Chii chinonzi kuzunungusa kwemutsetse?

Kudedera kwemutsetse: kusimba kwezvikamu zviri muhurongwa kunoenderana nemutemo waHooke, uye simba rekudzikisa rinogadzirwa panguva yekufamba rinoenderana ne equation yekutanga ye generalized velocity (nguva inobva kune generalized coordinates).

pfungwa

Sisitimu yemutsetse inowanzova muenzaniso we vibration yesystem chaiyo. Sisitimu ye vibration yemutsetse inoshandisa musimboti we superposition, kureva kuti, kana mhinduro yesystem iri y1 pasi pechiito che input x1, uye y2 pasi pechiito che input x2, saka mhinduro yesystem pasi pechiito che input x1 na x2 ndeye y1+y2.

Zvichienderana nepfungwa ye superposition, chinhu chinopinzwa chisina kurongeka chinogona kupatsanurwa kuita huwandu hwema "infinite simal impulses", uye ipapo mhinduro yese yesystem inogona kuwanikwa. Huwandu hwezvinhu zvinosanganiswa zve "periodic excitation" hunogona kuwedzerwa kuita "series" ye "harmonic components" ne "Fourier transform", uye mhedzisiro ye "harmonic component" yega yega pasystem inogona kuongororwa zvakasiyana. Nokudaro, hunhu hwemhinduro dze "linear systems" dzine "constant parameters" hunogona kutsanangurwa ne "impulse response" kana "frequency response".

Mhinduro yekukurumidza inoreva mhinduro yesystem kune unit impulse, iyo inoratidza hunhu hwemhinduro yesystem munzvimbo yenguva. Mhinduro yefrequency inoreva hunhu hwemhinduro yesystem kune unit harmonic input. Kuenderana pakati pezviviri kunotsanangurwa neFourier transform.

kupatsanura

Kudengenyeka kwemutsetse kunogona kukamurwa kuita kudengenyeka kwemutsetse kwehurongwa hwedhigirii rimwe chete rerusununguko uye kudengenyeka kwemutsetse kwehurongwa hwedhigirii dzakawanda dzerusununguko.

(1) kudedera kwemutsara kwehurongwa hwedhigirii rimwe chete-rerusununguko kudedera kwemutsara uko nzvimbo yako inogona kutsanangurwa nehurongwa hwakajairwa. Ndiko kudedera kuri nyore uko pfungwa dzakawanda dzekutanga uye hunhu hwekudedera zvinogona kuwanikwa. Kunosanganisira kudedera kuri nyore kweharmonic, kudedera kwemahara, kudedera kwekuderedza uye kudedera kwekumanikidzwa.

Kudengenyeka kuri nyore kweharmonic: kufamba kwechinhu chiri pedyo nenzvimbo yacho yekuenzana zvichienderana nemutemo we sinusoidal pasi pesimba rekudzorera zvinoenderana nekutama kwacho.

Kudengenyeka kwakapfava: kudengenyeka uko amplitude yayo inogara ichidzikira nekuda kwekuvapo kwekukweshana uye kuramba kwe dielectric kana kushandiswa kwesimba.

Kumanikidzwa kudedera: kudedera kwehurongwa huri pasi pekufara nguva dzose.

(2) kuzununguka kwemutsetse kwesystem ine madhigirii akawanda erusununguko ndiko kuzununguka kwesystem ine madhigirii n≥2 erusununguko. Sisitimu ine madhigirii n erusununguko ine mafrequency echisikigo n uye main modes n. Chero kugadzika kwe vibration yesystem kunogona kumiririrwa semusanganiswa wemutsetse we main modes. Nokudaro, nzira ye main mode superposition inoshandiswa zvakanyanya mukuongorora kwe dynamic response ye multi-dof systems. Nenzira iyi, kuyerwa uye kuongororwa kwe natural vibration hunhu hwesystem inova danho renguva dzose mukugadzirwa kwe dynamic yesystem. Hunhu hwe dynamic hwe multi-dof systems hunogonawo kutsanangurwa ne frequency hunhu. Sezvo paine frequency hunhu hunoshanda pakati pekupinda nekubuda kwega kwega, frequency hunhu hunoshanda hunovakwa. Pane hukama hwakakwana pakati pe frequency hunhu ne main mode. Amplitude-frequency hunhu hunoshanda hwe multi-freedom system yakasiyana neiyo ye single-freedom system.

