igitekerezo
Sisitemu y'umurongo mubisanzwe ni moderi idasobanutse yerekana ihindagurika rya sisitemu nyayo. Sisitemu yo kunyeganyeza umurongo ikoresha ihame rya superposition, ni ukuvuga, niba igisubizo cya sisitemu ari y1 munsi yinjiza x1, na y2 munsi yinjiza x2, noneho igisubizo cya sisitemu mugikorwa cyo kwinjiza x1 na x2 ni y1 + y2.
Hishimikijwe ihame rya superposition, ibyinjijwe uko bishakiye birashobora kubora mubiteranyo byuruhererekane rwibintu bitagira umupaka, hanyuma igisubizo rusange cya sisitemu kirashobora kuboneka. Igiteranyo cyimiterere ihuza ibice byibyishimo birashobora kwagurwa muburyo a Urukurikirane rwibintu bihuza na Fourier guhinduka, ningaruka za buri kintu cyuzuzanya kuri sisitemu gishobora gukurikiranwa ukundi.Niyo mpamvu, ibisubizo biranga sisitemu y'imirongo ifite ibipimo bihoraho bishobora gusobanurwa nigisubizo cyihutirwa cyangwa igisubizo cyinshyi.
Igisubizo cya Impulse bivuga igisubizo cya sisitemu kubice byihutirwa, biranga ibisubizo biranga sisitemu mugihe cyagenwe.Igisubizo cyinshuro bivuga igisubizo kiranga sisitemu kubice byinjira byinjira. Inzandiko zandikirwa zombi ziramenyekana na Fourier guhinduka.
gushyira mu byiciro
Kunyeganyega kumurongo birashobora kugabanywa muburyo bwo kunyeganyega kumurongo umwe-wubwisanzure hamwe no kunyeganyega kumurongo wa sisitemu nyinshi-yubwisanzure.
. kunyeganyega guhuza, kunyeganyega ku buntu, kunyeganyega kwa attenuation no kunyeganyega ku gahato.
Kunyeganyega byoroshye guhuza: icyerekezo cyo gusubiranamo cyikintu kiri hafi yumwanya wacyo ukurikije amategeko ya sinusoidal hakurikijwe imbaraga zo kugarura zijyanye no kwimuka kwayo.
Kunyeganyega kwangiritse: kunyeganyega amplitude ikomeza kwiyongera bitewe no guterana amagambo hamwe no kurwanya dielectric cyangwa ubundi buryo bwo gukoresha ingufu.
Kunyeganyezwa ku gahato: kunyeganyega kwa sisitemu guhora wishimye.
. ya sisitemu irashobora kugaragazwa nkumurongo uhuza uburyo bwingenzi.Niyo mpamvu, uburyo nyamukuru superposition uburyo bukoreshwa cyane muburyo bwo gusubiza imbaraga za sisitemu ya dof nyinshi. Muri ubu buryo, gupima no gusesengura ibintu biranga ihindagurika risanzwe rya sisitemu ihinduka intambwe isanzwe muburyo bwa dinamike ya sisitemu.Ibintu biranga imbaraga za sisitemu nyinshi-dof birashobora kandi gusobanurwa nibiranga inshuro.Kubera ko hariho imikorere iranga inshuro hagati ya buri cyinjira nibisohoka, hubatswe matrike iranga umurongo.Hariho ni isano isobanutse hagati yumurongo uranga nuburyo bukuru.Amplitude-frequency iranga umurongo wa sisitemu yubwisanzure bwinshi itandukanye niy'ubwisanzure bumwe.
Kunyeganyega kumurongo wa sisitemu imwe yubwisanzure
Kunyeganyega kumurongo aho umwanya wa sisitemu ushobora kugenwa na coordinateur rusange.Ni ihindagurika ryoroheje kandi ryibanze riva aho ibitekerezo byinshi byibanze nibiranga kunyeganyega. .
