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PONAŠANJE BRODA NA TALASIMA____________________________2 2ζG + 2μ 2ζζG + ωζζ G= ATωζaζsinωpt2μζωζ 2ΨζΛζγζ= arctg = arctg2 22 2 2 ψ + 2μψψ+ ωψψ = αωo ψaψcosωptωζ−ωp1−Λζ22μψωψ 2ΨψΛRešenja jednačina glaseψγψ= arctg = arctg2 2 2ζ () sin( )ω −ω 1−ΛGt = ζG ωo pt−γψ pψζRezultati deluju veoma slično rezultatimaψ() t = ψocos( ωpt−γψ)valjanja...2ζG ωoζ⋅ aζPζ= = = Postoje, međutim, dve (naizgled) male razlike...A2T2 2 2 2( ωζ− ωp)+ 4μζωFaktori poremećaja definisani su preko prividnepfrekvencije, odnosno prividnog perioda talasa...aζ=T1− Λ2 42 2ζψ ,ωp ωT + vko Tζ+ ΨζΛΛζψ,= = = =ζT ω ω( ) 2ω ⋅ a2 ψoψ ψψ= = =α2o2 2 2 2ω − ω + 4μψωpP=( ψ p)a( Λ )ψ22 2 2ψΨψΛψ1− + 4pζψ , ζψ ,ω vkT= + = +ω ω λT o T ( o)ζψ ,Λζψ,voζψ , ζψ, TTako da rezultati direktno zavise od brzinenapredovanja broda v o ...Bezdimenzione amplitude sile (momenta) a ζ , a ψzavise od parametra L/λ T ...PREDAVANJA 2009. 113
PONAŠANJE BRODA NA TALASIMA____________________________Ove “male” razlike bitno komplikuju problem...Analiziraćemo prvo funkcijeP Pζψfζ= , fψ=aζaψkoje nemaju veći fizički č ili tehnički č značaj, ali(formalno) imaju isti oblik kao prenosne funkcijekoje smo proučili u prethodnom odeljku...Jedina razlika je u prividnoj frekvenciji, odnosnofaktoru poremećaja...Sopstvene frekvencije poniranja i posrtanja imajubliske vrednosti...Podsetimo se, sopstveni periodi suδT1( + κζ)Tζ= 2πα g2πjyδ T1( + κ ψ)Tψ= =2πω i α gψyi ne razlikuju za više od 10%, tako da (grubo) važerelacijeω ≈ω , Λ ≈ Λζ ψ ζ ψBrod je u istoj oblasti ljuljanja(potkritičnoj, kritičnoj, natkritičnoj) i zaponiranje, i za posrtanje...Ukoliko je u rezonanciji...PREDAVANJA 2009. 114
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