ANNAS OF THE UNIVESITY OF AIOVA ANNAES DE UNIVESITÉ DE AIOVA ANAEE UNIVESITĂŢII DIN AIOVA SEIA: ININEIE EETIĂ SEIE: EETIA ENINEEIN SÉIE: INÉNIEIE ÉETIQUE A/Yea/Aée 9 No. 9, Vo. 9, Ie, 5 Decembe 5 ISSN 8-85 EDITUA UNIVESITAIA
ANNAS OF THE UNIVESITY OF AIOVA, A.I. za S., AIOVA 585 OMANIA We echage bcao wh ma o of coy ad fom aboad ANNAES DE UNIVESITÉ DE AIOVA e A.I. za, No., AIOVA 585 OUMANIE O fa de échage de bcao avec e o mae d ay e de éage Th joa bhed by he Facy of Eecca Egeeg fom he Uvey of aova. The aho ae fy eobe fo he ogay of he ae ad fo accacy of he oe. Th vome ha beefed by he faca o of he Aocao fo So of Egeeg Edcao. Edoa boad Pof. Ioa POPA edo chef, Uvey of aova, omaa Aoc. of. Mcea DIHIIU - edo chef, Uvey of aova, omaa Pof. Da MIHAI, Uvey of aova, omaa Pof. Maa IONTU, Uvey of aova, omaa Pof. Seg IVANOV, Uvey of aova, omaa Pof. ca MANDAHE, Uvey of aova, omaa Pof. Iva YAHEV, Techca Uvey of Sofa, Bgaa Pof. Savojb AESI, Uvey of Nš, Seba Pof. Segey YVIN, oo Ie, V.I.Taezov, a Pof. Mha IODAHE, Uvey Poehca of Bchae, omaa Pof. Vco SONTEA, Techca Uvey of Modova, ebc of Modova Pof. I DEESEA, Uvey Poehca of Tmoaa, omaa Pof. Dm-Mace ISTATE, Techca Uvey h. Aach, Ia, omaa Pof. Ncoae MUNTEAN, Uvey Poehca of Tmoaa, omaa Pof. a MUNTEANU, Techca Uvey of j-naoca, omaa ece Ioaa abea SÎBU, Uvey of aova, omaa II
EVIEWES OMMITTEE Mace ADAM "h. Aach" Techca Uvey of Ia, omaa Mhaea ABU Uvey Poehca of Bchae, omaa Savojb AESI Uvey of N, Seba Hoa BAAN Techca Uvey of j-naoca, omaa heoghe BAUTA "h. Aach" Techca Uvey of Ia, omaa Maa BOJBOIU Uvey of aova, omaa Ae AMPEANU Uvey of aova, omaa Em AZAU Uvey Poehca of Bchae, omaa Mha ENAT Tavaa Uvey of Baov, omaa Maa IONTU Uvey of aova, omaa Dae a ISMAU Uvey of aova, omaa goe IVIDJIAN Uvey of aova, omaa Zaa VETOVI Uvey of N, Seba Daea DANIU Uvey of aova, omaa Soa DEEATU Uvey of aova, omaa I DEESEA Uvey Poehca of Tmoaa, omaa Sva-Maa DIA Uvey of aova, omaa Pee DINEFF Techca Uvey of Sofa, Bgaa ad DOBESU Uvey Poehca of Bchae, omaa Mcea-Ada DIHIIU Uvey of aova, omaa ae Ma DUMITAN Uvey Poehca of Bchae, omaa So ENAHE Uvey of aova, omaa Vg FIETEANU Uvey Poehca of Bchae, omaa Da FOIAU Uvey Poehca of Bchae, omaa a FOSAAU "h. Aach" Techca Uvey of Ia, omaa Teodo ca IOIE Uvey of aova, omaa Mcea-Da USA "h. Aach" Techca Uvey of Ia, omaa Sefa HAAUS Uvey Poehca of Tmoaa, omaa Eea HEEEA Tavaa Uvey of Baov, omaa Ege HNATIU "h. Aach" Techca Uvey of Ia, omaa ema HOT Poyechc of Zageb, oaa Ege IANU Uvey of aova, omaa Naha IDA Uvey of Ao, USA Maa IOANNIDES Naoa Techca Uvey of Ahe, eece Vae IONITA Uvey Poehca of Bchae, omaa Mha IODAHE Uvey Poehca of Bchae, omaa Mace ISTATE "h. Aach" Techca Uvey of Ia, omaa Seg IVANOV Uvey of aova, omaa Vga IVANOV Uvey of aova, omaa Whem APPE Naoa eeach ad Deveome Ie fo Eecca Egeeg (IPE A) Bchae, omaa v EINDE Uvey Poehca of Bchae, omaa heoghe IVINT "h. Aach" Techca Uvey of Ia, omaa Dm Do UAHE "h. Aach" Techca Uvey of Ia, omaa ca MANDAHE Uvey of aova, omaa eoado-eo MANESU Uvey of aova, omaa heoghe MANOEA Uvey of aova, omaa III