Kudedera kwemutsetse kwedanho rimwe chete rehurongwa hwerusununguko

Kudengenyeka kwakanangana uko nzvimbo yehurongwa inogona kutsanangurwa nehurongwa hwakajairwa. Ndiko kudengenyeka kuri nyore uye kwakakosha uko pfungwa dzakawanda dzekutanga uye hunhu hwekudengenyeka zvinogona kuwanikwa. Kunosanganisira kudengenyeka kuri nyore kweharmonic, kudengenyeka kwakadzikama uye kumanikidzwa kudengenyeka.

Kudengenyeka kweHarmonic

Pasi pechiito chekudzorera simba zvinoenderana nekutama, chinhu chinodzokorodza nenzira ye sinusoidal pedyo nenzvimbo yacho yekuenzana (Mufananidzo 1). X inomiririra kutama uye t inomiririra nguva. Kutaurwa kwemasvomhu kwekudedera uku ndekwekuti:

(1)Apo A iri kukosha kwepamusoro-soro kwekusiyana x, iyo inonzi amplitude, uye inomiririra simba rekudzungaira; Omega n i amplitude Angle increase ye vibration pasekondi, iyo inonzi angular frequency, kana circular frequency; Iyi inonzi initial phase. Panyaya ye f= n/2, nhamba ye oscillations pasekondi inonzi frequency; Inverse yeiyi, T=1/f, inguva inotora kuti oscillate imwe cycle, uye iyoyo inonzi period. Amplitude A, frequency f (kana angular frequency n), iyo initial phase, inozivikanwa se simple harmonic vibration three elements.

Mufananidzo 1 mukobvu we vibration uri nyore we harmonic

Sezvakaratidzwa muMufananidzo 2, oscillator iri nyore inoumbwa nehukuru hwakasimba m hwakabatana nechitubu chakatsetseka. Kana kutenderera kwekutenderera kwaverengerwa kubva panzvimbo yekuenzanisa, equation yekutenderera ndeiyi:

Kuoma kwechitubu kuri kupi. Mhinduro huru ye equation iri pamusoro apa ndeiyi (1).A uye inogona kutsanangurwa nenzvimbo yekutanga x0 uye velocity yekutanga pa t=0:

Asi omega n inongoonekwa chete nehunhu hwesystem pachayo m na k, zvisingaenderane nemamiriro ekutanga ekuwedzera, saka omega n inozivikanwawo se natural frequency.

Mufananidzo 2. Dhigirii rimwe chete rehurongwa hwerusununguko

Kune oscillator iri nyore, huwandu hwesimba rayo rekinetic nesimba rinokwanisa kudzoserwa, kureva kuti, simba rese remakanika rehurongwa rinochengetwa. Mukufamba kwekuzununguka, simba rekinetic nesimba rinokwanisa kudzoserwa zvinogara zvichichinjana.

Kudengenyeka kwemvura

Kudedera uko amplitude yayo inogara ichidzikira nekuda kwekukweshana uye dielectric resistance kana kushandiswa kwesimba. Kune micro vibration, velocity kazhinji haisi yakakura zvakanyanya, uye medium resistance inoenderana nekumhanya kune simba rekutanga, iro rinogona kunyorwa se c ndiyo damping coefficient. Saka, vibration equation ye one degree of freedom ine linear damping inogona kunyorwa se:

(2)Apo, m = c/2m inonzi damping parameter, uye. Mhinduro yakajairika yefomula (2) inogona kunyorwa:

(3)Hukama hwenhamba pakati peomega n nePI hunogona kukamurwa muzvikamu zvitatu zvinotevera:

N > (kana paine damping small) particle yakaburitsa attenuation vibration, vibration equation ndeiyi:

Amplitude yayo inoderera nekufamba kwenguva zvichienderana nemutemo we exponential unoratidzwa mu equation, sezvakaratidzwa mumutsara une madotsi muMufananidzo 3. Kutaura chokwadi, kudedera uku hakuna nguva, asi frequency yekukwirira kwayo inogona kutsanangurwa se:

Inonzi amplitude reduction rate, uko kuri nguva yekudengenyeka. Iyo natural logarithm ye amplitude reduction rate inonzi logarithm minus (amplitude) rate. Zviri pachena kuti, =, muchiitiko ichi, yakaenzana ne 2/1. Yakananga kuburikidza ne experimental test delta uye, uchishandisa fomura iri pamusoro apa inogona kuverengerwa c.

