko zolungelelwaniso kujongano, kunye nemofoloji yokungcangcazela ngokubanzi. Ulwakhiwo lufunyanwa ngokusebenzisa imopholoji yokungcangcazela kwesakhelo ngasinye.

Ezi ndlela zimbini zihlukile kwaye zihambelana, kwaye zinokusetyenziswa njengereferensi.Indlela yokudibanisa i-modal ingaphinda idityaniswe ngokufanelekileyo kunye nokulinganisa kovavanyo ukwenza indlela yohlalutyo lwethiyori kunye novavanyo lokungcangcazela kweenkqubo ezinkulu.