Ade MAINESU eeach, Deveome ad Teg Naoa Ie fo Eecca Egeeg aova (IMET), omaa Iaa MAINOVA Techca Uvey of Sofa, Bgaa ada MATIS Techca Uvey of j-naoca, omaa Ee MATANE Uveé ahoqe de ova, Begm Da MIHAI Uvey of aova, omaa Aead MOEA Uvey Poehca of Bchae, omaa Mhaea MOEA Uvey Poehca of Bchae, omaa Nazh MOUBAYED ebaee Uvey, ebao a MUNTEANU Techca Uvey of j-naoca, omaa Fo MUNTEANU "h. Aach" Techca Uvey of Ia, omaa Vae NAVAPESU Uvey Poehca of Bchae, omaa Mca Ia NEAĂ Uvey of aova, omaa a NEMES "h. Aach" Techca Uvey of Ia, omaa Pee-Maa NIOAE Uvey of aova, omaa Pe NOTINHE Uvey Poehca of Bchae, omaa Vae NUTU May Techca Academy, omaa Teodo PANA Techca Uvey of j-naoca, omaa Ioa POPA Uvey of aova, omaa Da POPESU Uvey of aova, omaa Daea POPESU Uvey of aova, omaa Mhaea POPESU Uvey of aova, omaa Moav PSA Uvey of Nov-Sad, Seba Mcea M. ADUESU Techca Uvey of j Naoca, omaa Beo OBYNS Ecoe de Hae Ede d Igée de e, Face oa OTAU May Techca Academy, omaa Ae UDEMAN Emo Moo oo d, USA Segey YVIN Taezov Ie of oo Scece, a Aead SAEANU "h. Aach" Techca Uvey of Ia, omaa a abea SAAIN Uvey Poehca of Bchae, omaa oa SAMASANU "h. Aach" Techca Uvey of Ia, omaa Da SEISTEANU Uvey of aova, omaa Vco SONTEA Techca Uvey of Modova, Modova Aead STANU "A.I. za" Uvey of Ia, omaa Foa STEFANESU Uvey of aova, omaa Voe STOIAN Uvey of aova, omaa yzad STZEEI Uvey of Techoogy da, Poad Fav-Da SUIANU Uvey Poehca of Tmoaa, omaa oad SZABO Techca Uvey of j-naoca, omaa ad-ada TINOVAN Techca Uvey of j-naoca, omaa aa TZENEVA Techca Uvey of Sofa, Bgaa Ioa VADAN Techca Uvey of j-naoca, omaa Voe VAVAA "h. Aach" Techca Uvey of Ia, omaa Io VAD Uvey of aova, omaa Iva YATHEV Techca Uvey of Sofa, Bgaa IV
Aa of he Uvey of aova, Eecca Egeeg ee, No. 9, 5 ISSN 8-85 Modeg of Tafome Wdg ad omao of Vey Fa Tae Ove-Voage oa mbea *, So Deea, Mha Iodache *, a ea *, Neca aa *, Ao Aaae Moc * * Poehca Uvey of Bchae, Eecca Deame, S. Ideedee, 6 - Bchae, omaa, goa.gmbea@b.o, mha.odache@b.o,cacea@yahoo.com, ca.gaa@b.o, aa.o@gma.com Nohe Abea Ie of Techoogy, 76-6 See NW, Edmoo, aada, od@a.ca Abac - The ma objecve of h ae eeeed by aay ad modeg of he afome wdg eed by ove-voage wh dec mac o voage dbo aco he wdg. The aho codeed boh aoache modeg he wdg: wdg wh dbed eecca aamee eecvey comoed fom d co wh coceaed aamee. Boh