Kugwedezeka kwa mzere: elasticity wa zigawo zikuluzikulu mu dongosolo zimatengera lamulo la mbedza, ndipo damping mphamvu kwapangidwa pa kayendedwe ndi molingana ndi equation woyamba wa generalized liwiro (nthawi yochokera kwa generalized coordinates).
lingaliro
Linear system nthawi zambiri imakhala ngati chithunzithunzi chosamveka cha kugwedezeka kwa dongosolo lenileni. Dongosolo la kugwedezeka kwa mzere limagwiritsa ntchito mfundo yayikulu, ndiye kuti, ngati yankho la dongosololi ndi y1 pansi pakuchitapo kwa x1, ndi y2 pansi pa zolowetsa x2, ndiye kuyankha kwadongosolo pansi pakuchitapo x1 ndi x2 ndi y1 + y2.
Pamaziko a superposition mfundo, kulowetsa mosagwirizana kungathe kuwola mu kuchuluka kwa zikhumbo zopanda malire, ndiyeno yankho lathunthu la dongosololi likhoza kupezedwa. mndandanda wa zigawo za harmonic ndi Fourier kusintha, ndi zotsatira za chigawo chilichonse harmonic pa dongosolo akhoza kufufuzidwa payokha.Chotero, mayankho makhalidwe a liniya kachitidwe ndi nthawi zonse. magawo amatha kufotokozedwa ndi kuyankha mwachangu kapena kuyankha pafupipafupi.
Impulse response imatanthawuza kuyankha kwa dongosolo ku unit impulse, yomwe imasonyeza maonekedwe a machitidwe a dongosolo mu nthawi. ndi Fourier transform.
gulu
Kugwedezeka kwa liniya kumatha kugawidwa kukhala kugwedezeka kwa mzere umodzi wa digirii imodzi yaufulu ndi kugwedezeka kwa mzere wamitundu yambiri yaufulu.
(1) kugwedezeka kwa mzere wa dongosolo limodzi la digiri-ya-ufulu ndi kugwedezeka kwa mzere komwe malo ake angadziwike ndi coordinate.Ndiko kugwedezeka kosavuta komwe malingaliro ambiri ndi mawonekedwe a vibration angatengedwe. Zimaphatikizapo zosavuta. kugwedezeka kwa ma harmonic, kugwedezeka kwaulere, kugwedezeka kwamphamvu ndi kugwedezeka kokakamiza.
Kugwedezeka kosavuta kwa harmonic: kuyenda mobwerezabwereza kwa chinthu pafupi ndi malo ake ogwirizana malinga ndi lamulo la sinusoidal pansi pa mphamvu yobwezeretsa molingana ndi kusamutsidwa kwake.
Damped vibration: kugwedezeka komwe matalikidwe ake amachepetsedwa nthawi zonse ndi kupezeka kwa mikangano ndi kukana kwa dielectric kapena kugwiritsa ntchito mphamvu zina.
Kugwedezeka mokakamiza: kugwedezeka kwa dongosolo pansi pa chisangalalo chosalekeza.
(2) kugwedezeka kwa mzere wa dongosolo la ma degree-of-ufulu ndiko kugwedezeka kwa dongosolo la mzere ndi n≥2 madigiri a ufulu. Dongosolo la n madigiri a ufulu ali ndi maulendo achilengedwe ndi njira zazikulu. ya dongosolo likhoza kuyimiridwa ngati liniya kuphatikiza kwa modes zazikulu.Choncho, njira yaikulu ya superposition mode imagwiritsidwa ntchito kwambiri mu kusanthula kwamphamvu kwa machitidwe a multi-dof. kuyeza ndi kusanthula mawonekedwe achilengedwe a kugwedezeka kwa dongosolo kumakhala gawo lachizoloŵezi mu mapangidwe osinthika a dongosolo.Makhalidwe amphamvu a machitidwe a multi-dof amathanso kufotokozedwa ndi maulendo afupipafupi. linanena bungwe, pafupipafupi khalidwe masanjidwewo amapangidwa.Pali mgwirizano wotsimikizika pakati pa pafupipafupi khalidwe ndi mode waukulu.The matalikidwe-pafupipafupi khalidwe pamapindikira a dongosolo multi-ufulu ndi wosiyana ndi wa dongosolo laufulu umodzi.
