Linear vibration: elasticity yezvikamu muhurongwa inoenderana nemutemo wehuku, uye simba rekunyorovesa rinogadzirwa panguva yekufamba rinoenderana nekutanga equation ye generalized velocity (nguva inotorwa kubva kune generalized coordinates).
pfungwa
Linear system inowanzova abstract model yekuzunguzika kwe real system.The linear vibration system inoshandisa iyo superposition musimboti, kureva kuti, kana mhinduro yehurongwa iri y1 pasi pechiito chekuisa x1, uye y2 pasi pechiito chekuisa x2, zvino mhinduro yehurongwa pasi pechiito chekuisa x1 uye x2 ndeye y1+y2.
Pahwaro hwe superposition musimboti, kupinza kwechimbichimbi kunogona kuoreswa kuita hwerengedzo yenhevedzano yezvisinga peri zvekufurira, uyezve mhinduro yese yehurongwa inogona kuwanikwa.Kuwanda kwezvikamu zveharmonic zvenguva nenguva inogona kuwedzerwa kuita mutsara wezvikamu zveharmonic neFourier kushandura, uye mhedzisiro yechikamu chimwe nechimwe cheharmonic pane system inogona kuongororwa zvakasiyana.Saka, maitiro ekupindura emitsara yemasisitimu ane maparamendi anogara achitsanangurwa anogona kutsanangurwa neimpulse response kana frequency response.
Impulse response (impulse response) inoreva davidzo yegadziriro kuchikamu chepundutso, inotaridza maitiro emhinduro yechirongwa mudura renguva.Frequency mhinduro inoreva maitiro erudaviro rwegadziriro kuyuniti inopindirana. neFourier shanduko.
classification
Linear vibration inogona kukamurwa kuita linear vibration yeimwe-degree-ye-freedom system uye mutsara vibration yeakawanda-degree-ye-rusununguko system.
(1) mutsara vibration yeimwe-dhigirii-ye-rusununguko sisitimu ndeyekuzunguzika kwemutsara iyo nzvimbo yayo inogona kutsanangurwa neyakajairwa coordinate.Ndiko kudedera kwakapfava uko kunobva kwakawanda pfungwa dzekutanga uye maitiro ekudedera.Inosanganisira nyore harmonic vibration, mahara vibration, attenuation vibration uye kumanikidzira vibration.
Nyore harmonic vibration: kudzoreredza kufamba kwechinhu chiri padhuze nenzvimbo yacho yakaenzana maererano nemutemo we sinusoidal pasi pechiito chesimba rekudzoreredza zvinoenderana nekutamiswa kwayo.
Damped vibration: vibration iyo amplitude inoramba ichidzikiswa nekuvapo kwekupokana uye dielectric kuramba kana kumwe kushandiswa kwesimba.
Forced vibration: kuzunguzika kwechirongwa chiri pasi pekunakidzwa.
(2) iyo linear vibration ye-multi-degree-of-freedom system ndiko kuzununguka kwe linear system ine n≥2 madhigirii ekusununguka.A system ye n degree of freedom ine n natural frequencies and n main modes.Chero vibration configuration. yegadziriro yacho inogona kumiririrwa semutsetse wakasanganiswa wemamodhi makuru.Naizvozvo, iyo huru mode superposition nzira inoshandiswa zvakanyanya mukupindura kwesimba kuongororwa kwemulti-dof masisitimu.Neiyi nzira, kuyerwa nekuongororwa kwemaitiro echisikigo ekudengenyeka kweiyo sisitimu inova nhanho yenguva dzose mukugadzirwa kwesimba rehurongwa.Mafambiro emagetsi emhando dzakasiyana-siyana anogonawo kutsanangurwa nemaitiro enguva yakawanda.Sezvo paine mafrequency characteristic function pakati pekupinda nekubuda kwega ega, frequency characteristic matrix inovakwa.Iko hukama hwakajeka pakati pehuwandu hwemaitiro uye maitiro makuru.Iyo amplitude-frequency characteristic curve ye-multi-freedom system yakasiyana neyoyo ye-single-freedom system.