Kunyeganyega kwa Harmonic
Mubikorwa byo kugarura imbaraga zijyanye no kwimurwa, ikintu gisubirana muburyo bwa sinusoidal hafi yumwanya wacyo (FIG. 1) .X byerekana kwimuka naho t byerekana igihe. Imibare yerekana iyi vibrasiya ni:
(1)Aho A nigiciro kinini cyimurwa x, cyitwa amplitude, kandi kigaragaza ubukana bwikinyeganyeza; Omega n ni amplitude Angle yiyongera yinyeganyeza kumasegonda, ibyo bita inshuro zingana, cyangwa uruziga ruzenguruka; Ibi byitwa icyiciro cyambere.Mu bijyanye na f = n / 2, umubare w’inyeganyeza ku isegonda witwa inshuro; Inyuma yibi, T = 1 / f, nigihe cyo gufata kugirango uzunguruke ukwezi, kandi ibyo byitwa ikiringo. Ubunini A, inshuro f (cyangwa inguni ya n), icyiciro cyambere, kizwi nkibintu byoroheje bihuza ibintu bitatu.
FIG. 1 byoroshye guhuza umurongo uhindagurika
Nkuko bigaragara muri FIG. 2, oscillator yoroheje ihuza ikozwe na misa yibanze ya m ihujwe nisoko yumurongo.Iyo kwimuka kwa vibrasiya bibarwa uhereye kumwanya uringaniye, ikigereranyo cyo kunyeganyega ni:
Nihe gukomera kwamasoko. Igisubizo rusange kuburinganire bwavuzwe haruguru ni (1) .A kandi birashobora kugenwa numwanya wambere x0 n'umuvuduko wambere kuri t = 0:
Ariko omega n igenwa gusa nibiranga sisitemu ubwayo m na k, ititaye kumiterere yinyongera yambere, bityo omega n nayo izwi nkinshuro zisanzwe.
FIG. Urwego 2 rumwe rwubwisanzure
Kuri oscillator yoroshye ihuza, igiteranyo cyingufu za kinetic nimbaraga zishobora guhoraho, ni ukuvuga imbaraga zose za mashini za sisitemu zirazigamwa.Mu nzira yo kunyeganyega, ingufu za kinetic nimbaraga zishobora guhora zihinduka mubindi.
Kunyeganyega
Kunyeganyega amplitude ihora yongerwaho no guterana amagambo hamwe no kurwanya dielectric cyangwa ubundi buryo bwo gukoresha ingufu.Ku kunyeganyega kwa mikoro, umuvuduko muri rusange ntabwo ari munini cyane, kandi kurwanya iringaniza ugereranije n'umuvuduko n'imbaraga za mbere, zishobora kwandikwa nkuko c ari coefficient de damping. Kubwibyo, kugereranya kunyeganyega kurwego rumwe rwubwisanzure hamwe no gutondeka umurongo bishobora kwandikwa nka:
(2)Aho, m = c / 2m byitwa damping parameter, na.Umuti rusange wa formula (2) urashobora kwandikwa:
(3)Umubano wumubare hagati ya omega n na PI urashobora kugabanywamo imanza eshatu zikurikira:
N> (mugihe cya damping nto) ibice byabyaye attenuation vibration, ikigereranyo cyo kunyeganyega ni:
Amplitude yayo igabanuka nigihe ukurikije amategeko yerekanwe yerekanwe muburinganire, nkuko bigaragara kumurongo utudomo muri FIG. 3.Mu magambo make, uku kunyeganyega ni ibihe, ariko inshuro yimpinga yayo irashobora gusobanurwa nk:
Yitwa igipimo cyo kugabanya amplitude, nihe gihe cyo kunyeganyega. Logarithm naturel ya igipimo cyo kugabanya amplitude yitwa logarithm minus (amplitude) igipimo.Biragaragara, =, muriki kibazo, bingana na 2 / 1.Binyuze mu igeragezwa ryikigereranyo delta kandi, ukoresheje formula yavuzwe haruguru irashobora kubarwa c.