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

Pamwe chete nekwakananga kumhanya kwekutanga, inogona kukamurwa kuita zvikamu zvitatu zvisingadedere sezvakaratidzwa muMufananidzo 4.

N < (kana paine damping yakakura), mhinduro ye equation (2) inoratidzwa mu equation (3). Panguva ino, sisitimu haisisiri kudedera.

Kumanikidzwa kudedera

Kudengenyeka kwesystem pasi pekuwedzeredzwa nguva dzose. Kuongorora kwekudengenyeka kunonyanya kuongorora mhinduro yesystem kune excitation. Kuwedzeredzwa kwenguva nenguva iexcitation yakajairika. Sezvo excitation yenguva nenguva ichigona kugara ichisanganiswa kuita huwandu hweexcitation dzakawanda dzeharmonic, zvichienderana ne superposition principle, mhinduro yesystem kune excitation yega yega yeharmonic ndiyo inodiwa. Pasi pechiito cheexcitation yeharmonic, differential equation yekufamba kwe single degree of freedom damped system inogona kunyorwa:

Mhinduro yacho ihuwandu hwezvikamu zviviri. Chikamu chimwe chete imhinduro yekudedera kwakapfava, uko kunoora nekukurumidza nekufamba kwenguva. Mhinduro yechimwe chikamu chekudedera kwakamanikidzwa inogona kunyorwa:

Mufananidzo 3: damped vibration curve

Mufananidzo 4: Makombama matatu ekutanga ane damping yakakosha

Nyora mu

H /F0= h (), inhamba yehuwandu hwemhinduro dzakagadzikana kusvika pahuwandu hwekukurudzira, zvichiratidza hunhu hwehuwandu hwemhinduro dzakagadzikana, kana kuti basa rekuwana; mabhiti emhinduro dzakagadzikana uye kukurudzira kwechikamu, kutsanangurwa kwehunhu hwehuwandu hwezviitiko. Hukama huripo pakati pavo nehuwandu hwekukurudzira hunoratidzwa muMufananidzo 5 neMufananidzo 6.

Sezvatinoona kubva pa amplitude-frequency curve (Mufananidzo 5), kana paine damping diki, amplitude-frequency curve ine peak imwe chete. Kana damping idiki, peak inowedzera kukwira; Frequency inoenderana ne peak inonzi resonant frequency yesystem. Kana iri damping diki, resonance frequency haina kusiyana zvakanyanya ne natural frequency. Kana excitation frequency iri pedyo ne natural frequency, amplitude inowedzera zvakanyanya. Ichi chiitiko chinonzi resonance. Pa resonance, gain yesystem inowedzera, kureva kuti, kumanikidzwa vibration ndiko kwakanyanya. Saka, kazhinji, gara uchiedza kudzivirira resonance, kunze kwekunge zvimwe zvishandiso nemidziyo zvichishandisa resonance kuti zvibudirire vibration yakakura.

Mufananidzo 5: frequency curve ye amplitude

Zvinogona kuonekwa kubva pachikamu chefrequency (mufananidzo 6), zvisinei nehukuru hwe damping, mu omega zero phase difference bits = PI / 2, hunhu uhwu hunogona kushandiswa zvinobudirira pakuyera resonance.

Pamusoro pekukurudza kwakasimba, dzimwe nguva masisitimu anosangana nekukurudza kusina kugadzikana. Kunogona kukamurwa kuita mhando mbiri: imwe injodzi inongoerekana yaitika. Yechipiri imhedzisiro inogara kwenguva refu yekusada. Pasi pekukurudza kusina kugadzikana, mhinduro yesisitimu haina kugadzikanawo.

