"I-Blade Runner", "Con Air", "Imvula enkulu" - yintoni abafana ngayo aba bameli benkcubeko eyaziwayo? Zonke, ukuya kwinqanaba elithile okanye kwelinye, zibonisa ubugcisa bamandulo baseJapan bokusonga iphepha - i-origami. Kwiifilimu, imidlalo kunye nobomi bokwenyani, i-origami idla ngokusetyenziswa njengesimboli seemvakalelo ezithile, ezinye iinkumbulo okanye umyalezo okhethekileyo. Oku kungaphezulu kwecandelo leemvakalelo ze-origami, kodwa kwimbono yesayensi, iinkalo ezininzi ezinomdla ezivela kwiindawo ezahlukeneyo zifihliwe kumanani ephepha: ijometri, imathematika kunye ne-mechanics. Namhlanje siza kuqhelana nesifundo apho izazinzulu ezivela kwi-American Institute of Physics zenza isixhobo sokugcina idatha ngokugoqa / ukutyhila amanani e-origami. Isebenza njani imemori khadi yephepha, yeyiphi imigaqo ephunyeziweyo kuyo, kwaye ingakanani idatha enokugcinwa kweso sixhobo? Iimpendulo zale mibuzo siza kuzifumana kwingxelo yezazinzulu. Hamba.
Isiseko sophando
Kunzima ukuchaza ukuba i-origami yaqala nini kanye. Kodwa siyazi ngokuqinisekileyo ukuba akukho ngaphambili kwe-105 AD. Kwakulo nyaka apho uCai Lun wenza iphepha eTshayina. Kakade ke, ngaphambi kwalo mzuzu, iphepha sele likhona, kodwa alizange lenziwe ngamaplanga, kodwa ukusuka kwi-bamboo okanye isilika. Indlela yokuqala yayingelula, yaye eyesibini yayixabisa kakhulu. UCai Lun wanikwa uxanduva lokuza neresiphi entsha yephepha eliza kuba khaphukhaphu, lingabizi mali ininzi, kwaye kube lula ukulenza. Umsebenzi awulula, kodwa uCai Lun waphendukela kumthombo odumileyo wokuphefumlelwa - indalo. Kangangexesha elide wayebona oonomeva, abamakhaya abo enziwe ngamaplanga nemicu yezityalo. U-Tsai Lun wenza iimvavanyo ezininzi apho wasebenzisa izinto ezahlukeneyo kwiphepha elizayo (ixolo lomthi, umlotha kunye neminatha yokuloba) exutywe namanzi. Ubunzima obubangelwa bubekwe kwifom ekhethekileyo kwaye yomiswa elangeni. Isiphumo salo msebenzi mkhulukazi yaba yinto eyiprosaic kumntu wanamhlanje - iphepha.
Ngo-2001, ipaki ebizwa ngokuba yiCai Lun yavulwa kwisixeko saseLeiyang (eChina).
Ukusasazeka kwephepha kwamanye amazwe akuzange kwenzeke ngokukhawuleza; kuphela ekuqaleni kwekhulu le-7 iresiphi yayo yafika eKorea naseJapan, kwaye iphepha lafika eYurophu kuphela ngekhulu le-11-12.
Eyona nto icacileyo yokusetyenziswa kwephepha, kunjalo, yimibhalo-ngqangi kunye nokushicilela. Nangona kunjalo, amaJapan afumana ukusetyenziswa okuhle kakhulu kuyo - i-origami, i.e. imifanekiso yamaphepha asongayo.
Uhambo olufutshane kwihlabathi le-origami kunye nobunjineli.
Kukho iintlobo ezininzi zeenketho ze-origami, kunye nobuchule bokwenza: i-origami elula, kusudama (i-modular), ukugoqa okumanzi, i-origami iphethini, i-kirigami, njl. ()
Ukususela kumbono wesayensi, i-origami yi-metamaterial yomatshini, iipropati ezichongwa yijometri yayo, kwaye kungekhona ngeempawu zezinto ezivela kuyo. Kuye kwaboniswa ixesha elide ukuba izakhiwo ze-3D ezinokusebenziseka ngeendlela ezininzi ezineempawu ezizodwa zinokudalwa kusetyenziswa iipateni eziphindaphindiweyo ze-origami.