Liniya kugwedezeka kwa gawo limodzi laufulu dongosolo
Kugwedezeka kwa mzere komwe malo a dongosolo angadziwike ndi mgwirizano wokhazikika.Ndiko kugwedezeka kosavuta komanso kofunikira kwambiri komwe malingaliro ambiri oyambira ndi mawonekedwe a vibration amatha kutengera. Zimaphatikizapo kugwedezeka kosavuta kwa harmonic, kugwedezeka konyowa komanso kugwedezeka kokakamiza. .
Kugwedezeka kwa Harmonic
Pansi pa ntchito yobwezeretsa mphamvu molingana ndi kusamutsidwa, chinthucho chimabwereranso m'njira ya sinusoidal pafupi ndi malo ake ofanana (FIG. 1) .X imayimira kusamutsidwa ndipo t imayimira nthawi. Mafotokozedwe a masamu a kugwedezeka uku ndi:
(1)Kumene A ndiye mtengo wokwanira wosuntha x, womwe umatchedwa matalikidwe, ndipo umayimira kukula kwa kugwedezeka; Omega n ndiye matalikidwe a Angle increment of vibration pa sekondi imodzi, yomwe imatchedwa ma frequency aang'ono, kapena ma frequency ozungulira; Pamatchulidwe a f= n/2, chiwerengero cha oscillation pa sekondi iliyonse chimatchedwa ma frequency; Chosiyana cha izi, T=1/f, ndi nthawi zimatengera kuti oscillate mkombero umodzi, ndipo amatchedwa nthawi.Amplitude A, mafupipafupi f (kapena angular pafupipafupi n), gawo loyamba, lotchedwa yosavuta harmonic kugwedera zinthu zitatu.
CHITH. 1 yokhotakhota yosavuta ya harmonic
Monga zikuwonetsedwa mu FIG. 2, oscillator wosavuta wa harmonic amapangidwa ndi misa yokhazikika yolumikizidwa ndi kasupe wa mzere.
Kuwuma kwa kasupe kuli kuti.Njira yothetsera vutoli ili pamwambayi ndi (1) .A ndipo ikhoza kutsimikiziridwa ndi malo oyambirira x0 ndi liwiro loyambirira pa t=0:
Koma omega n amangotsimikiziridwa ndi mawonekedwe a dongosolo lokha m ndi k, popanda zina zowonjezera zoyamba, kotero omega n amadziwikanso kuti ma frequency achilengedwe.
CHITH. 2 digiri imodzi yaufulu dongosolo
Kwa oscillator yosavuta ya harmonic, kuchuluka kwa mphamvu zake za kinetic ndi mphamvu zomwe zingatheke ndizokhazikika, ndiko kuti, mphamvu zonse zamakina a dongosolo zimasungidwa.
Kugwedezeka kwamphamvu
Kugwedezeka komwe matalikidwe ake amachepetsedwa mosalekeza ndi kukangana ndi kukana dielectric kapena kugwiritsa ntchito mphamvu zina. Pa kugwedezeka kwapang'onopang'ono, liwiro nthawi zambiri si lalikulu kwambiri, ndipo kukana kwapakatikati kumayenderana ndi liwiro la mphamvu yoyamba, yomwe imatha kulembedwa ngati c ndi The damping coefficient.Chifukwa chake, kugwedera kwa gawo limodzi la ufulu wokhala ndi mizere yonyowa kumatha kulembedwa motere:
(2)Pamene, m =c/2m imatchedwa damping parameter, ndipo njira yothetsera (2) ikhoza kulembedwa:
(3)Ubale wa manambala pakati pa omega n ndi PI ukhoza kugawidwa m'magawo atatu awa:
N > (pankhani yaing'ono damping) tinthu timatulutsa attenuation kugwedera, kugwedera equation ndi:
Kukula kwake kumachepa ndi nthawi molingana ndi lamulo la exponential lomwe likuwonetsedwa mu equation, monga momwe tawonetsera pamzere wamadontho mu FIG. 3. Kunena zowona, kugwedezeka uku ndi kwanthawi pang'ono, koma kuchuluka kwa nsonga yake kumatha kufotokozedwa motere:
Amatchedwa kuchuluka kwa kuchepetsa matalikidwe, komwe kuli nthawi ya kugwedezeka.Logarithm yachilengedwe ya mlingo wochepetsera matalikidwe imatchedwa logarithm minus (amplitude) mlingo. kuyesa kuyesa delta ndipo, pogwiritsa ntchito njira yomwe ili pamwambapa ikhoza kuwerengedwa c.
