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PONAŠANJE BRODA NA TALASIMA____________________________4.7.2. Nelinearno valjanjeDiferencijalna jednačina nezavisnognelinearnog valjanja broda na bočnimtalasima glasi( J + m ) ϕϕ + M ( ϕ) + M ( ϕ) = M ( ω t)x r st T Tpri čemu sva tri momenta Mr, Mst,MTmogu biti nelinearna...Pod nelinearnim valjanjem, međutim,proučavamo samo uticaj momentastabiliteta...Do sada smo koristili aproksimacijuMst≈gD⋅ MG⋅ϕSada, stvarnu vrednostMst= gD⋅h( ϕ)Diferencijalna jednačina valjanja se tadasvodi na2 2 ϕ+ 2μ ϕ+ ω h( ϕ) = ωα cos( ωt+ε )gde jeϕ ϕ st ϕ o T Thst( )hϕst( ϕ ) =MGPotrebno je bezdimenzioni krak stabilitetaprikazati (npr) u formi polinoma3 5 7h= ϕ+ c ϕ + c ϕ + c ϕ + ...st 3 5 7i numerički rešiti diferencijalnu jednačinu...PREDAVANJA 2009. 137
PONAŠANJE BRODA NA TALASIMA____________________________Dobija seRešenja nelinearne jednačine, za razliku odlinearne, ne predstavljaju harmonijske funkcije...ali i ona su periodične funkcije vremena čijaamplituda, nakon početnog prelaznog perioda,postaje tj (makar prividno) iid )konstantna...tIako se i oblik, i period razlikuje se ododgovarajućeg linearnog rešenja,najvažnija razlika javlja se u amplitudamavaljanja...Prema linearnoj teoriji, brod se ne možeprevrnuti na bočnim talasima...Prenosne funkcije nelinearnog valjanjaimaju “krivu kičmu”,odnosno tipično izgledaju...PREDAVANJA 2009. 138
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