Umfanekiso #1
Kumfanekiso 1b ibonisa umzekelo wolwakhiwo olunjalo-imvulo enokubekelwa bucala, eyakhiwe kwiphepha elinye lephepha ngokomzobo 1. Ukusuka kwiinketho ezikhoyo ze-origami, izazinzulu ziye zachonga ukuhluka apho i-mosaic yeepaneli ze-triangular ezifanayo ezihlelwe kwi-cyclic symmetry, eyaziwa ngokuba yi-Kroesling origami, iphunyezwa.
Kubalulekile ukuba uqaphele ukuba izakhiwo ezisekelwe kwi-origami ziza kwiindidi ezimbini: eziqinileyo nezingaqinanga.
I-origid origami yisakhiwo esine-dimensional ezintathu apho kuphela iifolthi phakathi kweepaneli zihamba nge-deformation ngexesha lokutyhila.
Umzekelo ophawulekayo we-origami ye-origid yi-Miura-ori, esetyenziselwa ukudala i-metamaterials ye-mechanical kunye ne-negative ye-Poisson's ratio. Izinto ezinjalo zinoluhlu olubanzi lwezicelo: ukuhlola indawo, i-electronics deformable, izihlunu ezenziweyo kwaye, ngokuqinisekileyo, i-metamatadium enokuphinda ilungiswe.
I-origami engeyiyo i-origid origami yizakhiwo ezintathu-dimensional ezibonisa i-deformation engaguqukiyo i-elastic deformation yeepaneli phakathi kwee-folds ngexesha lokutyhila.
Umzekelo wenguqu enjalo ye-origami yindlela ekhankanywe ngaphambili ye-Kroesling, esetyenziswe ngempumelelo ekudaleni izakhiwo ezinobunzima obuzinzileyo, ukuqina, ukuguqulwa, ukuthambisa / ukuqina, kunye / okanye ukuqina kwe-zero.
Iziphumo zophando
Ephefumlelwe ubugcisa bamandulo, izazinzulu zagqiba ekubeni zisebenzise i-origami ye-Kroesling ukuphuhlisa i-cluster ye-binary switches yokutshintshela umatshini onokunyanzeliswa ukuba utshintshe phakathi kwamazwe amabini ahlukeneyo ahlukeneyo usebenzisa igalelo elilawulwayo elilodwa ngendlela yokuvuselela i-harmonic esetyenziswa kwisiseko sokutshintsha. .
Njengoko kubonwe kwi 1b, i-bellows igxininiswe kwelinye icala kwaye ixhomekeke kumthwalo wangaphandle kwicala le-x kwelinye isiphelo samahhala. Ngenxa yoku, ityhutyha ngaxeshanye kwaye ijikelezwe ecaleni kwe-x-axis. Amandla aqokelelwe ngexesha lokuguqulwa kwe-bellows akhululwa xa umthwalo wangaphandle ususiwe, obangela ukuba i-bellows ibuyele kwisimo sayo sokuqala.
Ukubeka nje ngokulula, sijonge kumthombo we-torsion amandla awo okubuyisela axhomekeke kubume bomsebenzi wamandla anokubakho we-bellows. Oku ke kuxhomekeke kwiparameters zejiyometri (a0, b0, γ0) zikanxantathu oyintlanganisela osetyenziswayo ukwenza imivundu, kunye nenani lilonke (n) labanxantathu (1).
Kudibaniso oluthile lweparameters zoyilo lwejometri, i-bellows enokubakho umsebenzi wamandla inobuncinane obunye obuhambelana nendawo enye ezinzileyo yokulingana. Kwezinye iindibaniselwano, umsebenzi onokwenzeka wamandla uneminima emibini ehambelana nolungelelwaniso lwemivumbo emibini ezinzileyo, nganye idityaniswe nobude obulinganayo bokulingana okanye, ngenye indlela, ukuphambuka kwentwasahlobo (1s). Olu hlobo lwentwasahlobo luhlala lubizwa ngokuba yi-bistable (ividiyo engezantsi).
Kumfanekiso 1d ibonisa iiparitha zejometri ezikhokelela ekubunjweni kwentwasahlobo ye-bistable kunye neeparitha ezikhokelela ekubunjweni kwentwasahlobo ye-monostable ye-n = 12.