Panthawiyi, yankho la equation (2) likhoza kulembedwa:
Pamodzi ndi mayendedwe a liwiro loyambirira, imatha kugawidwa m'magawo atatu osagwedezeka monga momwe FIG ikuwonetsera. 4.
N <(pankhani ya damping yayikulu), yankho la equation (2) likuwonetsedwa mu equation (3) .Panthawiyi, dongosololi silikugwedezekanso.
Kugwedezeka kokakamiza
Kugwedezeka kwa dongosolo pansi pa chisangalalo chokhazikika.Kusanthula kwa kugwedezeka kumafufuza momwe dongosololi limayankhira ku excitation.Kuthamanga kwapang'onopang'ono ndi chisangalalo chokhazikika. kuyankha kwa dongosolo ku chisangalalo chilichonse cha harmonic kumafunikira.Pansi pakuchitapo kanthu kwa chisangalalo cha harmonic, kusiyanitsa kwa kusuntha kwa digiri imodzi. ya ufulu damped dongosolo akhoza kulembedwa:
Yankho ndi kuchuluka kwa magawo awiri. Gawo limodzi ndi kuyankha kwa kugwedezeka konyowa, komwe kumawola mwachangu ndi nthawi. Yankho la gawo lina la kugwedezeka kokakamiza likhoza kulembedwa:
CHITH. 3 yopindika yopindika yopindika
CHITH. Ma 4 ma curve amikhalidwe itatu yoyambira yokhala ndi kunyowa kwambiri
Lembani mu
H / F0 = h (), ndi chiŵerengero cha kuyankha mokhazikika matalikidwe ku chisangalalo, kuzindikiritsa matalikidwe afupipafupi, kapena kupeza ntchito; Bits for steady state response and incentive of phase, characterization of phase frequency properties.Ubale pakati pawo ndi mafupipafupi osangalatsa akuwonetsedwa mu FIG. 5 ndi FIG. 6.
Monga momwe tingawonere kuchokera kumtunda-mafupipafupi pamapindikira (FIG. 5), pakakhala kuchepa kwazing'ono, mphuno ya amplitude-frequency imakhala ndi nsonga imodzi. amatchedwa resonant frequency of the system.Pankhani ya damping yaying'ono, ma frequency a resonance sali osiyana kwambiri ndi ma frequency achilengedwe. ili pafupi ndi mafupipafupi achilengedwe, matalikidwe amawonjezeka kwambiri. Chodabwitsa ichi chimatchedwa resonance.At resonance, kupindula kwa dongosolo kumakulitsidwa, ndiko kuti, kugwedezeka kokakamiza kumakhala koopsa kwambiri.Choncho, nthawi zonse, yesetsani kupeŵa resonance, pokhapokha zida zina ndi zipangizo zogwiritsira ntchito resonance kuti mukwaniritse zazikulu. kugwedezeka.
CHITH. 5 matalikidwe pafupipafupi pamapindikira
Itha kuwoneka kuchokera pamapindikidwe afupipafupi (chithunzi 6), mosasamala kanthu za kukula kwake, mu omega zero gawo kusiyana pang'ono = PI / 2, izi zitha kugwiritsidwa ntchito moyenera pakuyezera kumveka.
