Gutembera k'umurongo: uburimbane bw'ibice biri muri sisitemu bugengwa n'itegeko rya hooke, kandi imbaraga zo kugabanya zikorwa mu gihe cy'ingendo zihwanye n'ikigereranyo cya mbere cy'umuvuduko rusange (igihe gikomoka ku miyoboro rusange).
igitekerezo
Sisitemu y'umurongo ubusanzwe ni icyitegererezo cy'ihindagurika ry'uburyo sisitemu nyayo ikora. Sisitemu y'ihindagurika ry'umurongo ikoresha ihame rya superposition, ni ukuvuga ko niba igisubizo cya sisitemu ari y1 munsi y'igikorwa cy'inyongera x1, na y2 munsi y'igikorwa cy'inyongera x2, noneho igisubizo cya sisitemu munsi y'igikorwa cy'inyongera x1 na x2 ni y1+y2.
Hashingiwe ku ihame rya superposition, ikintu cyinjijwemo gishobora guhindurwamo igiteranyo cy'uruhererekane rw'ingufu ntoya, hanyuma igisubizo cyose cya sisitemu kikaboneka. Igiteranyo cy'ibice bya harmonic by'ingufu zidasanzwe gishobora kwaguka kikavamo urukurikirane rw'ibice bya harmonic na Fourier transform, kandi ingaruka za buri gice cya harmonic kuri sisitemu zishobora gusuzumwa ukwazo. Kubwibyo, imiterere y'ingufu zigororotse zifite ibipimo bihoraho ishobora gusobanurwa hakoreshejwe igisubizo cya impulse cyangwa igisubizo cya frequency.
Igisubizo cy'ingufu kivuga ku gusubiza kwa sisitemu kuri impufu y'igice, ari na byo bigaragaza imiterere y'ingufu mu gihe. Igisubizo cy'ingufu kivuga ku miterere y'ingufu mu gusubiza ku gice cya harmonic. Ihuza hagati y'ibyo byombi rigenwa na Fourier transform.
gushyira mu byiciro
Gutembagara k'umurongo bishobora kugabanywamo gutembagara k'umurongo umwe w'ubwisanzure n'ugutembagara k'umurongo umwe w'ubwisanzure bwinshi.
(1) gutigita umurongo umwe w’uburyo bwo kwigenga ni ugutigita umurongo umwe aho umwanya wabyo ushobora kugenwa n’umurongo rusange. Ni ugutigita kworoshye cyane aho ibitekerezo byinshi by’ibanze n’imiterere y’ugutigita bishobora guturuka. Birimo gutigita byoroshye, gutigita ku bwisanzure, gutigita kugabanya no gutigita ku ngufu.
Guhindagurika kw'ibintu mu buryo bworoshye: kugenda kw'ikintu kiri hafi y'aho kiri mu buryo bw'uburinganire hakurikijwe itegeko rya sinusoidal munsi y'imbaraga zigarura ibintu bingana n'uko cyimuka.
Gutembagara kwa Damped: gutembagara kwabyo kugabanuka bitewe no kuba hari uburyaryate n'ubudahangarwa bwa dielectric cyangwa izindi ngufu zikoreshwa.
Gutigita ku ngufu: gutigita kw'uburyo buri munsi y'ihungabana rihoraho.
(2) guhindagurika kw'umurongo wa sisitemu y'ubwisanzure bwinshi ni uguhindagurika kw'umurongo wa sisitemu y'ubwisanzure hamwe na dogere n≥2. Sisitemu ya dogere n y'ubwisanzure ifite imirongo karemano ya n na modes main ya n. Imiterere iyo ari yo yose ya sisitemu ishobora gugaragazwa nk'uruvange rw'umurongo wa modes main. Kubwibyo, uburyo bwa superposition bwa mode main bukoreshwa cyane mu isesengura ry'impinduka za sisitemu za dogere nyinshi. Muri ubu buryo, gupima no gusesengura imiterere ya vibration karemano ya sisitemu biba intambwe isanzwe mu gishushanyo mbonera cya sisitemu. Imiterere ya dynamic ya sisitemu za dogere nyinshi ishobora kandi gusobanurwa n'imiterere ya frequency. Kubera ko hari imikorere ya frequency hagati ya buri kwinjiza n'ibisohoka, hakorwa matrix ya frequency. Hari isano ihamye hagati ya frequency ya frequency na mode main. Inzira ya amplitude-frequency ya sisitemu ya multi-freedom itandukanye n'iya sisitemu ya single-freedom.