Muri iki gihe, igisubizo cyo kugereranya (2) gishobora kwandikwa:
Hamwe nicyerekezo cyumuvuduko wambere, irashobora kugabanywa mubice bitatu bitanyeganyega nkuko bigaragara muri FIG. 4.
N <.
Kunyeganyezwa ku gahato
Kunyeganyega kwa sisitemu mu byishimo bidahwema. Isesengura rya Vibrasiyo rikora iperereza cyane cyane ku gisubizo cya sisitemu yo kwishima. Ibyishimo byigihe ni ibintu bisanzwe bisanzwe bishimishije. Kubera ko kwishima rimwe na rimwe bishobora guhora byangirika muburyo bwo kwishima kwinshi, ukurikije ihame rya superpression, gusa harasabwa igisubizo cya sisitemu kuri buri kintu gishimishije. Mugihe cyigikorwa cyo kwishima guhuza, kugereranya itandukaniro ryimikorere yicyiciro kimwe cyubwisanzure bwangiritse burashobora kwandikwa:
Igisubizo nigiteranyo cyibice bibiri. Igice kimwe nigisubizo cyinyeganyeza cyangiritse, cyangirika vuba nigihe.Igisubizo cyikindi gice cyo kunyeganyezwa ku gahato gishobora kwandikwa:
FIG. 3 umurongo uhindagurika
FIG. Imirongo 4 yimiterere itatu yambere hamwe no kugabanuka gukomeye
Andika muri
F inshuro zishimishije zerekanwa muri FIG. 5 na FIG. 6.
Nkuko bigaragara kuri curve amplitude-frequency curve (FIG. 5), mugihe cyo kugabanuka guto, umurongo wa amplitude-frequency umurongo ufite impinga imwe. bita resonant frequency ya sisitemu.Mu gihe cyo gutonyanga gake, rezanse yumurongo ntaho itandukaniye cyane numurongo usanzwe.Iyo inshuro yo kwishima yegereye inshuro zisanzwe, amplitude iriyongera cyane. Iyi phenomenon yitwa resonance. Kuri resonance, inyungu za sisitemu zirenze urugero, ni ukuvuga, kunyeganyezwa ku gahato ni byo bikomeye cyane.Nuko rero, muri rusange, burigihe uharanira kwirinda resonance, keretse niba ibikoresho nibikoresho bimwe na bimwe byo gukoresha resonance kugirango bigere kuri binini kunyeganyega.
FIG. 5 amplitude frequency curve
Urashobora kugaragara uhereye kumurongo wikurikiranya (ishusho ya 6), utitaye ku bunini bwa damping, muri omega zeru itandukaniro rya bits = PI / 2, iyi miterere irashobora gukoreshwa neza mugupima resonance.
Usibye kwishima guhoraho, sisitemu rimwe na rimwe ihura nibyishimo bidahwitse.Bishobora kugabanywa muburyo bubiri: imwe ningaruka zitunguranye. Iya kabiri ningaruka zirambye zubushake. Mu byishimo bidashidikanywaho, igisubizo cya sisitemu nacyo ntigihagaze.
Igikoresho gikomeye cyo gusesengura kunyeganyega kutajegajega nuburyo bwo gusubiza impulse. Irasobanura imbaraga ziranga sisitemu hamwe nigisubizo cyigihe gito cyibice byinjira muri sisitemu. Impulse yingingo irashobora kugaragazwa nkigikorwa cya delta.Mu buhanga, delta. imikorere ikunze gusobanurwa nka:
Aho 0- yerekana ingingo kuri t-axis yegera zeru uhereye ibumoso; 0 wongeyeho niyo ngingo ijya kuri 0 uhereye iburyo.
