Chii chinonzi mutsara wekubvunzwa?

Linear vibration.

pfungwa

Linear System inowanzove isinganzwisisike yemhando yehurongwa hwechokwadi Ipapo mhinduro yehurongwa pasi pechiitiko chekuisa x1 uye x2 iri Y1 + y2.

Pahwaro hwehunyanzvi hwekuzvimiririra, kuiswa kweanopokana kunogona kuiswa muhuwandu hwehuwandu hwekusanzwisisika kwesangano, uye mhinduro yehurongwa Series of Harmonic zvikamu nezvishandiso zvechinjiki, uye mhedzisiro yechiitiko chega chega chegungano pane iyo system inogona kuongororwa zvakasiyana.Naizvozvo, maitiro emhinduro ye mutsara masisitimu ane nguva yekugara ichirondedzerwa inogona kutsanangurwa nekupindura kwemhinduro kana mhinduro yekuwedzera.

Kupindura kwemhinduro kunoreva mhinduro yehurongwa kune iyo unit inokurudzira, iyo inoratidza mhinduro yehurongwa hwekupindura nechishanduro chechina.

kuiswa

Linear vibration inogona kukamurwa kuita mutsara wetsetse weiyo-degree-ye-ye-rusununguko system uye mutsara wetsetse wehuwandu hwehuwandu-hwesimba-remahara.

. Harmonic vibration, yemahara yekubvunda, kutungamira vibration uye kumanikidzwa vibration.

Kureruka kweHarmonic

Yakapfeka vibration: Vibration iyo Yemepitude inogara ichivapo nekuvapo kwekupokana uye dielectric kuramba kana kumwe kushandiswa kwesimba.

Yakamanikidzwa Vibration: Vibration yehurongwa pasi pekugara tichifembera.

. yehurongwa inogona kumiririrwa semutsara wemhando huru.Nguva huru, iyo nzira huru yemhando inoshandiswa zvakanyanya mukunyorwa kwekunyora kweiyo madiki-madhora system. izvi nzira uye kuyerwa uye kuongororwa kwechisikigo chehurongwa hwegadziriro yehurongwa hwegadziriro yehurongwa hweSystem. Imwe neimwe yekuisa uye yekubuda, huwandu hwehunhu hwematrix hwakagadzirwa.Zvirevo chokwadi chehukama pakati peiyo frequency hunhu uye iyo main mode.The Amplitude-frequency hunhu curve yeiyo yakawanda-rusununguko system yakasiyana neiyo yeiyo-rusununguko rwekusununguka.

Mutsara wekubvunda weimwe degree reruzivo rweRusununguko

Iyo Linear Vibration umo chinzvimbo chehurongwa chinogona kutsanangurwa nehurongwa hwechirongwa hwakaenzana neicho chinhu chakanyanya kukosha che.V.Nehukama hwenhamba dzichigona kuve neyakajeka humbocess .

Harmonic vibration

Pasi pechiitiko chekudzoreredza simba zvakabatana kuti zvidzorerwe, icho chinhu chinodzoreredzwa nenzira isingazivikanwe padyo neyakaenzana (Fig. 1). Kutaura kwemasvomhu kweiyi vibration ndeye:

(1)Iko kune kukosha kwakanyanya kwekudzingwa X, iyo inonzi iyo yekukwirisa, uye inomiririra kukura kweiyo vibration; Omega n ndeyekuwedzera kona yechipiri, iyo inonzi learlar frequency, kana iyo circular frequency; izvi inonzi yekutanga chikamu.in-n / 2, huwandu hwe itscillation pane yechipiri inonzi iyo frequency; iyo itsvhu yeiyi, t = 1 / f, ndiyo nguva Zvinotora kuOscillat kutenderera kumwe, uye izvo zvinonzi nguva.APLLUDE A, frequency f (kana jigular frequency n), inozivikanwa seyakareruka kusawirirana zvinhu zvitatu zvinhu.

Fig. 1 yakapusa Harmonic vibration curve

Sezvinoratidzwa muPi. 2, Iyo Yakareruka Hoscillator yakaumbwa neyekuumbwa misa m yakabatanidzwa neiyo linear Spring.Mutsara wekusvitswa kwekuverengerwa kubva kuEquilibrium chinzvimbo, iyo vibration equation ndeye:

Iko kushungurudzika kweiyo tsime.Iye general solution kune iyo yepamusoro equation ndeye (1) .a uye inogona kutsanangurwa nenzvimbo yekutanga X0 uye yekutanga velocity at t = 0:

Asi omega n anongofunga nezvehunhu hwegadziriro yacho m uye k, yakazvimirira yemamiriro ekutanga, saka Omega n inozivikanwa seinozivikanwa seyakasikwa.