Chishandiso chine simba chekuongorora vibration isina kugadzikana inzira yemhinduro ye impulse. Inotsanangura hunhu hwesimba hwesystem nemhinduro yenguva pfupi yekupinda kwe unit impulse yesystem. Iyo unit impulse inogona kuratidzwa se delta function. Muinjiniya, delta function inowanzotsanangurwa se:

Apo 0- inomiririra poindi iri pa t-axis inosvika zero kubva kuruboshwe; 0 plus ndiyo poindi inoenda ku 0 kubva kurudyi.

Mufananidzo 6 wechikamu chefrequency curve

Mufananidzo 7. Chero chinhu chipi zvacho chinogona kutorwa sehuwandu hwezvinhu zvinotevedzana zve impulse

Sisitimu iyi inoenderana nemhinduro h(t) inogadzirwa neyuniti impulse pa t=0, iyo inonzi basa remhinduro yekukurumidza. Tichifunga kuti sisitimu iyi yakamira isati yatanga kutenderera kweropa, h(t)=0 ye t<0. Tichiziva basa remhinduro yekukurumidza kwesisitimu, tinogona kuwana mhinduro yesisitimu kune chero chinhu chinopinzwa x(t). Panguva ino, unogona kufunga nezve x(t) sehuwandu hwezvinhu zvinotevedzana zvekukurumidza (Mufananidzo 7). Mhinduro yesisitimu ndeiyi:

Zvichibva papfungwa ye superposition, mhinduro yese yesystem inoenderana ne x(t) ndeiyi:

Iyi integral inonzi convolution integral kana kuti superposition integral.

Kudengenyeka kwemutsetse kwehurongwa hwerusununguko rwemadhigirii akawanda

Kudengenyeka kwesystem ine mutsetse ine madhigirii erusununguko rwe n≥2.

Mufananidzo 8 unoratidza masisitimu maviri akareruka e resonant akabatana nechitubu chekubatanidza. Nekuti isystem ine rusununguko rwemadhigirii maviri, ma coordinates maviri akazvimiririra anodiwa kuti aone nzvimbo yayo. Kune ma frequency maviri echisikigo musystem iyi:

Frequency yega yega inoenderana nenzira yekudzungudza. Maharmonic oscillators anoita harmonic oscillations yefrequency imwe chete, achipfuura nepanzvimbo yekuenzana uye achisvika panzvimbo yakanyanya. Mu vibration huru inoenderana ne omega one, x1 yakaenzana ne x2; Mu vibration huru inoenderana ne omega omega two, omega omega one. Mu vibration huru, displacement ratio yehuremu hwega hwega inochengetedza hukama hwakati uye inoumba imwe nzira, inonzi main mode kana natural mode. Orthogonality yehuremu nekuomarara iripo pakati pema main modes, iyo inoratidza kuzvimiririra kwe vibration yega yega. Natural frequency uye main mode zvinomiririra hunhu hwe vibration hwe multi-degree of freedom system.

Mufananidzo 8 sisitimu ine madhigirii akawanda erusununguko

Sisitimu ye n degrees of freedom ine n natural frequency uye n main modes. Chero vibration configuration yesisitimu inogona kumiririrwa se linear musanganiswa we major modes. Nokudaro, main mode superposition method inoshandiswa zvakanyanya mu dynamic response analysis ye multi-dof systems. Nenzira iyi, kuyerwa uye kuongororwa kwe natural vibration characteristics yesisitimu inova nhanho yenguva dzose mu dynamic design yesisitimu.

Hunhu hunochinja-chinja hwemasystem e-multi-dof hunogonawo kutsanangurwa nemaitiro efrequency. Sezvo paine basa refrequency pakati pechinhu chimwe nechimwe chinopinzwa uye chinobuda, matrix yefrequency inogadzirwa. Curve yeamplitude-frequency yesystem yerusununguko rwakasiyana neyesystem yerusununguko rumwe chete.