FIG. Icyiciro 6 cyumurongo
FIG. 7 ibyinjijwe byose birashobora gufatwa nkigiteranyo cyurukurikirane rwibintu byihutirwa
Sisitemu ihuye nigisubizo h (t) cyakozwe nigice cya impulse kuri t = 0, bita imikorere yo gusubiza impulse. Tuvuze ko sisitemu ihagaze mbere yimpanuka, h (t) = 0 kuri t <0.Kumenya imikorere yo gusubiza impulse ya sisitemu, dushobora kubona igisubizo cya sisitemu kubintu byose byinjijwe x (t) .Muri iyi ngingo, urashobora gutekereza kuri x (t) nkigiteranyo cyurukurikirane rwibintu (FIG. 7) .Igisubizo cya sisitemu ni:
Ukurikije ihame rya superposition, igisubizo rusange cya sisitemu ihuye na x (t) ni:
Iyi integral yitwa incamake integral cyangwa superposition integral.
Kunyeganyega kumurongo wa sisitemu nyinshi-yubwisanzure
Kunyeganyega sisitemu y'umurongo hamwe na dogere 2 z'ubwisanzure.
Igicapo 8 cerekana uburyo bubiri bworoshye bwa resonant sisitemu ihujwe nisoko ihuza.Kubera ko ari sisitemu ya dogere ebyiri-yubwisanzure, hakenewe imirongo ibiri yigenga kugirango hamenyekane aho ihagaze.Hariho imirongo ibiri isanzwe muri iyi sisitemu:
Buri frequence ihuye nuburyo bwo kunyeganyega. Ihungabana ryimikorere ikora ihuzagurika rihuza inshuro imwe, igahita inyura mumwanya uringaniye kandi igahita igera kumwanya ukabije.Mu kunyeganyeza nyamukuru guhuye na omega, x1 ihwanye na x2 Muri; ihindagurika nyamukuru rihuye na omega omega abiri, omega omega imwe.Mu kunyeganyeza nyamukuru, igipimo cyo kwimuka kwa buri misa gikomeza isano runaka kandi kigakora uburyo runaka, bwitwa uburyo nyamukuru cyangwa uburyo bwa kamere.Imikorere ya misa na gukomera bibaho muburyo bwingenzi, bugaragaza ubwigenge bwa buri kunyeganyega. Inshuro karemano nuburyo nyamukuru byerekana imiterere ihindagurika iranga urwego rwubwisanzure.
FIG. Sisitemu 8 ifite impamyabumenyi nyinshi
Sisitemu ya n dogere yubwisanzure ifite n inshuro zisanzwe hamwe nuburyo bukuru.Ibintu byose byo guhindagurika kwa sisitemu birashobora kugaragazwa nkumurongo uhuza uburyo bukomeye.Niyo mpamvu, uburyo nyamukuru bwo kugereranya ibintu bukoreshwa cyane mubisesengura ryibisubizo bya byinshi -ibikorwa bya sisitemu.Muri ubu buryo, gupima no gusesengura ibintu biranga ibinyeganyega biranga sisitemu bihinduka intambwe isanzwe mugushushanya kwa sisitemu.
Ibiranga imbaraga za sisitemu nyinshi-dof birashobora kandi gusobanurwa nibiranga inshuro.Kubera ko hariho imikorere iranga inshuro hagati ya buri cyinjira nigisohoka, hubatswe matrisa iranga umurongo.Amplitude-frequency iranga umurongo wa sisitemu yubwisanzure butandukanye. uhereye kuri sisitemu y'ubwisanzure bumwe.
Elastomer iranyeganyega
Ibice byinshi byavuzwe haruguru - urwego rwubwisanzure nuburyo bugereranijwe bwa mashini ya elastomer. Kuri elastomer ifite umubare utagira ingano wubwisanzure.Hariho itandukaniro ryinshi, ariko nta tandukaniro ryingenzi riri hagati yibi byombi. Buri elastomer afite umubare utagira ingano yumurongo wa kamere kandi umubare utagira ingano wuburyo buhuye, kandi hariho orthogonality hagati yuburyo bwa misa no gukomera.Ibintu byose bya vibrational iboneza rya elastomer nabyo birashobora kugaragazwa nkumurongo ugaragara muburyo bukomeye.Niyo mpamvu, kubisesengura ryibisubizo bya elastomer, uburyo bwa superposition bwuburyo bukuru buracyakoreshwa (reba umurongo uhindagurika wa elastomer).
