動揺の不規則性とスペクトル分布

抄録

Spectral distribution of oscillation of a ship has a strong peak at its frequency of resonance.
Then, index numbers of irregularity are as follows :
(I) By Cartwright & Longuet-Higgins (Theory of maxima)
ε⁽ⁿ⁾²=1-ψ₀^(2n+2)2/ψ₀⁽²ⁿ⁾ψ₀⁽²ⁿ⁺⁴⁾
where, (-1) ⁿψ ⁽²ⁿ⁾ means r. m. s. of oscillation, and for amplitude n=0, for velocity n=1, and for acceleration n=2. Usually ε²>ε′²>ε″² so regularity increases toward higher time derivative.
For narrow-banded spectrum ε²_??_ε′²_??_ε″²=0, but when it is widely distributed, ε²_??_2/3, ε′²_??_2/5, ε″ ²_??_2/7.
(II) By Rice (Theory of envelope)
α ⁽ⁿ⁾ =Ppⁿ√ (-1) ⁿψ₀ ^*(2n)
where p=2π_fm is circular frequency of resonance and P is amplitude of resonance. (-1) ⁿψ₀ ^*(2n) causes slowly varying amplitude of oscillation and generally forms Gauss distribution above f=0. So that.
(a″/a′) ²=1/3 (a′/a) ²·
These results are summarized by the author's index number
n″ -n′=n′-n=1.