ye of voage aed aco he afome wdg w geeae fee ocao whch ae aayzed fhe o. Accodg o he mode, he afome wdg ae dvded evea d co wh coceaed ow aamee. Th e a comee eecca ewo ed fo mao. A mao have bee efomed g he ofwae acage SYSE (SYmboc Sae Eqao eeao). eywod: afome, ove-voage, modeg, d co, mao, eoace, egevae. I. INTODUTION Whe codeg he me vaao oe ca cafy he ove-voage a fa ae (FTO), eecvey vey fa ae (VFTO). The ove-voage aco he afome wdg ca be ggeed by eea (amohec eecca dchage he eghbohood of he aao coag he afome o eve oo ) o ea (commao foowg coeco/ dcoeco ocede he aao coag e ad afome, fa ae heomea, fay ao ec.) cae. Two ye of ove-voage ae ae o codeao: aeodc e of ho dao, eecvey eodc wavefom avaabe, [-, ]. Boh have magde whch ca gfcay eceed he aed voage vae of he afome. The ocao of he ove-voage wavefom ae dageo de o he eoace heomeo ay ecoded fo fa ae. Th caed by he caacace ad dcve of ovea afome wdg. De o he fac ha fo hgh feqece he magec fed doe eeae he feomagec coe of he afome, he oy magec fed ae o codeao he eaage oe odced by he hgh voage wdg. Dee he fac ha he ae ee coeced, he ce hogh he ee wdg doe have he ame vae. Th fac eaed by he eece of he hee oca caaco fomed bewee he wdg ad he god, eecvey bewee he hgh voage wdg ad he adjace wdg. oeqey, he ace dbo of he magec fed become moe comcaed, [-, ]. II. MODEIN THE HIH VOTAE WINDIN OF THE TANSFOME FO OVE-VOTAES STUDY PUPOSES Mo of he de code wo caegoe of mode egadg he hgh voage wdg ove-voage e aay: a) The mode b wh he codeao of he e wh dbed aamee (ma o he og eecca e heoy) b) The mode baed o coceaed aamee. Each of he mode ha wo veo de o he fac ha he ea o of he wdg (wye-coeced) ehe oaed o coeced o he god. I em of he occece of hyca heomea he wdg, he acao he wo mode deve gfcay dffee e whe aayzg he dbo ad oagao of he ove-voage wavefom aco he wdg. I he ame me, he wo mode ea dffeey he heomeo of he ove-voage wavefom efeco a he bode bewee he wdg zoe whch ae chaacezed by dffee vae fo aamee. A. Modeg he Syem wh Dbed Paamee Fo he hee-haed afome wh dbed aamee, he vae of he caacace ad codcace bewee oe hae hgh voage wdg (AX) ad he ohe wo (BY, Z) ae codeed eggbe. The ooed eqvae cc fo he mode wh dbed aamee eeed Fg.. The oao fo he ecfc aamee e of egh ed fhe ae,,,, ad. Whe ayg he chhoff e aw () he ode a, a, foowed by he chhoff Voage aw aog he coed cc oo aa bb, oe ca oba he yem of eqao (). The oao fo he ecfc aamee e of egh ed fhe ae,,,, ad. Whe ayg he chhoff e aw () he ode a, a, foowed by he chhoff Voage aw aog he coed cc oo aa bb, oe ca oba he yem of eqao (). I eqao () he ymbo ad eee he voage, eecvey he ce a he dace fom he ema A ( cofomy wh he heoy of he og eecc e).