Kuwonjezera pa chisangalalo chokhazikika, machitidwe nthawi zina amakumana ndi chisangalalo chosakhazikika.Ikhoza kugawidwa pafupifupi mitundu iwiri: imodzi ndi zotsatira zadzidzidzi.Chachiwiri ndi zotsatira zotsalira za kusagwirizana.
Chida champhamvu chowunikira kugwedezeka kosakhazikika ndi njira yoyankhira mofulumizitsa.Imalongosola mawonekedwe osinthika adongosolo ndi kuyankha kwakanthawi kwa unit impulse input of the system.The unit impulse imatha kuwonetsedwa ngati delta function.In engineering, the delta ntchito nthawi zambiri imatanthauzidwa motere:
Kumene 0- amaimira mfundo yomwe ili pa t-axis yomwe imayandikira ziro kuchokera kumanzere; 0 kuphatikiza ndi mfundo yomwe imapita ku 0 kuchokera kumanja.
CHITH. 6 gawo pafupipafupi pamapindikira
CHITH. 7 zolowetsa zilizonse zitha kuganiziridwa ngati kuchuluka kwa mndandanda wazinthu zotengera
Dongosololi limafanana ndi yankho h (t) lopangidwa ndi unit impulse pa t=0, yomwe imatchedwa impulse response function.Kungoganiza kuti dongosololi lidayima patsogolo pa kugunda, h(t)=0 kwa t<0.Kudziwa ntchito ya impulse response ya dongosolo, titha kupeza kuyankha kwadongosolo kuzinthu zilizonse x(t) zinthu (FIG. 7) .Yankho la dongosolo ndi:
Kutengera mfundo ya superposition, kuyankha kwathunthu kwa dongosolo lolingana ndi x(t) ndi:
Chophatikizika ichi chimatchedwa convolution integral kapena superposition integral.
Kugwedezeka kwa mzere wadongosolo lamitundu yambiri-ya-ufulu
Kugwedezeka kwa dongosolo la mzere wokhala ndi n≥2 madigiri a ufulu.
Chithunzi 8 chikuwonetsa magawo awiri osavuta a resonant olumikizidwa ndi kasupe wolumikizana. Chifukwa ndi dongosolo la magawo awiri aufulu, makonzedwe awiri odziyimira pawokha amafunikira kuti adziwe malo ake.Pali ma frequency awiri achilengedwe mu dongosolo lino:
Mafupipafupi aliwonse amafanana ndi kugwedezeka. Ma oscillator a harmonic amachita kusinthasintha kwa ma frequency omwewo, ndikudutsa molumikizana ndi malo ofananirako ndikufikira pamalo opitilira muyeso. kugwedezeka kwakukulu kolingana ndi omega omega two, omega omega one. Pakugwedezeka kwakukulu, chiŵerengero cha kusamuka kwa misa iliyonse chimasunga ubale wina ndi kupanga njira inayake, yomwe imatchedwa main mode kapena chilengedwe mode.The orthogonality wa misa ndi stiffness alipo pakati pa modes waukulu, amene amasonyeza kudziimira pa aliyense kugwedera. zamitundu yambiri yaufulu.
CHITH. 8 dongosolo ndi magawo angapo a ufulu
Dongosolo la n madigiri a ufulu ali ndi ma frequency achilengedwe ndi njira zazikulu za n.Kusinthika kulikonse kwa kugwedezeka kwa dongosololi kumatha kuyimiridwa ngati kuphatikiza kwa mizere yayikulu yamitundu yayikulu. -dof systems.Mwa njira iyi, kuyeza ndi kusanthula kwachilengedwe kugwedezeka kwa machitidwe kumakhala gawo lachizoloŵezi mu mapangidwe amphamvu a dongosolo.
Makhalidwe amphamvu a machitidwe a multi-dof amathanso kufotokozedwa ndi machitidwe afupipafupi.Popeza pali ntchito yafupipafupi pakati pa kulowetsa ndi kutulutsa, matrix odziwika pafupipafupi amapangidwa. kuchokera ku dongosolo la ufulu umodzi.
