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PONAŠANJE BRODA NA TALASIMA____________________________Gde je1a ≈ ζb( x)cosk TxdxA ∫VLL1a ≈ ψxb ( x)sin k TxdxkI∫TyLU slučaju valjanjaDobija seM = A sin( ω t+δ )( p)xA ≈ gD ⋅MG ⋅k A ⋅aϕTϕTϕTδϕϕπ≈2Baϕ= 1 za = 0λa →0 zaϕT,B→∞λT,Za pravougaonu vodnu liniju moguse odrediti analitički...aaζψλ⎛T π L ⎞= sin ⎜ ⎟πL⎝ λT⎠3Bλ ⎡T ⎛πλT ⎞ πλT ⎛πλT⎞⎤= sincos3 ⎢ ⎜ −4πIyL⎟ ⎥L⎜L⎟⎣ ⎝ ⎠ ⎝ ⎠⎦VažiB / λ 1,a ≈ 1TϕPREDAVANJA 2009. 93
PONAŠANJE BRODA NA TALASIMA____________________________4.2 Rešenja jednačina, prenosne funkcijeNezavisne (približne) diferencijalnejednačine koje opisuju ljuljanje broda natalasima imaju oblik2 2Z+ 2 Z+ Z = A a t+μ ω ω ω δsin ( )Z Z Z Z p Zgde jeA = A T kod poniranja,A = α = k A kod posrtanja i valjanjao T TRešenje diferencijalne ij jednačine je− μZ Zt () = Z thoe sin( ωZt+ εZ) +opšte rešenjehomogenog dela jednacine+ Zo sin( ωpt+ γZ)partikularno rešenjenehomogene jednacineRešenje homogenog dela jednačineodumire, tako da posle izvesnog prelaznogperioda važiZ() t = Z sin( ω t + γ )o p ZAmplituda i fazni pomeraj ovog kretanja suZγo2AωZ= =22 2 2 2ω − ω + 4μ ω=gde su( )Z p Z p( Λ )A22 2 2ZΨZΛZ1− + 422μZωZ 2Ψ ZΛZ= arctg = arctgω −ω 1−ΛZ 2 2 2Z p ZΨZμZ=ωZωpTZΛZ= =ω TZpPREDAVANJA 2009. 94
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