Intwasahlobo ye-bistable inokumisa kwenye yeendawo zayo zokulinganisa ngokungabikho kwemithwalo yangaphandle kwaye inokuvulwa ukuba itshintshe phakathi kwabo xa umthamo ofanelekileyo wamandla ukhona. Yile propati isiseko solu phononongo, oluphonononga ukudalwa kwe-Kroesling mechanical switches (KIMS ukusuka I-Kresling-ephefumlelweyo yokutshintsha oomatshini) ngeemeko ezimbini zokubini.
Ngokukodwa, njengoko kubonisiwe kwi 1c, ukutshintshwa kunokwenziwa kusebenze kwinguqu phakathi kwamazwe ayo amabini ngokunikezela amandla okwaneleyo ukunqoba umqobo onokuthi uphumelele (∆E). Amandla anokunikezelwa ngendlela yokucotha i-quasi-static actuation okanye ngokusebenzisa umqondiso we-harmonic kwisiseko sotshintshi kunye ne-excitation frequency kufuphi ne-resonant frequency ye-resonant yendawo yokutshintsha kwiindawo ezahlukeneyo zokulingana. Kolu phononongo, kwagqitywa ekubeni kusetyenziswe ukhetho lwesibini, ekubeni ukusebenza kwe-harmonic resonant kuphezulu kune-quasi-static operation kwezinye iinkalo.
Okokuqala, i-resonant actuation ifuna amandla amancinci okutshintsha kwaye ikhawuleza ngokubanzi. Okwesibini, ukutshintshwa kwe-resonant akukhathaleli ukuphazamiseka kwangaphandle okungahambelani nokutshintsha kwiindawo zayo zendawo. Okwesithathu, ekubeni umsebenzi onokuthi utshintshe udla ngokungafaniyo ngokubhekiselele kwindawo engazinzanga ye-equilibrium point U0, iimpawu zokuvuselela i-harmonic ezifunekayo ekutshintsheni ukusuka kwi-S0 ukuya kwi-S1 zihlala zihluke kwezo zifunekayo ekutshintsheni ukusuka kwi-S1 ukuya kwi-S0, okukhokelela ekubeni kunokwenzeka imincili-ekhetha ukutshintshela kokubini .
Olu qwalaselo lwe-KIMS lufanelekile ekudaleni ibhodi yememori yee-bit ezininzi usebenzisa iiswitshi ezininzi zokubini ezineempawu ezahlukeneyo ezibekwe kwiqonga elinye eliqhutywa yi-harmonic. Ukwenziwa kwesixhobo esinjalo kungenxa yovakalelo lobume bomsebenzi wamandla onokuthi utshintshe utshintsho kwiiparamitha zejometri zepaneli eziphambili (1s).
Ngenxa yoko, i-KIMS ezininzi ezineempawu zokuyila ezahlukeneyo zinokufakwa kwiqonga elifanayo kwaye zivuyiswe ukuguquka ukusuka kwelinye ilizwe ukuya kwelinye, ngabanye okanye ngokudibanisa usebenzisa iiseti ezahlukeneyo zeeparameters zokuvuselela.
Kwinqanaba lovavanyo olusebenzayo, utshintsho lwenziwe kwiphepha elinobuninzi be-180 g / m2 kunye neeparitha zejometri: γ0 = 26.5 °; b0/a0 = 1.68; a0 = 40 mm kunye n = 12. Ezi zi parameters, ukugweba ngezibalo (1d), kwaye ikhokelela ekubeni intwasahlobo ibe yi-bistable. Ubalo lwenziwa kusetyenziswa imodeli elula ye-axial truss (isakhiwo sentonga) ye-bellows.
Kusetyenziswa i-laser, imigca enemingxuma yenziwa ephepheni (1), ziindawo ezisongayo. Iifolthi zenziwa ecaleni kwemiphetho b0 (igophe ngaphandle) kunye no-γ0 (igophe ngaphakathi), kwaye imiphetho yeephelo ezikude zadityaniswa ngokuqinileyo. Umphezulu kunye nomgangatho ophantsi wokutshintsha uqiniswe ngeepoligoni ze-acrylic.
I-curve yamandla yokubuyisela yokutshintsha yafunyanwa ngovavanyo ngokunyanzeliswa kunye neemvavanyo ze-tensile ezenziwe kumatshini wokuvavanya jikelele kunye nokusekwa okukhethekileyo okuvumela ukuba isiseko sijikelezwe ngexesha lovavanyo (1f).