d Fg.. The eqvae cc fo he mode wh dbed aamee.. : ) ( : ) ( : ) ( d d d d d d d bb aa d d a a () I he yem (), whe devg wh eec o he vaabe ad bg he ce, oe ca oba a dffeea eqao wh aa devave () em of he voage.. 5 () The eqao () eee a eeo of he aeady ow eqao of he yem wh dbed aamee. Fo, ad he eqao () become:. () Whe he ea o coeced o he god, he eqao () ha he oo: ρ Γ,...,, co, U () whee:,,, Γ π ρ. Whe he ea o aed he eqao () ha he oo: ρ Γ,...,, co, U (5) Whe mog ad, he eqao () become he caca voage eqao of he og e, whe fo, eqao () ed o ove ad dy he ove-voage dbo aog aco he wdg of he afome. Deecc o, whch cao be egeced a hgh feqece, movae he eece of he ao codcace ad. Fo mfcao eao, we ve codeed. Whe ayg he aace Tafom fo eqao (), he voage eqao ehaed (6):. (6) Wh adeqae a codo () w oba he eqao (7):. λ λ (7) A geec oo of he eqao (6) gve he eao (8) by:. o h B ch A B e A e λ λ λ λ (8) The vae of he coa A ad B ae qey deemed fo bode codo ( ad ), whee he egh of he wdg. Eqao () fo ca be eeed me, ceae ad eae o e oe afomed eqao (9). Aa of he Uvey of aova, Eecca Egeeg ee, No. 9, 5 ISSN 8-85
Aa of he Uvey of aova, Eecca Egeeg ee, No. 9, 5 ISSN 8-85 ρ β ( ρ γ) ρ γ. The foowg oao cobed o he mfcao of he voage eqao fom above: β ρ. γ (9) () I ode o oba he oo of eqao (5) me doma, oe ca chooe cea ecazed ofwae acage(), o avaaby. Howeve, he eg meca mehod have he caaby of dec egao fo he eqao () o (9). The aho hghgh aohe ocede fo obag he oo of he eqao wh aa devave fo () whe. Th we-ow mehod of eaao of vaabe, whch amed a oo of he foowg ye: ( ) X T,. () Whe bg (8) he eqao wh aa devave (9), w e: X X " " " " T ρ X T β X T " X T () ( ρ γ) X T () X T " " X [ T () ρt () βt() ] " [ T () ( ρ γ) T () ρ T() ] " " X T () ( ρ γ) T () ρ T() " X T () ρt () βt() ρ c. () The eqao wh aa devave eqvae o wo dffeea eqao of ecod ode wh coa coeffce. Thee eqao ca be oved eaaey. The eqao wh he deede vaabe eqe bode codo, whe he oe wh deede vaabe eqe a codo. B. Modeg he Syem wh med Paamee Thee ae wo caegoe of cacao mode eaed he eae: ay Bo Mode ad Bac Bo Mode. ay Bo Mode ycay ed fo deg oe, whe dyg he afome wdg de he eoace codo, hghghg he voage dbo aco he wdg. Th mode co of a combao of adde Newo ad M-codco Tamo e Mode MT [-]. The adde Newo a mode whch,, ae coceaed aamee. Ia veo of he mode (baed o fa co ) had med feqecy age em of ohez whe he ee veo (baed o -by - ) ca offe modeg caabe he Fg.. The D o ad j fom he ewo []. age of megahez. The adde Mode he be choce whe vovg he ae dy de ovevoage codo. The ma eao eeeed by he obe of aembg vey accae ad come eqvae cc of he afome wdg. Howeve, fo hgh owe ag, hgh voage afome, modeg he afome wdg o -by- ba wh he oe of dyg he dbo of he ovevoage aco ca become cmbeome ad ee dffce o mae. Whe modeg he afome wdg, he d co ha a eqvae cc wh me ce ad aamee dayed Fg., [, ]. The bae eeme of he mode comoed by he d co wh a of he hee bache coeced aae wh he caacace