Gutemba kw'umurongo w'urwego rumwe rw'ubwisanzure
Gutembera k'umurongo aho umwanya w'uburyo runaka ushobora kugenwa n'umurongo rusange. Ni ugutembera koroheje kandi kw'ibanze cyane aho ibitekerezo byinshi by'ibanze n'imiterere y'ugutembera bishobora guturuka. Birimo gutembera koroheje, gutembera gutose no gutitira ku ngufu.
Gutigita kwa harmonic
Mu gikorwa cyo kugarura imbaraga ukurikije ukwimuka, ikintu gisubira mu buryo bwa sinusoidal hafi y'aho gihagaze (ISHUSHO YA 1). X ihagarariye ukwimuka naho t ihagarariye igihe. Imiterere y'iki gihinda ni iyi:
(1)Aho A ari agaciro ntarengwa ka displacement x, kitwa amplitude, kandi kikerekana ubukana bwa vibration; Omega n ni amplitude Increment ya Angle ya vibration kuri segonda, kitwa angular frequency, cyangwa circular frequency; Iki kitwa icyiciro cy'ibanze. Mu bijyanye na f= n/2, umubare wa vibration kuri segonda witwa frequency; Inyuranya n'iyi, T=1/f, ni igihe bifata kugira ngo cycle imwe ihinduke, kandi icyo kitwa igihe. Amplitude A, frequency f (cyangwa angular frequency n), icyiciro cy'ibanze, kizwi nka simple harmonic vibration three elements.
ISHUSHO YA 1: Umuvuduko woroshye wo guhindagurika kw'imivuduko
Nkuko bigaragara ku ISHUSHO YA 2, oscillator yoroshye ihuza ikorwa n'uburemere bunini bwa m buhujwe n'isoko y'umurongo. Iyo ihinduka ry'ihindagurika ry'ihindagurika ribarwa uhereye ku mwanya w'uburinganire, ikigereranyo cy'ihindagurika ni:
Ubukomere bw'impeshyi buri he? Igisubizo rusange cy'ikigereranyo cyavuzwe haruguru ni (1). A kandi gishobora kugenwa n'umwanya w'ibanze x0 n'umuvuduko w'ibanze kuri t=0:
Ariko omega n igenwa gusa n'imiterere y'umubiri ubwawo m na k, hatitawe ku miterere y'inyongera y'ibanze, bityo omega n izwi kandi nk'umuvuduko karemano.
ISHUSHO YA 2: Sisitemu y'ubwisanzure bw'urwego rumwe
Ku gikoresho cyoroshye cyo gupima imbaraga, igiteranyo cy'ingufu zacyo za kinetiki n'ingufu zishobora kubaho nta guhindagurika, ni ukuvuga ko ingufu zose za mekanike z'urusobe rw'ibintu zibikwa. Mu gihe cyo guhindagura, ingufu za kinetiki n'ingufu zishobora kubaho bihora bihinduka kimwe kimwe.
Ihindagurika ry'amazi
Gutembagara aho ubushobozi bwabyo buhora bugabanuka bitewe no gukururana no kudakoresha ingufu cyangwa izindi ngufu. Ku gutimba guto, umuvuduko muri rusange ntabwo ari munini cyane, kandi ubwiyongere buciriritse bungana n'umuvuduko ugera ku mbaraga za mbere, zishobora kwandikwa nka c ari coefficient ya damping. Kubwibyo, ikigereranyo cya vibration cya dogere imwe y'ubwisanzure hamwe na linear damping gishobora kwandikwa gitya:
(2)Aho, m = c/2m yitwa parameter ya damping, na. Igisubizo rusange cya formula (2) gishobora kwandikwa:
(3)Isano y'imibare iri hagati ya omega n na PI ishobora kugabanywamo ibice bitatu bikurikira:
N > (mu gihe cyo kugabanya ubushyuhe) uduce duto twakoze ku kugabanya ubushyuhe, ikigereranyo cy'ihindagurika ni:
Ubwinshi bwayo bugabanuka uko igihe kigenda gihita hakurikijwe itegeko ry’impinduka rigaragara muri iki gipimo, nk’uko bigaragara ku murongo w’utudomo uri ku ISHUSHO YA 3. Mu by’ukuri, uku guhindagurika ni ikintu kidahinduka, ariko inshuro y’agahenge kayo ishobora gusobanurwa gutya:
Itwa igipimo cyo kugabanya amplitude, aho ni igihe cyo guhindagura. Logarithm karemano y'igipimo cyo kugabanya amplitude yitwa igipimo cyo gukuramo logarithm (amplitude). Birumvikana ko, =, muri uru rubanza, ingana na 2/1. Binyuze mu buryo butaziguye mu igerageza rya delta kandi, hakoreshejwe formula yavuzwe haruguru, ushobora kubara c.