Linear vibration yeimwe dhigirii yerusununguko system
Kudengenyeka kwemutsara uko nzvimbo yehurongwa inogona kutsanangurwa neyakajairwa coordination.Ndiyo yakapfava uye yakakosha vibration kubva panogona kutorwa pfungwa dzakawanda nehunhu hwekudedera.Inosanganisira kutetereka kwakapfava, kudedera kwakanyorova uye kudzungudza kunomanikidza. .
Harmonic vibration
Pasi pechiito chekudzorera simba zvakaenzana nekutamiswa, chinhu chacho chinodzokorora nenzira ye sinusoidal pedyo nenzvimbo yayo yakaenzana (FIG. 1) .X inomiririra kutama uye t inomiririra nguva. Kuratidzwa kwemasvomhu kwekudedera uku ndiko:
(1)Iko A ndiko ukoshi hwepamusoro hwekutama x, inodaidzwa kuti amplitude, uye inomiririra kusimba kwekudengenyeka; Omega n ndiyo amplitude Angle increment yekuzunguza pasekondi, inodaidzwa kuti angular frequency, kana denderedzwa frequency; inodaidzwa kunzi chikamu chekutanga nguva.Amplitude A, frequency f (kana angular frequency n), chikamu chekutanga, chinozivikanwa se simple harmonic vibration zvinhu zvitatu.
FIG. 1 yakapusa harmonic vibration curve
Sezvinoratidzwa muFIG. 2, yakapfava harmonic oscillator inoumbwa neiyo concentrated mass m yakabatana ne linear spring.Apo iyo vibration displacement inoverengwa kubva panzvimbo yakaenzana, vibration equation ndeiyi:
Kuoma kwechitubu kuri kupi.Mushonga mukuru kuequation iri pamusoro ndi(1) .A uye unogona kutariswa nenzvimbo yekutanga x0 uye kumhanya kwekutanga pat=0:
Asi omega n inongotemerwa nehunhu hweiyo system pachayo m uye k, yakazvimiririra yekuwedzera mamiriro ekutanga, saka omega n inozivikanwawo seyakajairika frequency.
FIG. 2 imwe dhigirii yerusununguko system
Kune iri nyore harmonic oscillator, huwandu hwesimba rayo rekinetic uye simba ringave risingaperi, kureva kuti, iyo yakazara mechanical simba regadziriro inochengetedzwa.Mukuita kwekudengenyeka, simba rekinetic uye simba rinogona kushandurwa nguva dzose kune rimwe nerimwe.
The damping vibration
A vibration ane amplitude anoramba akadzikiswa nekukweshana uye dielectric resistance kana mamwe mashandisirwo emagetsi.Kune micro vibration, velocity yacho kazhinji haina kukura zvakanyanya, uye kupikisa kwepakati kunoenderana nevelocity kune simba rekutanga, rinogona kunyorwa se c is. the damping coefficient.Naizvozvo, vibration equation yedhigirii rimwe rerusununguko nekunyorovesa kwemutsara kunogona kunyorwa se:
(2)Apo, m =c/2m inodaidzwa kunzi damping parameter, uye.Mushonga mukuru weformula (2) unogona kunyorwa:
(3)Hukama hwenhamba pakati peomega n nePI hunogona kukamurwa kuita zvinotevera zvitatu:
N > (munyaya yekunyorovesa kudiki) chidimbu chakagadzirwa attenuation vibration, iyo vibration equation ndeye:
Kukura kwayo kunodzikira nekufamba kwenguva zvichienderana nemutemo weexponential unoratidzwa muequation, sezvakaratidzwa mumutsara une doti muFIG. 3.Kunyatsotaura, kuzunguzika uku kunoitika nguva nenguva, asi kuwanda kwepamusoro peak yayo kunogona kutsanangurwa se:
Inonzi amplitude reduction rate, iripi nguva yekuzunguzika.The natural logarithm of the amplitude reduction rate inonzi logarithm minus (amplitude) rate. Zviripachena, =, munyaya iyi, yakaenzana ne2/1. kuyedza bvunzo delta uye, uchishandisa iri pamusoro fomula inogona kuverengerwa c.
