The subject of boundary layers which have a small regular fluctuating flow superimposed on the mean boundary layer flow has been developed by Lighthill (1954) and Stuart (1955). When the disturbing velocity by wave is small compared with the velocity of plate, the laminar frictional resistance of plate moving in wave is obtained by applying these considerations. The amplitude of resistance fluctuation and the phase lead of the resistance over the main stream velocity fluctuation vary with frequency and wave length. The ratio of resistance increment is proportional to the square of wave height.

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Periods of sea waves are irregular as well as in their wave height. Usually the mean value of intervals of wave amplitudes in records is always shorter than the period of the maximum energy density of spectrum. From the fact that the higher the amplitudes become, the rarer they occur, we notice that if we choice suitable heights of successive two waves and observe this time interval, this may correspond to the above-mentioned most prevailing wave period. This problem is theoretically analysed, and it is found that the significant wave height must be preferred. If we develope the Rice's theory of distribution of zeros to that of arbitrary heights, the results are as follows: Let ξ(t) be wave height, and ψ(τ) be correlation function, w(f) be spectral distribution, ψ(τ)=∫^∞_0w(f)cos2πfτdf, then the probability density of intervals that ξ(t) passes ξ_1 with positive and ξ_2 with negative gradient, [numerical formula] so, distribution function becomes when ξ_1=ξ_2=ξ, [numerical formula] where [numerical formula] and μrs=χ_rχ_s,r,s=1,2,3,4. M_<rs> is cofactor of μrs [numerical formula] Here, if we take the expression at the minimum value of τ which satisfies ψγ'=0. [numerical formula] This formula shows good accordance with the results of actual observation in extensive range of τ. This leads the following results: [numerical formula] whith tells us that the time interval of significant wave is approximately the most predominant wave period.

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The theoretical analysis of the behaviour of the transverse section of the ship with many decks in the free vibration state has been made. The effect of the many decks, seen in the passenger ships, the engine rooms of the cargo ships, and others, to the eigenvalues and modes of the main structure, which is constructed with the members of the lowest deck, both side frames and the bottom, has been studied analytically and numerically. The generalized analysis was made in the condition that the transverse section with many decks was divided into the two elementary systems, that is, the main structure system explained above and named by the first system, and the other systems constructed with decks and both side frames connected to the main structure and named by the second system in Fig. 2. These analyses and results proposed here may be applied to the other structure than ship, which can be divided into the two elementary systems, in the same way. The eigenvalues and the eigenfunctions of these structure can be calculated from eqs. (12), (15), (16) and (18) for the symmetrical vibration, and eqs. (21), (24), (25) and (27) for the asymmetrical one. Numerically computed examples of the practical ship transverse section, which have two decks, are shown in Figs. 5 and 6, and also compared with the section of single deck. Another examples of the section with three decks constructed with the members of same scantling are shown in Figs. 7 and 8.

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In this paper, the author gives his view concerning the causes of the stern vibration of a ship, believing there are three, that is, (a) damping imposed on a ship in case of hull vibration (b) local vibration induced near the vibrating point at the stern of a ship, (c) the smallness of [mass×rigidity] of stern compared to that of amidship (a) It is theoretically proved in this paper that if there is resistance against vibration, the vibrating wave started from vibrating point is damped off on its way and that the amplitude decreases exponentially with the increase of the distance from the vibrating point. Since logarithmic decrement generally increases with the higher made of vibration, the stern vibration due to this cause occurs more easily, in the higher mades. with such a magnitude of damping as was obtained in former experiments, however, it is not good enough to cause the stern vibration such as we experience. If the stern vibration, therefore, be caused by this reason, it can possibly cause very large damping in higher mode of vibration in case of spiral cargo. (b) If vibrating waves sent forth from the vibrating point give rise to local vibration on the way of its propagation, the vibrating energy is adsorbed in the locally vibrating body and the vibration that is conveyed to farther part decreases. Especially, it is proved in this paper that if natural frequency of local vibration coincides with that of exciting force, there occurs no vibration in the distant part, total energy being absorbed in the local vibrating body. Loser's "Vibration neutraliser" corresponds to the case in which local vibrating body is at the vibration exciting point. The inherent frequency of the panel forming a ship is apt to be about 300〜500/m due to the effect of water in contact. Accordingly, the greater part of the stern vibration experienced by us seems to be due to this cause. Assuming, by the way, as frequency of local vibration=σ, frequency of the vibration of n th mode of the ship=ω_n frequency under the effect of local vibration =ω'_n, it follows that ω'_n<ω_n when ω_n≦σ ω'_n>ω_n when ω_n≦σ In case of ω_n≒σ, therefore, there appear two frequencies, and moreover, the curves representing the relation between ω'_n, and the degree of mode assumes two curves that jump discontinuously at n. And in case that a local vibration body is in the node of i th mode, there appears no effect of local vibration in the amplitude and frequency of the vibration of i th mode. The cause of the irregular form of the experimental curves that show the relation between frequency and number of nodes might be explained by local vibration. (c) At the stern, virtual mass in vibration as well as rigidity decreases rapidly. The author has theoretically solved in this paper the vibration in which two uniform beams of different mass and rigidity are connected each other and vibrating force acts at the free end. Consequently, it has been proved, as a matter of course, that the amplitude of the beam of small [mass×rigidity] becomes larger than that of large beam. This fact shows the possibility of stern vibration caused by the gradual decrease of [mass×rigidity] at the stern. with an actual ship, it has each of these three causes more or less, though any one of them is likely to play main part.

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There is strong indication these days that the idea of plastic design will be applied to the determination of hull structure. Also, in this shipyard, we have been making examinations for application of the idea of plastic design to some parts of hull construction members, and reports on the matter have been made at some meetings. This paper deals with the results of these investigations. The following are the conclusions of the investigations. (1) Shape factor of bar with plate is 1.4-1.5. (2) Effect of axial force upon plastic modulus of bar with plate is small. (3) There is an extreme unbalance between collapse loads of bottom longitudinal frames, deck girders, beams and pillars. It is very important in designing hull construction with the idea of plastic design to determine safety factor and allowable deformation of construction members under the fixed safety factor. However, this matter will be taken up for investigation in the future.

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Under severe conditions of high seas, the ship rolls seriously with a maximum roll of 30° to 40°, in some cases. We have experienced some troubles that introduction of air from the suction pipe of lubricating oil pump has happened by heavy fluctuation of oil level in the lubricating oil sump tank built integrally with the ship's double bottom. The authors carried out some model experiments with a 1/10 scale model of sump tank having usual construction (not so long in longitudinal length, shallow and having longitudinal and transverse girders inside for strengthening) and a fluctuating mechanism of pendulum type, so as to find the oil level fluctuation similar to the actual ship. After carrying out a theoretical analysis in parallel with the model test, the authors were able to find the condition of oil level fluctuation in the sump tank by calculation. It is possible to proceed with the design based upon the calculation in the following procedures, so as to obtain the design of lubricating oil suction system sufficiently safe fer the ship's rolling. (1) To decide the size of compartment devided with girders and oil passage on the girders in the tank. (2) To keep the maximum distance between the oil level and the pump suction mouth, so far as available with the usual construction of sump tank.

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