Muri iki gihe, igisubizo cy'ikigereranyo (2) gishobora kwandikwa:
Hamwe n'icyerekezo cy'umuvuduko w'ibanze, gishobora kugabanywamo ibice bitatu bidahindagurika nk'uko bigaragara ku ISHUSHO YA 4.
N < (mu gihe cyo kugabanya cyane), igisubizo cy'ikigereranyo (2) kigaragara muri icyo kigereranyo (3). Kuri iyi ngingo, sisitemu ntabwo ikinyeganyega.
Gutigita ku ngufu
Gutigita kwa sisitemu munsi y'ingufu zihoraho. Isesengura ry'ingufu risuzuma ahanini uburyo sisitemu isubiza iyo ishyushye. Gutigita buri gihe ni ugutigita buri gihe. Kubera ko gutigita buri gihe bishobora guhindurwamo igiteranyo cy'ingufu nyinshi zihuriweho, hakurikijwe ihame rya superposition, ni bwo gusa uburyo sisitemu isubiza buri gutigita buri harmonic ari byo bisabwa. Mu gihe cy'igikorwa cy'ingufu zihuriweho, ikigereranyo cy'ingendo y'urwego rumwe rw'ubwisanzure gishobora kwandikwa:
Igisubizo ni igiteranyo cy'ibice bibiri. Igice kimwe ni igisubizo cy'ihindagurika ry'ikirere, ribora vuba uko igihe kigenda gihita. Igisubizo cy'ikindi gice cy'ihindagurika ry'ikirere gishobora kwandikwa:
ISHUSHO YA 3: Umugozi wo guhindagurika utose
ISHUSHO YA 4: Imiterere y'imiterere itatu y'ibanze ifite imiterere ikomeye
Andika mu
H /F0= h (), ni igipimo cy'ubwinshi bw'igisubizo gihamye ku bwinshi bw'igishyushya, kigaragaza imiterere y'ubwinshi bw'igishyushya, cyangwa imikorere yo kwiyongera; Bits zo gusubiza mu buryo buhamye no gushishikariza icyiciro, kugaragaza imiterere y'ubwinshi bw'igishyushya. Isano iri hagati yabyo n'ubwinshi bw'igishyushya igaragara ku ISHUSHO YA 5 N'ISHUSHO YA 6.
Nkuko bigaragara ku murongo wa amplitude-frequency (ISHUSHO YA 5), mu gihe cyo gushonga gato, umurongo wa amplitude-frequency ufite peak imwe. Uko gushonga guto, niko peak iba ndende; Frequency ijyanye n'agasongero yitwa frequency ya resonant ya sisitemu. Mu gihe cyo gushonga guto, frequency ya resonance ntabwo itandukanye cyane n'iy'umwimerere. Iyo frequency yo gushyushya iri hafi y'inshuro karemano, amplitude iriyongera cyane. Iki kintu cyitwa resonance. Mu gihe cyo gushonga, inyungu ya sisitemu irazamuka cyane, ni ukuvuga ko gutitira ku ngufu ari byo bikomeye cyane. Bityo rero, muri rusange, jya uhora wihatira kwirinda resonance, keretse ibikoresho bimwe na bimwe bikoresha resonance kugira ngo bigere ku gutitira gukomeye.
ISHUSHO YA 5: Inzira y'umuvuduko w'ubunini bw'ikirere
Bigaragara uhereye ku murongo wa phase frequency (ishusho ya 6), hatitawe ku bunini bwa damping, muri omega zero phase difference bits = PI / 2, iki kimenyetso gishobora gukoreshwa neza mu gupima resonance.
Uretse gushyuha guhoraho, sisitemu rimwe na rimwe zihura n’ishyuha ridahamye. Rishobora kugabanywamo ubwoko bubiri: bumwe ni ingaruka zitunguranye. Ubwa kabiri ni ingaruka zirambye zo kwihitiramo ibintu uko biri. Mu gihe cyo gushyuha gukomeye, igisubizo cy’isi na cyo ntigihamye.