Iziphelo ze-acrylic switch zepolygon zazigxininiswe ngokungqongqo, kwaye ukufuduswa okulawulwayo kusetyenziswe kwipolygon ephezulu kwisantya esijoliswe kuyo se-0.1 mm / s. Ukufuduswa kwe-tensile kunye noxinzelelo kusetyenziswe umjikelo kwaye kunqunyelwe kwi-13 mm. Ngaphambi nje kovavanyo lwangempela lwesixhobo, iswitshi ihlengahlengiswa ngokwenza imijikelo yomthwalo enjalo elishumi phambi kokuba amandla okubuyisela abhalwe kusetyenziswa iseli yomthwalo we-50N. Vula 1g ibonisa amandla okubuyisela igophe lotshintsho olufunyenwe ngokomfuniselo.
Okulandelayo, ngokudibanisa umndilili wokubuyisela amandla okutshintsha ngaphezulu koluhlu lokusebenza, umsebenzi onokwenzeka wamandla (1h). Ubuncinci bokusebenza kwamandla obunokubakho bumele ukulingana okumileyo okuhambelana neemeko ezimbini zokutshintsha (i-S0 kunye ne-S1). Ngolu lungelelwaniso oluthile, i-S0 kunye ne-S1 zenzeke kwiindawo eziphakamileyo zokuthunyelwa u = 48 mm kunye ne-58.5 mm, ngokulandelanayo. Umsebenzi wamandla onokubakho ngokucacileyo u-asymmetric kunye nezithintelo zamandla ezahlukeneyo ∆E0 kwindawo ye-S0 kunye ne-E1 kwindawo ye-S1.
Ukutshintsha kwafakwa kwi-shaker ye-electrodynamic, ebonelela ngokuvuselela okulawulwayo kwesiseko kwicala le-axial. Ekuphenduleni ukuvuselela, indawo ephezulu yokutshintsha i-oscillates kwicala elithe nkqo. Isikhundla somphezulu wokutshintsha ngokumalunga nesiseko salinganiswa kusetyenziswa i-laser vibrometer (2).
Umfanekiso #2
Kwafunyaniswa ukuba i-resonant frequency yendawo yokutshintshela kumazwe ayo amabini yi-11.8 Hz ye-S0 kunye ne-9.7 Hz ye-S1. Ukuqalisa inguqu phakathi kwamazwe amabini, oko kukuthi, phuma inokwenzeka kakuhle*, Ukucotha kakhulu (0.05 Hz / s) ukutshayela i-directional linear frequency sweep kwenziwa malunga nee-frequencies ezichongiweyo kunye ne-base acceleration ye-13 ms-2. Ngokukodwa, i-KIMS yayibekwe ekuqaleni kwi-S0 kwaye ukunyuka kwamaxesha okutshayela kwaqaliswa kwi-6 Hz.
Inokwenzeka kakuhle* - ummandla apho kukho ubuncinci bendawo bamandla anokubakho esuntswana.
Njengoko kubonwe ngaphambili 2bXa i-frequency yokuqhuba ifikelela malunga ne-7.8 Hz, iswitshi ishiya i-S0 enokwenzeka kakuhle kwaye ingena kwi-S1 enokubakho kakuhle. Ukutshintsha kwaqhubeka kuhlala kwi-S1 njengoko i-frequency yanda ngakumbi.
Umtshintshi waphinda wamiselwa kwi-S0 kwakhona, kodwa ngeli xesha ukwehla kwaqaliswa kwi-16 Hz. Kule meko, xa i-frequency isondela kwi-8.8 Hz, i-switch ishiya i-S0 kwaye ingene kwaye ihlale kwindawo enokubakho i-S1.
I-State S0 inebhendi yokuvula ye-1 Hz [7.8, 8.8] kunye nokukhawuleza kwe-13 ms-2, kunye ne-S1 - 6...7.7 Hz (2s). Oku kulandela ukuba i-KIMS inokutshintsha ngokukhethayo phakathi kwamazwe amabini ngokusebenzisa i-harmonic excitation yesiseko sobukhulu obufanayo kodwa i-frequency eyahlukileyo.