Fig. 2 Dhigirii yeRusununguko

Kuti uwane kuyaruka kwechiHarmonic, huwandu hwenzvimbo yayo yekinetic uye inogona kugara ichiripo, iyo isimba rehurongwa hwakachengetedzwa.Chinicho mari yekubvunzwa, kusimba kwesimba uye zvinogona kuve simba nguva dzose zvinogara zvichishandurwa mukati.

Kudzvinyirira

A Vibration Yayo Yemblumble inogara ichirwiswa neyekupokana neDilelectric Kuwedzera. Iko kudzvinyirira coeffert.Naizvozvo, iyo vibration equation yerudzi rumwe rusununguko rwemutsara runyararo runogona kunyorwa se:

(2)Kupi, m = c / 2m inonzi yakadanwa paramende, uye.The general solution ye formula (2) inogona kunyorwa:

(3)Hukama hwehuwandu pakati peOMEGA n uye pi inogona kukamurwa muzvikamu zvitatu zvinotevera:

N> (mune nyaya yekushomeka kudhonzwa)

Yayo amplitude inoderera nenguva zvichienderana neyekupedzisira mutemo unoratidzwa mu equation, sezvakaratidzwa mumutsara wedunhu muPi. Izvi zvinoreva kuti kutaura, iyi vibration iri aPeriodic, asi iyo yekufambisa yeiyo peak yayo inogona kutsanangurwa se:

Anonzi anonzi Amplitude yekudzora chiyero Kuedza Test Delta uye, uchishandisa iyo iri pamusoro mafomula inogona kuverengerwa c.

Panguva ino, mhinduro ye equation (2) inogona kunyorwa:

Pamwe chete neyekutungamira kwekutanga velocity, inogona kukamurwa kuita matatu asiri-vibration kesi sezvakaratidzwa muPi. 4.

N <(mune nyaya yekushomeka kukuru), mhinduro ye equation (2) inoratidzwa mu equation (3).

Kumanikidzwa vibration

Vibration yehurongwa pasi pekugara uchiziva.VAKUZIVA ZVINOGONESESESA KUNYANYA KUNYANYA KUNYANYA KUNYANYA KUNYANYA KUNYANYA KUTI Uwane KUTI Uwane KUTI UCHINONZWA HERE. Mhinduro yeiyo system kune yega yega kuwirirana inobvumirwa.Ndoita chiito cheHarmonic Kubvumirana, iyo yakasarudzika equation yekufamba kwerusununguko rwakadzikira inogona kunyorwa:

Mhinduro yacho ndeyehuwandu hwezvikamu zviviri. Chimwe chikamu ndechekupindura kwekurwadziswa kwehuwandu, izvo zvinopera nekukurumidza nenguva.

Fig. 3 yakadzama vibration curve

Fig. 4 curves yematatu matatu ekutanga mamiriro ekutsamwa

Nyora mukati

H / f0 = h (), ndeyekupindura kwemhinduro yakamanikidzwa kuti uwedzere kukwikwidza, kana kuwana chikamu chesimba. Achibudirira Frequency inoratidzwa muPi. 5 uye Fig 6.

Sezvazvinogona kuoneka kubva kuAmplitude-frequency curve (fig. 5), mune madiki madiki, madiki madiki madiki, iyo freeper inoenderana nepamusoro inonzi resonant frequency yehurongwa iyo amplide inowedzera zvakanyanya. Ichi chiitiko chacho chinonzi Resonance.at Resonance, iyo mari inowedzerwa, ndiko kuti, iyo, kazhinji, kunze kwekunge zvimwe zviridzwa nemidziyo yekushandisa resonance kuti uwane hombe vibration.

Fig. 5 amplitude frequency curve

Inogona kuoneka kubva kuChikamu Frequency Curve (Mufananidzo 6), zvisinei nekukura kwekudzvinyirira, muOmega Zero Phero Bits = PI / 2, hunhu uhu hunogona kushandiswa zvinobudirira mumararamiro ekuyera.

Pamusoro pekuregerera kwakasimba, masisitimu dzimwe nguva anosangana neyakajairwa kuImunyorwa maviri: Imwe ndeyekunyatsoita mitezo yekukonzerwa nekusagadzikana kwekupokana.

Chishandiso chine simba chekuongorora zvisina kufanira chekusimbisa nzira yekupokana nehurongwa hwegadziriro yeyunivhesiti. Basa rinowanzotsanangurwa se:

Iko kune 0- inomiririra iyo poindi pane t-axis iyo inoswedera zero kubva kuruboshwe; 0 kuwedzera ndiyo pfungwa inoenda ku0 kubva kurudyi.

