Estimation of the Natural Frequency of the Hull in the early Stage of Design

Abstract

We Propose here a Method of estimating the Natural Frequency of 2-Noded Vertical Vibration For Three Islander or similar type Cargo Ship, on the basis of the measured datas at trials which had been carriedout for about 15 years.Eventualy, the Natural Frequency of the hull (N) is derived From the Following Formula.N=k·307√Ie×108/ {0.88Wh+Σ (e, ω) + (0.98-0.34Cb) (0.21+0.32B/d) Δ} Lp3/min.where Lp : length between perpendiculars in M.B : breadth moulded in M.d : mean draft in M.Cb : block coefficientΔ : displacement in KT.Wh : hull weight in KT.ω : added weight (Cargo, fuel, machinery etc.) in KT.e : a coefficient depending on the position of an added weightle=I⊗+ (Ib-I⊗) 2lh/Lp in M4I⊗ : moment of inertia to upper deck of the midship section in M4.Ib : moment of inertia to bridge deck in M4.lb : length of bridge in M.kx : to be a coefficient bared on the node position and decided after the measured datas.For estimating the natural frequency range in the early stage of design, the approximate values of the natural frequencies at trial and full load conditions are given by the Following formulas. For trial conditionNT=228√Ie×108/ΔTLp3/min.where ΔT is the displacemnet at trial about 40% of full load displacement For full load conditionNF=283√Ie×108/ΔFLp3/min.where, ΔF is the full load displacement