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PONAŠANJE BRODA NA TALASIMA____________________________Desnu stranu jednačina čineVaži Laplasova jednačina2 2 2∂ φ ∂ φ ∂ φhidrodinamičke sile i momenti...+ + = 02 2 2∂ξ ∂η ∂ζSprega Dinamike i Mehanike fluida...i Koši-Lagranžov integral Ojlerove jednačine...Na svaki element e e podvodnog og dela∂φbroda deluju p i τ ... p( ξηζ , , , t) = pat−ρgζ−ρ−∂t2 2 2⎡⎛ 1∂φ ⎞ ⎛ ∂φ ⎞ ⎛ ∂φ⎞ ⎤− ρ ⎢2 ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ ⎥⎢ ∂ξ ∂η ∂ζ⎣⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎥⎦ FV=− pndS∫Postupak, u principu:Srešiti Laplasovu jednačinu sa odgovarajućimZanemarujemo viskoznost... τ = 0 graničnim uslovima....(pokušaćemo da izbegnemo...)Strujanje je potencijalno...Potencijal brzine φ = φ( ξ, η, ζ , t)Pretpostavka opravdana...sem za valjanja...Postoje šest ljuljanja, šest pomeranja u odnosu naravnotežni položaj...Samo za tri kretanja, to je položaj stabilneravnoteže... rezonancija...koja?PREDAVANJA 2009. 9
PONAŠANJE BRODA NA TALASIMA____________________________2. LJULJANJE BRODA NA MIRNOJ VODIProblemi ljuljanja broda na mirnojvodi, sami po sebi, nemaju većitehnički značaj za brodogradnju...Međutim, dovoljno su jednostavnida preko njih uvedemo...2.1. Poniranje brodaPretpostavljamoϕ= 0, ψ = 0, vo= 0Tražimo ζ G (t) = ?Kada je brod u ravnoteži, O = GKada ponire, važiformalno jeFζD ⋅ ζ = F −D⋅gSGζ=− ν ⋅ ∫pndSAli, da (za sada) izbegnemo Laplasovujednačinu... pretpostavljamo direktno( o)Fζ Fζ F ′ ζp = po+ p′...= +Hidrostatička komponenta(prema Arhimedovom zakonu) ( o)Fζ= ρgρgVV = Vo−V′V′ = V′() t ≈ζG()t AVLza ζ G «1( o )Fζ = ρgVo −ρgζGAVLPREDAVANJA 2009. 10
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