Fig. 6 Phase Frequency Curve

Fig. 7 Chero ipi neipi yekuisa inogona kutariswa seyakajaira huwandu hwezvinhu zvisina kujairika

Iyo system inoenderana nemhinduro h (t) inogadzirwa neyunivhesiti paT = 0, iyo inonzi iyo inosimudzira mhinduro yekushandisa isati yasvika pulse, Iyo yekukurudzira kupindura kwehurongwa, tinogona kuwana mhinduro yehurongwa kune chero kuisirwa x (t). 7) .Mhinduro yehurongwa ndeye:

Zvichienderana neyekutanga nhungamiro, mhinduro yakazara yeiyo system inoenderana ne x (t) ndeye:

Ichi chiitiko chinonzi chinonzi convolution conderral kana superposition inobatanidza.

Mutsara wekubvunda kweiyo yakawanda-degree-ye-rusununguko system

Vibration yetsika yehurongwa neN≥2 madhigirii erusununguko.

Mufananidzo 8 unoratidza maviri ari nyore resonant subsystems akabatana neyekupedzisira kutsvazwa

Kugara kwega kwega kunoenderana nemamiriro ekunyora. Iyo huru yekubvunda inoenderana neOmega Omega maviri, Omega ema one.in The Main vibration, iyo yekudzingwa kwehuremu hwega yega inoita kuti ive imwe nzira, iyo inonzi iyo huru maitiro kana kuomarara kwehuwandu pakati penzvimbo huru, iyo inoratidza kuzvimiririra kweimwe vibration yega yega. Nzvimbo dzepanyama uye main mode mode inomiririra chisikwa chechiitiko chechiitiko cheiyo yakawanda-degree reruzivo system.

Fig. 8 sisitimu ine akawanda madhigirii erusununguko

Hurongwa hwe n madhigirii er rusununguko ine narirwo freques uye n main modes.Nykurumidzira mimwe nzira yakakura kwazvo. -Dof systems. Iyi nzira, iyo kuyerwa uye kuongororwa kweiyo yakasikwa vibration hunhu hwegadziriro inova nhanho yehurongwa mukugadzirwa kwegadziriro yehurongwa.

Hunhu hwesimba hwehukama hwemari dzakawanda hunogona kutorondedzerwa nemari yekuwedzera.Nexthiction maitiro ekupinda mukati mevakagadzirwa kubva pane iyo yerimwe-rusununguko system.

Elastomer vijates

Iyo iri pamusoro nhamba isingaperi yemhando inoenderana, uye pane orthogonality pakati pemhando dzeMis misa uye Stiffness.Many vibrational kurongedzwa kweiyo Elastomer inogona zvakare kumiririrwa seyenzuro supposition yemhando huru.Nguva yekunyorwa kweElastomer

Tora iyo yekubvunda yetambo.Let's inotaura kuti tambo yakatetepa yemasuru misa misa misa misa misa misa, inoshongedzwa pamigumo yese iyi, uye nguva ino yetambo yetambo yakatemwa nekutevera equation:

F = NA / 2L (n = 1,2,3 ...).

Kupi, iko kusarudzika vhezheni yekufambisa munzira yetambo.Tambo dzechisikigo dzinoitika kuve dzakawanda frequency pamusoro pe 2l.This huwandu hwehuwandu hwehuwandu hwekuwirirana neyakawirirana yakadaro interger akawanda hukama pakati pezvakasikwa maElasomer.

Iyo yekutanga matatu modes yetambo inosimbisa inoratidzwa muPi. 9. Pane mamwe ma node pane iyo main mode. Iyo huru yekubvunda, iyo nodes haidi.fig. 10 Inoratidza akati wandei maitiro ekutsigirwa kwakatsigirwa nenzvimbo dzakatenderedza nemimwe mitsara yemanheru yakaumbwa nedenderedzwa uye diamita.

Kuumbwa chaiko kweElasomer kwehukama dambudziko kunogona kugumiswa sekukoshesa kukosha kwechikamu cheCommunations vibration dambudziko. System) mune imwe chete yakawanda-degree yerusununguko system (discerte system)

Fig. 9 Mode yetambo

Fig. 10 mode yeiyo circelar ndiro

Finite Element Nzira iyo Inoshamisa chimiro icho chinobatanidza chimiro chakaomarara kuita nhamba yezvinhu zvoupfumi uye nekuvaburitsa nhamba yeiyo elasomer yekuparadza Kugovera maratidziro ezvimwe chinhu kwakamisikidzwa kune imwe neimwe node mune imwe chimiro, uye iyo mechanical muenzaniso weiyo discrete system inowanikwa.

Modhesis synthesis yekuita kwechimiro chakaoma kuita zvinokonzeresa.Shenek yehunhu hwega hwega hwega hwega hwega hwega hwemagariro maererano nemamiriro ekurongedza pane iyo interface, uye iyo yekubvunda morphology yemukuru chimiro chinowanikwa nekushandisa iyo vibration morphology yeimwe neimwe nzira.

Nzira mbiri idzi dzakasiyana uye dzinoenderana neyekuita.