I-bandwidth yokutshintsha kwe-KIMS inokuxhomekeka okuyinkimbinkimbi kwimilo yemisebenzi yayo yamandla enokubakho, iimpawu zokudambisa, kunye neeparitha ze-harmonic excitation (i-frequency kunye nobukhulu). Ukongezelela, ngenxa yokuthomalalisa ukuziphatha okungaqhelekanga kokutshintsha, i-bandwidth yokuvula ayibandakanyi i-resonant frequency. Ngoko ke, kubalulekile ukuba imephu yokuvula inguqu yenzelwe i-KIMS nganye. Le mephu isetyenziselwa ukubonisa ukuphindaphinda kunye nobukhulu bovuselelo olukhokelela ekutshintsheni ukusuka kwelinye ilizwe ukuya kwelinye kwaye ngokuphambeneyo.
Imephu enjalo inokudalwa ngokomfuniselo ngokutshayela rhoqo kumanqanaba ahlukeneyo ovuselelo, kodwa le nkqubo inzima kakhulu. Ke ngoko, izazinzulu zagqiba kweli nqanaba ukuba ziqhubele phambili kwimodeli yokutshintsha, zisebenzisa amandla anokuthi amiselwe ngexesha lovavanyo (1h).
Imodeli ithatha ukuba ukuziphatha okuguquguqukayo kokutshintsha kunokuqikelelwa kakuhle yi-dynamics ye-asymmetric bistable Helmholtz-Duffing oscillator, i-equation yentshukumo enokuthi iboniswe ngolu hlobo lulandelayo:
apho u - ukuphambuka kobuso obushukumayo bepolygoni ye-acrylic xa kuthelekiswa nesigxina; m - ubunzima obusebenzayo bokutshintsha; c — i-viscous damping coefficient imiselwe ngokomfuniselo; i-ais-i-bistable yokubuyisela amandla e-coefficients; u-ab kunye no-Ω bubukhulu besiseko kunye nobuninzi bokukhawuleza.
Owona msebenzi wokulinganisa kukusebenzisa le fomyula ukuseka indibaniselwano ye-ab kunye no-Ω evumela ukutshintsha phakathi kweemeko ezimbini ezahlukeneyo.
Izazinzulu ziqaphela ukuba i-excitation frequencies apho i-oscillator ye-bistable itshintsha ukusuka kwelinye ilizwe ukuya kwelinye inokuqikelelwa ngamaza amabini. ii-bifurations*: ixesha lokuphinda kabini i-bifurcation (PD) kunye ne-cyclic fold bifurcation (CF).
I-Bifurcation* - utshintsho olusemgangathweni lwenkqubo ngokutshintsha iiparamitha exhomekeke kuyo.
Ukusebenzisa i-approximation, i-frequency response curves ye-KIMS yakhiwa kwiindawo zayo ezimbini. Kwitshathi 2s ibonisa iijika zokuphendula rhoqo zokutshintsha kwi-S0 kumanqanaba amabini ahlukeneyo okukhawulezisa isiseko.
Kwisiseko sokunyuka kwe-5 ms-2, i-curve ye-amplitude-frequency ibonisa ukuthambisa okuncinci, kodwa akukho ukungazinzi okanye i-bifurcations. Ke, utshintsho luhlala lukwimeko ye-S0 kungakhathaliseki ukuba i-frequency itshintsha njani.
Nangona kunjalo, xa ukukhawuleza kwesiseko kunyuswa ukuya kwi-13 ms-2, ukuzinza kuyancipha ngenxa ye-PD bifurcation njengoko i-frequency yokuqhuba iyancipha.
Ukusebenzisa iskimu esifanayo, iijika zokuphendula rhoqo zokutshintsha kwi-S1 zifunyenwe (2f). Kwi-acceleration ye-5 ms-2, iphethini ephawulweyo ihlala ifana. Nangona kunjalo, njengoko ukukhawuleziswa kwesiseko kunyuka ukuya kwi-10ms-2 I-PD kunye ne-CF bifurcation ziyavela. Ukutshintsha okuvuyisayo nangaliphi na ixesha phakathi kwezi zibini ze-bifurcations kubangela utshintsho ukusuka kwi-S1 ukuya kwi-S0.
