横揺と縦揺の混振について

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Spectral distribution of oscillation of a ship has, in general, two peaks, which originate the resonances of pitching or heaving and rolling.This phenomena increase the irregularity of motion compared with the case when they are completely isolated with each other, and furthermore, also freqnency distribution of amplitude hastwo peaks, the larger portion of which is due to combined oscillation.According to Rice's theory of envelope, letting R be the amplitude of envelope, which is irregular, P, Q be rolling and pitching, which are supposed to be regular, then the probability density which lies between R and R+dR is p(R)=R∫^∞_0 rJ_o(Pr)J_o(Qr)J_o(Rr)e^<-(ψ0/2)r^2>dr.This integral can be developed further as follows : R/ψ_0exp[-1/(2ψ)_0(P^2+Q^2+R^2)]・{I_0((PR)/(ψ_0))I_0((QR)/(ψ_0))I_0((PQ)/(ψ_0))+2Σ^^∞___<m=1>Im((PR)/(ψ_0))Im((QR)/(ψ_0))Im((PQ)/(ψ_0))} where ψ_0 is mean square of forced oscillation components.This distribution becomes R≫0. p(R)≑(I_0(PQ/ψ_0))/(2π√<PQ>))exp[-1/(2ψ_0)(R-P-Q)^2] and when there is only one resonance Q=0. p(R)=R/(ψ_0)exp[-1/(2ψ_0)(P^2+R^2)]・I_0((PR)/(ψ_0))≑1/(√<2πψ_0)>[-1/(2ψ_0)(R-P)^2] so that the maximum frequency shifts from R=P to R=P+Q, namely at the amplitude of sum of P and Q.So that combined resonance oscillation sometimes causes extraordinary large amplitude.Letting circular frequencies be p and q for the amplitudes P and Q, irregularity reaches at the extreme value when : P_p=Q_q
社団法人日本船舶海洋工学会の論文

横揺と縦揺の混振について

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