wh eec o he god (accodg o Fg. ) See coeced eeme ad eee he eace, eecvey he dcace of he d co, whe he eqvae caacace bewee he co. The caaco ha deecc oe ymbozed hee by he eace. The oy ma dcve j accoed fo he mode ae hoe bewee wo co (I ad j fo eame), whe he ma dcve bewee he beogg o he ame co ae egeced. The ee mode ffe vey beefca mfcao h way. Whe ayg chhoff eqao oe ca oba he eqao fo ce, voage ad oeaoa medace efeg he N ode, aembed a ma fom. Sma mode ae cey ed fo he dy of he ove-voage a he ema of oaoa moo [5, 6].. Eecca Paamee Ued Modeg ad Sdyg he Ove-Voage Pheomea The owedge of eecca aamee e eace, codcvy, dcvy ad caacace, o a cea degee of accacy wa ove eea whe modeg he afome wh he oe of dyg he ovevoage. May ae fom he eae, foced o he oc of he ove-voage e of he afome wdg ae avaabe [7-], ad hey eee cea ad gfca cobo. Th eco dedcaed fhe o o moa eeme coceg he eecca aamee. I evey modeg ocede, eace, a aamee, m be evaaed cdg he comee effec whch occg a hgh feqece ad fo fa ae of he ce hogh codco. Whe he effec occ, he ce dbed owad he ode face of he codco, wh a deh of eeaoδ. The ecfc eace e of egh
Aa of he Uvey of aova, Eecca Egeeg ee, No. 9, 5 ISSN 8-85 of codco wh a abay choe ae gve by eaoh (). I he eeo () ρ he eecca evy, he magec emeaby (fo coe ), whe he emee of he codco. δ δ ρ δ δ π f σ ρ ω ρ σ π σ f () I he eeo () ρ he eecca evy, he magec emeaby (fo coe ), whe he emee of he codco. The codcvy of he ao maea deed o aga feqecy ω, caacace, ad he deecc o faco gδ z, ad ca be cacaed wh he eaoh () accodg o []. ω g δ π f g δ () Whe g a eg afome fo efomg ecfc me e, vaabe e become daa fo cacag he caacve eeme of he mode []. Whe owg he geomeca dmeo of he wdg, oe ca cacae he caacace g aayca e fo he ae o cydca caaco. Fo he afome wdg, he bgge chaege aea o be he cacao of ef ad ma dcace. Whe deemg he dcvy e of egh, hee ae wo comoe: oe eaed o he eea magec fed odg he codco e, he ohe oe o he magec fed de he codco. Fo he evaao of he comoe e, oe ca he oagao eed of he ove-voage wave, whch oagae hogh a deecc maea wh magec emeaby ad eecca emvy ε ε ε, (ε he eave emvy of he maea). The eave emvy of he maea modfe he vae of he caacace oy, whch ead o he foowg eaoh. I he eao (), he eed of gh deemed by he coa ad ε fo each geomec cofgao of he caaco, he caacace oooa o he emvy ε ε ε, o he caacace defed by he eaoh ε, whch he caacace of he maea wh emvy ε. v ε e ε c ε c ε z. (5) The caacace aea eavey eay o cacae ad mmedaey he dcvy e e fom (5). The cacao of he ea comoe of he dcvy eqe he e obaed whe codeg he eeao of he eecomagec fed de of he codcve em-ace. The codco a agh e, wh a cydca hae, he co-ecoa aea S. Whe he codo δ << S / ffed, he e -effec codo ffed. I cae of he ffme of he -effec codo, he wave medace ha he ea a eqa o magay oe (6). Z E H j ω. ω π f ω (6) Th mea ha fo a gve ao ω he dcvy deemed agh fom he eace. The oa dcvy come fom he addo of he eea ad ea dcve: e. I [9], he