Fata kunyeganyega k'umugozi. Reka tuvuge ko umugozi muto wa mass m kuri buri burebure, uburebure l, uhagaritswe ku mpande zombi, kandi impagarara ni T.Kuri iki gihe, inshuro karemano yumugozi igenwa nibi bikurikira ikigereranyo:
F = na / 2l (n = 1,2,3…).
Aho, ni umuvuduko wo gukwirakwiza umuvuduko uhindagurika werekeza ku cyerekezo cyumugozi. Inshuro karemano yimigozi iba inshuro nyinshi kumurongo wibanze hejuru ya 2l.Ubu bwinshi bwuzuye buganisha kumiterere ishimishije.Muri rusange, nta iyo mibare myinshi ihuza inshuro zisanzwe za elastomer.
Uburyo butatu bwambere bwumugozi uhagaritswe bwerekanwe muri FIG. 9. Hariho imitwe imwe kumurongo wuburyo bukuru.Mu kunyeganyeza nyamukuru, imitwe ntinyeganyega.FIG. 10 yerekana uburyo bwinshi busanzwe bwuruziga rushyigikiwe nuruziga rufite imirongo imwe ya nodal igizwe nuruziga na diameter.
Gutegura neza ikibazo cyo guhindagurika kwa elastomer birashobora kurangizwa nkikibazo cyagaciro kimbibi zingana zingana zingana.Nyamara, igisubizo nyacyo gishobora kuboneka gusa murimwe murubanza rworoshye, bityo rero tugomba kwifashisha igisubizo cyagereranijwe kuri elastomer igoye. ikibazo cyo kunyeganyega.Ibisubizo byibisubizo bitandukanye byagereranijwe ni uguhindura umupaka ukageza ku ndunduro, ni ukuvuga, gutandukanya ingingo-zidafite urwego-rwinshi rwubwisanzure (sisitemu ikomeza) muburyo butandukanye bwubwisanzure (sisitemu yihariye) .Hariho ubwoko bubiri bwuburyo bwa discretisation bukoreshwa cyane mubisesengura ryubuhanga: uburyo bwa finite nuburyo bwa synthesis.
FIG. Uburyo 9 bwumugozi
FIG. Uburyo 10 bw'isahani
Uburyo bwanyuma nuburyo nuburyo bukomatanya bukuramo imiterere igoye mumibare itagira ingano yibintu kandi ikabihuza kumubare utagira ingano. Buri gice ni elastomer; Ikwirakwizwa ryimiterere ryibintu bigaragazwa nibikorwa bya interpolation yo kwimura node.Noneho the gukwirakwiza ibipimo bya buri kintu byibanze kuri buri node muburyo runaka, kandi imashini ya sisitemu ya discret irabonetse.
Modal synthesis ni ugusenyuka kwimiterere igoye muburyo butandukanye bworoshye.Ku shingiro ryo gusobanukirwa ibiranga kunyeganyega biranga buri nyubako, insimburangingo ikomatanyirizwa muburyo rusange ukurikije imiterere yo guhuza ibice, hamwe na morphologie ya vibration ya rusange. imiterere iboneka ukoresheje vibration morphologie ya buri cyiciro.
Uburyo bubiri buratandukanye kandi bufitanye isano, kandi burashobora gukoreshwa nkibisobanuro.Uburyo bwa synthesis modal burashobora kandi guhuzwa neza hamwe no gupima ubushakashatsi kugirango habeho uburyo bwo gusesengura ibyerekeranye nubushakashatsi hamwe nubushakashatsi bwo kunyeganyega kwa sisitemu nini.
Igihe cyo kohereza: Apr-03-2020