Panguva ino, mhinduro ye equation (2) inogona kunyorwa:
Pamwe chete negwara rekutanga velocity, inogona kukamurwa kuita matatu asina-kuzunguzika makesi sezvakaratidzwa muFIG. 4.
N < (munyaya yekunyorovesa kukuru), mhinduro yekuenzanisa (2) inoratidzwa mukuenzanisa (3) .
Kudzvinyirirwa
Kudengenyeka kwegadziriro iri pasi penguva dzose yekunakidzwa.Ongororo yeVibration inonyanya kuferefeta mhinduro yegadziriro kune excitation.Periodic excitation is a normal excitation.Sezvo periodic excitation inogona nguva dzose yakaora muhuwandu hwehuwandu hwehurmonic excitation, maererano nepamusoro-soro musimboti, chete. mhinduro yegadziriro kune imwe neimwe harmonic excitation inodiwa.Pasi pechiito che harmonic excitation, the different equation of motion of a single degree of freedom damped system inogona kunyorwa:
Mhinduro ihuwandu hwezvikamu zviviri. Chimwe chikamu imhinduro yekudedera kwakanyorova, iyo inoora nekukurumidza nekufamba kwenguva.Mhinduro yechimwe chikamu chekudzvinyirirwa kwekumanikidzwa inogona kunyorwa:
FIG. 3 yakanyoroveswa vibration curve
FIG. 4 curves yemamiriro matatu ekutanga ane yakaoma damping
Nyora mu
H / F0 = h (), ireshiyo yemhinduro yakatsiga amplitude kune excitation amplitude, inoratidza amplitude-frequency maitiro, kana kuwana basa; Bits for steady state response and incentive of phase, characterization of phase frequency maitiro.Hukama huripo pakati pavo uye Kuwedzeredza frequency kunoratidzwa muFIG. 5 uye FIG. 6.
Sezvinoonekwa kubva pa amplitude-frequency curve (FIG. 5), kana iri diki damping, iyo amplitude-frequency curve ine peak imwe chete.Iyo diki yekunyorovesa, inokwirisa iyo peak; Iyo frequency inoenderana nepamusoro ndeye. inonzi resonant frequency of the system.Panyaya yekunyorovesa kudiki, iyo resonance frequency haina kusiyana zvakanyanya neyechisikigo frequency.Apo iyo yekuwedzeredza frequency iri pedyo neyakasikwa frequency, iyo amplitude inowedzera zvakanyanya. Chiitiko ichi chinonzi resonance.At resonance, kuwana kwehurongwa kunowedzera, kureva kuti, kudengenyeka kwekumanikidzika ndiko kwakanyanya.Saka, kazhinji, nguva dzose edza kudzivisa resonance, kunze kwekunge zvimwe zviridzwa uye zvishandiso zvekushandisa resonance kuti uwane guru. vibration.
FIG. 5 amplitude frequency curve
Inogona kuoneka kubva pachikamu frequency curve (mufananidzo 6), zvisinei nekukura kwekunyorova, mune omega zero chikamu musiyano bits = PI / 2, hunhu uhu hunogona kunyatso shandiswa pakuyera resonance.
Pamusoro pekusimudzira kwakadzikama, masisitimu dzimwe nguva anosangana nemanyawi asina kugadzikana.Inogona kuganhurwa zvakaganhurwa kuva marudzi maviri: imwe ndeyekungoerekana yaitika.Yechipiri ndiyo mhedzisiro yenguva refu yekusagadzikana.Pasi pekusagadzikana kwekunakidzwa, mhinduro yehurongwa zvakare haina kugadzikana.