aho hghgh he fac ha he magec coe of he afome aembed fom amaed mea hee of aooc ye. Th mea ha he emeaby of he afome magec coe day dffee vae o dffee deco: aog he com z ad eedca o he com oe. III. ASSEMBIN THE TANSFOME WIDIN MODE FO OVE-VOTAE STESS STUDY The aoy egme ecoeed fo ove-voage codo eqe a aay whe g he adde Newo mode. The eecca ewo b- eqe he dvo deca d co. Hee, he aho codeed a cydca wdg, dvded d co wh coceaed aamee (Fg. ), [, ]. The mao aea decy o he chemac cc fom Fg. ad he e co of he me vaao of he voage aco he d co, aowg hyca eeao ad evaao. A. Smao egadg he Voage Dbo Aco he Tafome Wdg Whe g he ewo fom Fg., hee ae wo veo: oe wh a homogeeo wdg whch he eecca aamee ae he ame fo a d co ad oe o-homogeeo veo. I he ae, he co fom he begg of he wdg have efoced ao whch e a agmeed ace bewee he ad deceaed vae fo caacace. Fo homogeeo wdg cae, he eecc aamee have he foowg vae, gve by he eao (7): 7 6 9 5 8-6 H 5 8 7 6 5 - Ω 6 9 5 8 (7) 7 6 F 7 8 9 5 6 7 8 9 F. The vae have bee cacaed fom he geomeca dmeo of he afome havg he foowg daa: S 6 VA U h.5//9.5 V ad U. V. Fo he o-homogeeo wdg cae, he oy modfed vae fo caacace, 6 9 ae:
Aa of he Uvey of aova, Eecca Egeeg ee, No. 9, 5 ISSN 8-85 Fg.. adde Newo fo ove-voage dy whe he ea o ehe aed (oe beae) o coeced o he god (coed beae). 6 9 7 F. (8) The ohe aamee of he adde ewo (Fg. ) have he ame vae a he eeo (). B. The Deco of Pogam SYSE The SYSE ogam, [, 5], caabe of he ymboc, mec-ymboc, eecvey mec deco fo he ae eqao fo a boad ca of aaog cc ea ad/o oea. Whe efomg he edco ad mfcao of he eeo, he ae eqao ae coveed o a comac, ymboc fom. SYSE Pogam ca defy he eeme of he f ad ecod caegoy beg ece ad mae dco bewee he ye, [, 5]. Fhemoe, SYSE ha addoa caabe egadg he deveace of he mace coag: he ae eqao of he cc, he ecao ga, he devave of he ecao ga, he o ga. The SYSE ogam fay caabe of me doma aay of he cc whe owg dffee meca vae of o aamee. I he cae of he ea cc, he SYSE ogam geeae he ae eqao oeaoa fom ad he me doma aay ca be efomed g he vee aace afom, [, 5].. e Obaed Foowg he Ue of SYSE Pogam The ma objecve of he mao wa he evaao of me voage vaao fo, 6, 9 ad 6 (he voage aco he f hee d co o caacace eecvey aco he a oe fom he mode of Fg. hee ae he voage aco he caacace, 6, 9 ad 6 ) fo boh cae: homogeeo ad o-homogeeo afome wdg de ove-voage e. The commao ove-voage of oda ye, dffee fom zeo fo 5 cyce accodg o he eeo (6): π ω, e ω e (8) π > ω Aga feqecy ha wo vae: oe vae ω coed o he ao of fee ocao ω ad aohe oe, ω havg a way owe vae ha ω. De o he fac ha ω 8 ad/, he ao ae: ω 7 ad/ ad ω. 6 ad/. ) Sb-beco eame Fo ch a wdg, a of he d co have he ame eecc aamee. odeg he hae of he ove-voage e (8), he me doma of he vaao ha wo emaabe beva: [, ] ad [, ). Fo he f eva he a codo ae, whe fo he ecod o he foowg ema ae vad fo he ao ω : ω 7 ad/, -7, e.(ω ) V ad he a codo ae e ad a codo dffee fom zeo () (, -7 ) ae veco fom o ) ad ae veco fom o ). Smay, fo he ao ω : ω 6 ad/, -6, e.