Idatha yokulinganisa iphakamisa ukuba kukho imimandla emikhulu kwimephu yokuvula apho urhulumente ngamnye unokusebenza ngendlela ekhethekileyo. Oku kukuvumela ukuba utshintshe ngokukhethayo phakathi kweemeko ezimbini ngokuxhomekeke kubuninzi kunye nobukhulu be-trigger. Kwakhona kunokubonwa ukuba kukho indawo apho zombini amazwe angatshintsha ngaxeshanye.
Umfanekiso #3
Indibaniselwano yee-KIMS ezininzi zingasetyenziswa ukwenza inkumbulo yomatshini wamasuntswana amaninzi. Ngokutshintsha ijiyometri yokutshintsha ukwenzela ukuba ubume bomsebenzi wamandla obunokubakho kuzo naziphi na iitshintshi ezimbini zihluke ngokwaneleyo, kunokwenzeka ukuyila i-activation bandwidth yokutshintsha ukuze bangadlulanga. Ngenxa yoku, utshintsho ngalunye luya kuba neeparamitha zokuvuselela ezizodwa.
Ukubonisa obu buchule, ibhodi ye-2-bit yenziwe ngokusekelwe kwiiswitshi ezimbini ezineempawu ezahlukeneyo ezinokubakho (3): bit 1 - γ0 = 28 °; b0/a0 = 1.5; a0 = 40 mm kunye n = 12; bit 2 - γ0 = 27 °; b0/a0 = 1.7; a0 = 40 mm kunye n = 12.
Kuba isuntswana ngalinye linamazwe amabini, iyonke yamazwe amane awohlukeneyo S00, S01, S10 kunye ne-S11 inokufezekiswa (3b). Amanani emva kuka-S abonisa ixabiso leetshintshi zekhohlo (bit 1) nasekunene (bit 2).
Ukuziphatha kokutshintsha kwe-2-bit kuboniswe kwividiyo engezantsi:
Ngokusekelwe kwesi sixhobo, unokwenza kwakhona iqela lokutshintsha, elinokuthi libe sisiseko seebhodi zememori ze-multi-bit.
Ukuze ufumane ulwazi oluthe kratya malunga nee-nuances zophononongo, ndincoma ukujonga и kuye.
Ipilo
Akunakwenzeka ukuba nabani na wabadali be-origami banokucinga ukuba indalo yabo iya kusetyenziswa njani kwihlabathi lanamhlanje. Ngakolunye uhlangothi, oku kubonisa inani elikhulu lezinto ezinzima ezifihliweyo kwimifanekiso yephepha eqhelekileyo; kwelinye icala, ukuba inzululwazi yale mihla iyakwazi ukusebenzisa ezi zinto ukwenza into entsha ngokupheleleyo.
Kulo msebenzi, izazinzulu ziye zakwazi ukusebenzisa i-origami yejometri ye-Kroesling ukwenza i-switch ye-mechanical elula enokuthi ibe kumazwe amabini ahlukeneyo, kuxhomekeke kwiiparitha zokufaka. Oku kunokuthelekiswa no-0 no-1, eziziiyunithi zakudala zolwazi.
Izixhobo ezibangelwayo zidityaniswe kwinkqubo yememori yomatshini ekwazi ukugcina iibhithi ezi-2. Ukwazi ukuba unobumba omnye uthatha i-8 bits (1 byte), umbuzo uvela: zingaphi i-origami efanayo eya kufuneka ukuba ubhale "Imfazwe noxolo," umzekelo.
Izazinzulu zikuqonda kakuhle ukuthandabuza okunokubangelwa luphuhliso lwabo. Nangona kunjalo, ngokutsho kwabo, olu phando luphononongo kwicandelo lememori yomatshini. Ukongezelela, i-origami esetyenziswe kwiimvavanyo akufanele ibe nkulu;
Kungakhathaliseki ukuba kunjalo, lo msebenzi awukwazi ukubizwa ngokuba yinto eqhelekileyo, i-banal okanye i-boring. Inzululwazi ayisoloko isetyenziselwa ukuphuhlisa into ethile, kwaye izazinzulu azisoloko zisazi ukuba yintoni kanye kanye eziyidalayo. Emva kwayo yonke loo nto, uninzi lwezinto eziqanjiweyo kunye nezinto ezifunyenweyo ziziphumo zombuzo olula - kuthekani ukuba?
Enkosi ngokufunda, hlala unomdla kwaye ube nempelaveki emnandi bafana! 🙂
Intengiso encinci
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