Elastomer imanjenjemera
Pamwambapa Mipikisano digiri ya ufulu dongosolo ndi pafupifupi mawotchi chitsanzo cha elastomer.Elastomer ndi wopandamalire chiwerengero cha madigiri a ufulu.Pali kusiyana kachulukidwe koma palibe kusiyana kofunikira pakati pa ziwirizi.Elastomer iliyonse ili ndi chiwerengero chosawerengeka cha ma frequency achilengedwe ndipo chiwerengero chopanda malire cha mitundu yofananira, ndipo pali orthogonality pakati pa mitundu ya misa ndi kuuma. Ikhozanso kuyimiridwa ngati mawonekedwe apamwamba amitundu yayikulu.Chifukwa chake, pakuwunika kwakuyankhidwa kwa elastomer, njira yapamwamba kwambiri yamachitidwe akuluakulu ikugwirabe ntchito (onani kugwedezeka kwa mzere wa elastomer).
Tengani kugwedezeka kwa chingwe.Tiyeni tinene kuti chingwe chochepa kwambiri cha mita pa kutalika kwa unit, kutalika l, kumangiriridwa kumapeto onse awiri, ndipo kugwedezeka ndi T.Panthawiyi, mafupipafupi achilengedwe a chingwe amatsimikiziridwa ndi zotsatirazi: equation:
F =na/2l (n= 1,2,3…).
Kumene, ndi kuthamanga kwa kufalikira kwa mafunde odutsa motsatira njira ya chingwe.Mafuridwe achilengedwe a zingwe amapezeka kuchulukitsa kwa ma frequency a 2l. mgwirizano wophatikizika woterewu pakati pa ma frequency achilengedwe a elastomer.
Njira zitatu zoyambirira za chingwe chokhazikika zikuwonetsedwa mu FIG. 9. Pali mfundo zina pamzere waukulu wa mode. 10 ikuwonetsa mitundu ingapo ya mbale zozungulira zozungulira zomwe zimakhala ndi mizere yozungulira yokhala ndi mabwalo ndi ma diameter.
Mapangidwe enieni a vuto la kugwedezeka kwa elastomer akhoza kumalizidwa ngati vuto la malire a ma equation ang'onoang'ono. Chofunikira cha mayankho osiyanasiyana oyerekeza ndikusintha wopandamalire kukhala wamalire, ndiye kuti, kusiyanitsa miyendo yocheperako yamitundu yambiri. ya dongosolo laufulu (dongosolo lopitilira) mu dongosolo lomaliza la magawo ambiri a ufulu (discrete system) .Pali mitundu iwiri ya njira za discretization zomwe zimagwiritsidwa ntchito kwambiri pakuwunika uinjiniya: njira yomaliza yazinthu ndi njira yophatikizira modal.
CHITH. 9 njira ya chingwe
CHITH. 10 njira yozungulira mbale
Finite element ndi njira yophatikizika yomwe imapangitsa kuti zinthu zikhale zovuta kuziyika muzinthu zowerengeka ndikuzilumikiza pa nambala yowerengeka ya node. Chigawo chilichonse chimakhala ndi elastomer; magawo ogawa a chinthu chilichonse amawunikidwa ku mfundo iliyonse mumtundu wina, ndipo mtundu wamakina wadongosolo la discrete umapezeka.
Modal kaphatikizidwe ndi kuwonongeka kwa dongosolo zovuta mu substructures zingapo zosavuta. Pamaziko a kumvetsa kugwedera makhalidwe a gawo lililonse, substructure ndi apanga dongosolo lonse malinga ndi kugwirizana zikhalidwe pa mawonekedwe, ndi kugwedera morphology wa ambiri. Kapangidwe kake kamapezedwa pogwiritsa ntchito mawonekedwe a vibration pagawo lililonse.
Njira ziwirizi ndizosiyana komanso zogwirizana, ndipo zingagwiritsidwe ntchito monga reference.The modal synthesis njira ingathenso kuphatikizidwa bwino ndi kuyeza koyesera kuti apange njira yowonongeka ndi yoyesera kuti agwedezeke machitidwe akuluakulu.
Nthawi yotumiza: Apr-03-2020