Chishandiso chine simba chekuongorora kuzununguka kusina kugadzikana inzira yekupindura kwechimbichimbi.Inotsanangura maitiro ane simba ehurongwa nemhinduro yechinguvana yeyuniti impulse input of the system.The unit impulse inogona kuratidzwa se delta function.In engineering, the delta basa rinowanzotsanangurwa se:
Iko 0- inomiririra poindi pa-t-axis inoswedera paziro kubva kuruboshwe; 0 plus ndiyo poindi inoenda kuna 0 kubva kurudyi.
FIG. 6 phase frequency curve
FIG. 7 chero ipi neipi inogona kutorwa sehuwandu hwenhevedzano yezvinhu zvinokurudzira
Sisitimu inofambirana nemhinduro h(t) inogadzirwa neyuniti impulse pa t=0, inodaidzwa kuti impulse response function.Kungofungidzira kuti system yakamira pamberi pepuruzi, h(t)=0 ye t<0.Kuziva iyo impulse response function of the system, tinogona kuwana mhinduro yegadziriro kune chero ipi zvayo inopinza x(t) .Panguva ino, unogona kufunga nezve x(t) sehuwandu hwehuwandu hwezvinhu zvinokurudzira (FIG. 7) .Mhinduro yehurongwa ndeiyi:
Zvichienderana neiyo superposition musimboti, mhinduro yese yehurongwa inoenderana ne x(t) ndeye:
Ichi chinosanganisa chinonzi convolution integral kana superposition integral.
Linear vibration ye-multi-degree-of-freedom system
Vibration ye linear system ine n≥2 madhigirii erusununguko.
Figure 8 inoratidza maviri akareruka resonant subsystems akabatanidzwa ne coupling spring.Nekuda kwekuti imbiri-degree-of-freedom system, maviri akazvimirira coordinates anodiwa kuti aone nzvimbo yawo.Pane maviri echisikigo mafambiro muhurongwa uhu:
Mafambiro ega ega anoenderana nemodhiyo yekuzunguza.Maharonic oscillator anoita harmonic oscillations of the same frequency, synchronously passing through the equilibrium position and synchronously kusvika panzvimbo yakanyanyisa.Mukuzunguzika kukuru kunoenderana neomega one, x1 yakaenzana ne x2;In the main vibration inoenderana neomega omega two, omega omega one.Mukuzunguzika kukuru, displacement ratio yehuremu hwega hwega inochengeta humwe hukama uye inoita imwe modhi, inodaidzwa kuti main mode kana kuti natural mode.The orthogonality of mass and kuomarara kuripo pakati pemamodhi makuru, ayo anoratidza kuzvimirira kwekuzunguzika kwega kwega.Mafambiro echisikigo uye maitiro makuru anomiririra maitiro ekudengenyeka kwehuwandu hwehuwandu hwekusununguka.
FIG. 8 system ine madhigirii akawanda erusununguko
A system of n degrees of freedom ine n natural frequencies and n main modes.Chero vibration configuration of the system inogona kumiririrwa semutsara wakasanganiswa wemamodhi makuru.Saka, main mode superposition method inoshandiswa zvakanyanya mu dynamic response analysis of multi. -dof systems.Nenzira iyi, kuyerwa uye kuongororwa kwemaitiro ekudengenyeka kwechisikigo kwegadziriro inova nhanho yenguva dzose mukugadzirwa kwemasimba ehurongwa.
Mamiriro ekuchinja maitiro e-multi-dof systems anogonawo kutsanangurwa nemaitiro e-frequency.Sezvo kune maitiro e-frequency characteristic function pakati pekupinda kwega kwega uye kubuda, a frequency characteristic matrix inovakwa.Iyo amplitude-frequency characteristic curve ye-multi-freedom system yakasiyana. kubva kune iyo ye single-freedom system.