Elastomer inodedera

Sisitimu yerusununguko rwemhando dzakasiyana-siyana iri pamusoro apa imhando ye elastomer. Elastomer ine huwandu husina muganho hwemadhigirii erusununguko. Pane musiyano wehuwandu asi hapana musiyano unokosha pakati pezviviri. Chero elastomer ine huwandu husina muganho hwema frequency echisikigo uye huwandu husina muganho hwema modes anoenderana, uye pane orthogonality pakati pema modes ehukuru nekuomarara. Chero gadziriro ye vibrational ye elastomer inogonawo kumiririrwa se linear superposition ye main modes. Saka, pakuongorora mhinduro ye dynamic ye elastomer, nzira ye superposition ye main mode ichiri kushanda (ona linear vibration ye elastomer).

Tora kudedera kwetambo. Ngatitii tambo yakatetepa yehukuru m pahurefu hweyuniti, l refu, yakamanikidzwa kumativi ese, uye kumanikidzwa kuri T. Panguva ino, frequency yechisikigo yetambo inotsanangurwa ne equation inotevera:

F =na/2l (n= 1,2,3…).

Kupi, ndiko kumhanya kwekupararira kwewave inochinjika munzira yetambo. Ma frequencies ezvitambo anowanikwa ari ma multiples e fundamental frequency pamusoro pe 2l. Kuwanda uku kwenhamba kunotungamira kune harmonic structure inonakidza. Kazhinji, hapana hukama hwakadaro hwenhamba yakawanda pakati pema frequencies e elastomer.

Maitiro matatu ekutanga etambo ine simba anoratidzwa muMufananidzo 9. Kune mamwe ma nodes ari pakorivhe yemodhi huru. Mukudengenyeka kukuru, ma nodes haadengenyeki. Mufananidzo 10 unoratidza maitiro akati wandei eplate yakatenderera yakatsigirwa nedenderedzwa ine mitsetse ine ma nodal yakagadzirwa nemadenderedzwa nemadhayamita.

Kuumbwa chaiko kwedambudziko re elastomer vibration kunogona kupedzwa sedambudziko remuganhu we partial differential equations. Zvisinei, mhinduro chaiyo inogona kuwanikwa chete mune dzimwe dzenyaya dziri nyore, saka tinofanira kushandisa mhinduro inonzwisisika yedambudziko rakaoma re elastomer vibration. Chinangwa chemhinduro dzakasiyana-siyana dzinofungidzirwa ndechekuchinja infinite kuita finite, ndiko kuti, kuparadzanisa limb-less multi-degree of freedom system (continuous system) kuita finite multi-degree of freedom system (discrete system). Kune mhando mbiri dze discretization methods dzinoshandiswa zvakanyanya mu engineering analysis: finite element method uye modal synthesis method.

Mufananidzo 9 nzira yetambo

Mufananidzo 10. Nzira yeplate yakatenderera

Nzira yeFinite element chimiro chakabatanidzwa chinobvisa chimiro chakaoma kuita nhamba yakaganhurirwa yezvinhu uye chinozvibatanidza panhamba yakaganhurirwa yema nodes. Chigadziko chimwe nechimwe i elastomer; Kupararira kwechinhu kunoratidzwa nebasa re interpolation re node displacement. Zvadaro ma parameter ekugoverwa kwechinhu chimwe nechimwe anounganidzwa kune node yega yega mune imwe fomati, uye modhi ye mechanical ye discrete system inowanikwa.

Kugadzira modal ndiko kupatsanura chimiro chakaoma kuita zvimiro zviri nyore. Zvichibva pakunzwisisa hunhu hwe vibration yechikamu chimwe nechimwe, chikamu chinogadzirwa kuita chimiro chakajairika zvichienderana nemamiriro ekubatana ari painterface, uye vibration morphology yechimiro chakajairika inowanikwa nekushandisa vibration morphology yechikamu chimwe nechimwe.

Nzira mbiri idzi dzakasiyana uye dzine hukama, uye dzinogona kushandiswa senzira yekutarisa. Nzira yekugadzira modal inogonawo kubatanidzwa zvinobudirira nekuyera kwekuyedza kuti igadzire nzira yekuongorora dzidziso uye yekuedza yekudedera kwemasisitimu makuru.