Igikoresho gikomeye cyo gusesengura vibration idahamye ni uburyo bwo gusubiza impulse. Busobanura imiterere y'imikorere ya sisitemu hamwe n'impinduka y'igihe gito y'ingufu z'igice cya sisitemu. Impulse y'igice ishobora kugaragazwa nk'imikorere ya delta. Mu buhanga, imikorere ya delta ikunze gusobanurwa nka:
Aho 0- ihagarariye ingingo iri ku murongo wa t yerekeza kuri zeru uturutse ibumoso; 0 plus ni ingingo ijya kuri 0 uturutse iburyo.
ISHUSHO YA 6: Ingano y'impinduka z'icyiciro
ISHUSHO YA 7. Ibyinjira byose bishobora gufatwa nk'igiteranyo cy'uruhererekane rw'ibintu bitera imbaraga
Sisitemu ihuye n'igisubizo h(t) cyakozwe n'ingufu y'igice kuri t=0, cyitwa imikorere y'igisubizo cy'ingufu. Dufashe ko sisitemu ihagaze mbere y'ingufu, h(t)=0 kuri t<0. Tuzi imikorere y'igisubizo cy'ingufu cy'isi, dushobora kubona igisubizo cy'isi ku kintu icyo ari cyo cyose cyashyizwemo x(t). Kuri iyi ngingo, ushobora gutekereza kuri x(t) nk'igiteranyo cy'uruhererekane rw'ibintu by'ingufu (ISHUSHO YA 7). Igisubizo cy'isi ni:
Hashingiwe ku ihame rya superposition, igisubizo cyose cya sisitemu gihuye na x (t) ni:
Iyi integral yitwa convolution integral cyangwa superposition integral.
Gutembera k'umurongo kwa sisitemu y'ubwisanzure bwinshi
Guhindagurika kwa sisitemu igororotse ifite dogere n≥2 z'ubwisanzure.
Ishusho ya 8 igaragaza sisitemu ebyiri zoroshye zihuza n'isoko y'amazi. Kubera ko ari sisitemu ifite ubushobozi bwo gushyiramo imbaraga, hakenewe imirongo ibiri yigenga kugira ngo hamenyekane aho iherereye. Hari imirongo ibiri karemano muri iyi sisitemu:
Buri frequency ihuye n'uburyo bwo guhindagura. Ingufu zihuza zikora imihindagurikire y'imihindagurikire imwe, zinyura mu mwanya w'uburinganire kandi zigagera ku mwanya udasanzwe. Mu guhindagura kw'ingenzi bihuye na omega imwe, x1 ingana na x2; Mu guhindagura kw'ingenzi bihuye na omega omega ebyiri, omega omega imwe. Mu guhindagura kw'ingenzi, igipimo cyo kwimuka kwa buri misa gikomeza isano runaka kandi kigakora uburyo runaka, bwitwa uburyo bw'ingenzi cyangwa uburyo bw'umwimerere. Imiterere y'uburemere n'ubukomere biri mu buryo bw'ingenzi, bigaragaza ubwigenge bwa buri guhindagura. Imihindagurikire y'umwimerere n'uburyo bw'ingenzi bigaragaza imiterere y'imihindagurikire y'urwego rwinshi rw'ubwisanzure.
ISHUSHO YA 8 sisitemu ifite ubwisanzure bwinshi
Sisitemu ya dogere n y'ubwisanzure ifite imirongo karemano ya n n n n'uburyo bw'ingenzi bwa n. Imiterere iyo ari yo yose ya vibration ya sisitemu ishobora gugaragazwa nk'uruvange rw'uburyo bw'ingenzi. Kubwibyo, uburyo bwa superposition ya mode main bukoreshwa cyane mu isesengura ry'impinduka zihindagurika za sisitemu nyinshi. Muri ubu buryo, gupima no gusesengura imiterere y'impinduka karemano ya sisitemu biba intambwe isanzwe mu miterere y'impinduka za sisitemu.
Ibiranga imikorere ya sisitemu za dof nyinshi bishobora kandi gusobanurwa n'ibiranga imikorere ya frequence. Kubera ko hari imikorere iranga frequence hagati ya buri kwinjiza n'isohoka, hakorwa matrix iranga frequence. Inzira iranga frequence ya amplitude-frequency ya sisitemu ya frequence nyinshi itandukanye n'iya sisitemu ya frequence imwe.