Iyo elastomer inodedera
Iyo iri pamusoro yakawanda - dhigirii yerusununguko system ndeye approximate mechanical model ye elastomer.Elastomer ine nhamba isingaperi yemadhigirii erusununguko.Pane musiyano wehuwandu asi hapana mutsauko unokosha pakati pezviviri.Chero elastomer ine nhamba isingaperi yezvakasikwa uye nhamba isingaperi yemamodhi anofambirana, uye pane orthogonality pakati pemamodhi ehuremu nekuoma.Chero gadziriso yevibrational ye elastomer inogonawo kumiririrwa semutsetse wepamusoro wemodhi hombe.Naizvozvo, kune dynamic mhinduro yekuongorora elastomer, superposition nzira. yemhando huru ichiri kushanda (ona mutsara vibration ye elastomer).
Tora kuzunguzika kwetambo.Ngatitii tambo yakatetepa yehuremu m pahurefu hweyuniti, kureba l, yakatsikirirwa kumagumo ese, uye tension iT.Panguva iyi, kuwanda kwechisikigo kwetambo kunotsanangurwa nezvinotevera. equation:
F =na/2l (n= 1,2,3…).
Ndekupi, ndiko kukurumidza kwekufambisa kwemafungu anochinjika achitevedza nhanho yetambo.Mafambiro echisikigo etambo anoitika kuva akawanda eiyo frequency frequency pamusoro pe2l.Iyi integer multiplicity inotungamira kune inofadza harmonic chimiro.Pazhinji, hapana hukama hwakakwana hwakawanda pakati pemafambiro echisikigo eelastomer.
Matatu ekutanga maitiro etambo yakamanikidzwa anoratidzwa muFIG. 9. Pane dzimwe nodes pane main mode curve.Mukudzungudza kukuru, nodes haizununguki.FIG. 10 inoratidza akati wandei akajairwa modhi yedenderedzwa yakatsigirwa ndiro yedenderedzwa ine mimwe mitsetse inoumbwa nemadenderedzwa nemadhayamita.
Magadzirirwo chaiwo eiyo elastomer vibration dambudziko rinogona kupedzwa sedambudziko remuganho wekukosha kwechikamu chekusiyanisa equations.Zvisinei, mhinduro chaiyo inogona kuwanikwa chete mune dzimwe nyaya dzakareruka, saka isu tinofanirwa kutendeukira kune yakagadziriswa mhinduro yeiyo yakaoma elastomer. dambudziko revibration.Chinokosha chemhinduro dzakasiyana-siyana ndechekushandura zvisingaperi kusvika kune zvinogumira, kureva kuti, kujekesa nhengo-shoma yakawanda-dhigirii yerusununguko system (inoenderera mberi system) muinogumira yakawanda-dhigirii yerusununguko system (discrete system) .Kune marudzi maviri ediscretization nzira dzinoshandiswa zvakanyanya mukuongorora engineering: finite element method uye modal synthesis method.
FIG. 9 nzira yetambo
FIG. 10 mode yedenderedzwa ndiro
Finite element method is a composite structure inobvisa chimiro chakaoma kuita nhamba inogumira yezvinhu uye inozvibatanidza panhamba inogumira yemanodhi.Chikwata chega chega ielastomer;Kuparadzirwa kwechinhu chinotaridzwa neinterpolation function ye node displacement.Ipapo the kugovera maparamendi echinhu chimwe nechimwe anonamirwa kune imwe neimwe node mune imwe fomati, uye mechanical modhi ye discrete system inowanikwa.
Modal synthesis ndiko kuparara kwechimiro chakaomarara kuita zvidiki zvidiki zvakareruka.Pachikonzero chekunzwisisa hunhu hwekuzunguzika kwechikamu chimwe nechimwe, substructure inogadzirwa kuita chimiro chakajairwa zvinoenderana nemamiriro ekubatanidza pane iyo interface, uye vibration morphology ye general. chimiro chinowanikwa nekushandisa vibration morphology yeimwe neimwe substructure.
Nzira mbiri idzi dzakasiyana uye dzine hukama, uye dzinogona kushandiswa sereferensi.Iyo modal synthesis nzira inogonawo kunyatsobatanidzwa nechiyero chekuedza kugadzira dzidziso uye yekuongorora nzira yekuongorora kudengenyeka kwemaitiro makuru.
Nguva yekutumira: Kubvumbi-03-2020