(ω ) V ad he a codo ae e ad he a codo dffee fom zeo () (, -6 ) ae veco fom o ) ad ae veco fom o ). The o fo he mao e ae he voage aco he caacace ad 6, whch mea aco he f d co ad he a oe fom he mode (Fg. ). The f bach of mao ae efomed wh eec o he ao of owe vae ω 6 ad/. ae A. Smao fo ao ω 6 ad/ Whe codeg he ao ω 6 ad/ (whch ha a mch owe vae ha he ao of fee ocao ω ), he me voage vaao fo oaed ea aea (Fg..a) eaaey fom he goded ea cae (Fg..b). Th voage wa fod aco he f co (Fg. ) hogh mao. Whe codeg he oaed ea, dg he eva ffg he codo e, he voage amde ae gfcay mae (amo haf) ha fo he ao whch he ea goded. oveey, fo e, day hghe vae fo oaed he wdg wh oaed ea comao o he ao whch he ea goded. Fg.. Tme vaao of he voage fo ω 6 ad/: a) wdg wh oaed ea b) wdg wh goded ea. (a) (b) 5
Aa of he Uvey of aova, Eecca Egeeg ee, No. 9, 5 ISSN 8-85 Th eaed by he fac ha whe he ea goded, he vaao of voage deed ecvey o he ove-voage e whe he ea oaed, hee a occece of ove-voage wavefom aco he afome wdg a he ode 5 (Fg. ), de o he fac ha ode 5 deeme a eaao bewee zoe of he cc wh mch dffee vae fo he eecca aamee. Whe codeg he feqecy (ao) doma, o majo eaco bewee he ao of ove-voage e ad fee ocao ao ω ca be accoed fo. I fac, he ao of he fee ocao ω ha a mch age vae ha ω, whch mae he me vaao of he voage o be deemed may by he ove-voage e ad he efeco of he ove-voage wavefom ode whch eaae cc zoe wh dffee vae of eecca aamee. The me vaao of he voage 6 (Fg. 5) gfcay dffee fom, eecay whe he wdg ha he ea oaed. I h cae hee he ove-voage dbo ofody o-fom. The voage aco he a co ha way owe amde vae wh eec o he voage ad 6 fo boh eva (e ad e ). Fo he wdg wh goded ea hee ae vey e vaao fo he voage ad 6. The ove-voage dbo amo fom h cae. The obevao ad coco cove a µ eva afe a oge dao, a he voage aco he d co w aoach vae. The ma dffeece bewee he wo cae eeeed by he ode 5. The voage 8 aco he caaco 8 offe a good eao fo he dffeece ecoed boh ao egad he ea o of he wdg. Fg. 6. Tme vaao of he voage 8 fo ω 6 ad/ ad wdg wh oaed ea Whe he ea o oaed, de o he me efeco occed a he ode 5, mo of he ovevoage ecoded a he ema of he caaco 8. The ove-voage aed aco he a of he afome wdg ha dageoy hgh vae h cae. ae B. Smao fo he ao ω 7 ad/. Th ao, havg mch coe vae o he fee ocao ao ha ω, he ogao of mch hghe voage aco he d co ha dy cae A. A of he heomea aayzed cae A ae ee, ye gfca comao wh he eoace heomea occg bewee he ao of he ove-voage e ad he fee ocao. Fo cae B, he ecoded ove-voage ad 6 aco he d co have mch hghe amde ha cae A (ee Fg. 7 ad 8). The voage aco he d co day a gh decay oce he dace wh eec o he ema A ceae. The a co fom he mode (Fg. ) whad he hghe voage e whe he ea o coeced o he god (Fg. 8). (a) (a) (b) Fg. 5. Tme vaao of he voage 6 fo ω 6 ad/: a) wdg wh oaed ea b) wdg wh goded ea. (b) Fg. 7. Tme vaao of he voage fo ω 7 ad/: a) wdg wh oaed ea b) wdg wh goded ea. 6