Elastomer irahinda umushyitsi
Sisitemu y’ubwisanzure bwinshi yavuzwe haruguru ni icyitegererezo cya elastomer gisanzwe. Elastomer ifite umubare utagira ingano w’ubwisanzure. Hari itandukaniro ry’ingano ariko nta tandukaniro ry’ingenzi riri hagati ya zombi. Elastomer iyo ari yo yose ifite umubare utagira ingano w’imirongo karemano n’umubare utagira ingano w’uburyo bujyanye, kandi hariho imiterere hagati y’uburyo bw’uburemere n’ubukomezi. Imiterere iyo ari yo yose ya elastomer ishobora kandi kugaragazwa nk’igenamiterere ry’umurongo w’uburyo bw’ingenzi. Kubwibyo, ku isesengura ry’impinduka za elastomer, uburyo bwa superposition bw’uburyo bw’ingenzi buracyakoreshwa (reba vibration ya elastomer).
Fata uburyo umugozi utembera. Reka tuvuge ko umugozi muto w'uburemere m kuri buri gice cy'uburebure, l ndende, utembera ku mpera zombi, kandi umugozi ni T. Muri iki gihe, ingano karemano y'umugozi igenwa n'ikigereranyo gikurikira:
F = na/2l (n= 1,2,3…).
Aho, umuvuduko wo gukwirakwiza w'umuraba unyura mu cyerekezo cy'umugozi uri. Imivuduko karemano y'imigozi iba ari inshuro nyinshi z'umuvuduko fatizo urenze 2l. Uku kwiyongera kw'imigozi bitanga imiterere myiza ya harmonic. Muri rusange, nta sano nk'iyo y'imigozi myinshi hagati y'imivuduko karemano ya elastomer.
Uburyo butatu bwa mbere bw'umugozi uhambiriye bugaragara ku ISHUSHO YA 9. Hari utudomo ku murongo w'uburyo bw'ibanze. Mu guhindagurika kw'ingenzi, utudomo ntabwo duhinda. ISHUSHO YA 10 igaragaza uburyo butandukanye busanzwe bw'icyuma gifatanye n'uruziga gifite imirongo imwe n'imwe y'uduti igizwe n'uruziga n'umurambararo.
Uburyo nyabwo bwo gusesengura ikibazo cya elastomer bushobora gufatwa nk'ikibazo cy'agaciro k'umupaka w'ibigereranyo by'itandukaniro ry'igice. Ariko, igisubizo nyacyo gishobora kuboneka gusa muri bimwe mu bihe byoroshye, bityo tugomba gukoresha igisubizo cy'ikibazo cy'ihindagurika ry'ilastomer. Ishingiro ry'ibisubizo bitandukanye bya hafi ni uguhindura ishingiro ritarangira rijya ku rindi, ni ukuvuga, guhindura sisitemu y'ubwisanzure idafite urwego rwinshi (sisitemu ihoraho) muri sisitemu y'ubwisanzure idafite urwego rwinshi (sisitemu ihoraho). Hari ubwoko bubiri bw'uburyo bwa discretization bukoreshwa cyane mu gusesengura injeniyeri: uburyo bwa finite element na modal synthesis method.
ISHUSHO YA 9 uburyo bw'imigozi
ISHUSHO YA 10: Uburyo bw'icyuma gikikije
Uburyo bw'ibintu birangira ni imiterere ihuriweho ihuza imiterere igoye mu mubare ntarengwa w'ibintu hanyuma ikabihuza ku mubare ntarengwa w'ibintu. Buri gice ni elastomer; Ihererekanya ry'ibintu rigaragazwa n'imikorere yo gushyira hamwe kw'ibintu. Hanyuma ibipimo by'ihererekanya rya buri kintu bihurizwa kuri buri node mu buryo runaka, hanyuma hakaboneka icyitegererezo cya mekanike cya sisitemu itandukanye.
Uburyo bwo guhuza ibintu ni ugusenya imiterere y’imiterere igoye mu miterere myinshi yoroshye. Hashingiwe ku gusobanukirwa imiterere y’imitingito ya buri miterere, imiterere y’imiterere y’imiterere y’imiterere rusange hakurikijwe imiterere y’imikoranire ku buryo bwo guhuza ibintu, kandi imiterere y’imitingito y’imiterere rusange iboneka hakoreshejwe imiterere y’imitingito ya buri miterere.
Ubwo buryo bubiri buratandukanye kandi bufitanye isano, kandi bushobora gukoreshwa nk'icyitegererezo. Uburyo bwo guhuza modal bushobora kandi guhuzwa neza n'igipimo cy'igerageza kugira ngo habeho uburyo bwo gusesengura inyigisho n'igerageza kugira ngo habeho uburyo bwo gusesengura ibintu binini bihindagurika.
Igihe cyo kohereza: Mata-03-2020
