As a fundamental problem of the local vibration of Ship, I investigated the vibration of a rectangular plate with N columns whose spring constants are k₁, k₂, …k_N-1 and k_N, and the coupled vibration of N rectangular plates which are connected by (N-1) columns whose spring constants are k₁, k₂…, k_N-2, and k_N-1.
First, I calculated natural frequencies of free vibration, then, I studied the best position of columns when plates are under some external forces.

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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/ {0.88W_h+Σ (e, ω) + (0.98-0.34C_b) (0.21+0.32B/d) Δ} L_p³/min.
where L_p : length between perpendiculars in M.
B : breadth moulded in M.
d : mean draft in M.
C_b : block coefficient
Δ : displacement in KT.
W_h : hull weight in KT.
ω : added weight (Cargo, fuel, machinery etc.) in KT.
e : a coefficient depending on the position of an added weight
le=I⊗+ (I_b-I⊗) 2l_h/L_p in M⁴
I⊗ : moment of inertia to upper deck of the midship section in M⁴.
I_b : moment of inertia to bridge deck in M⁴.
l_b : length of bridge in M.
k_x : 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 condition
N_T=228√I_e×10⁸/Δ_TL_p³/min.
where Δ_T is the displacemnet at trial about 40% of full load displacement For full load condition
N_F=283√I_e×10⁸/Δ_FL_p³/min.
where, Δ_F is the full load displacement

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It is the wellkuown conception that the position of the main engine of ships should be located to the nodal point of the flexural vibration to make minimum the flexural vibration of ships excited by the unbalanced force of the main engine.
Recently Dr. Yoshiki and others made clear the above conception when the mass of the engine and the stiffness of the engine bed were concidered.
In case of the flexural vibration having damping forces due to ship's inner damping and viscous forces due to surrounding water, the author treated this problem theoretically, and examined the quantitative change of the amplitude due to the location of engine. Introducing the damping term the differential equation is expressed in complex form. The damping coefficient of actual ships may be considered as small quantity of first order, so the eqnation can be expanded by damping coefficient. Neglecting the higher order of damping coefficient, the author obtained the equation of amplitude (33) (34) and vibration form (43) (44). The real part of the amplitude indicates the component whose phase is equall to the exciting force, and the imaginary part advancing by 90°. Comparing the resultant amplitude the conclusion is obtained, that the main engine should be located a little inward from the nodal point (Fig. 9, 10), the phase angle distribution changes gradnally (Fig. 6) and the nodal point with zero amplitulde does not exist (Fig.5)

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The effect of the surface of water on a submerged wing has a practical significance because it is connected not only with the problem of the hydrofoil but with the problem of the action on the screw propeller blade moving near the surface of water. The writer investigated the action on a submerged wing considering the action of gravity on the water surface. The conclusions were so obtained as follows. When the speed of advance is not extremely low, the submerged wing receives more drug and less lift than in the unbounded fluid. The more the depth increases the more the effect decreases, and when the depth becomes larger than the breadth of the wing the effect becomes so small that it can approximately be neglected.

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With the intention of researching on the method of estimating the shaft horsepower of a ship moving through the shallow or restricted water, we have made some tank experiments, namely resistance test, wake test, and self propulsion test, on several deep and shallow conditions of the depth of water, using a model of a twin screw ferry boat, and varying her displacement and trim.
As the result of these experiments, following facts have been brought to light : -
As for the resistance and wake of a ship moving through the restricted water, the method of calculating these quantity, that one of the authors M. Kinoshita had derived from the modified J. Kreitner's theorem, had proved to be proper for such a ship form like this.
And by the self propulsion test, we have made clear that
(i) On account of the suction of screw propellers, the lower limit of the critical range of speed in the self propulsion test shifts to a lower speed than in the resistance test.
(ii) In the critical range of speed, the rate of the increase of thrust, torsion and number of revolution with the increase of speed are very little, so in this range shaft horsepower and thrust horsepower do not increase but a little.
(iii) Except these points, the curves of thrust, torsion and number of revolution show the similar variation as the curve of resistance on the same condition.
(iv) In the restricted water, the propulsive efficiency falls down generally as compared with in the deep water, but the diminution is especially very large in the neighbourhood of the speed of lower limit of critical range, for the reason of the fact related in (i).

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The author showed an integral-equation to determine the fluid field of an annular lifting surface in his previous paper. He now porposes a method of calculating the pressure distribution over the annular lifting surface by solving the integral-equation.
In §1 the fundameatal concepts for calculating the pressure distribution are treated. In§2and § 3 a method for transforming the integral-operator in matrices is extended.Finally, § 4 deals with some numerical examples.

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Normal and shearing stress distribution in ship's structure are obtained theoretically, when ship is subjected to large bending moment and bending stress is over yielding point. And numerical calculations for the standard ship of A type are performed and following results are obtained :
(1) When bending moment coefficient C=displacement×length of ship/bending moment reaches to the value of 24.41, upper deck begins to yield. When C=19.77, second deck begins to yield. And generally the buckling of deck plates between beams occurs after yielding of deck plates.
(2) When C=19.58, double bottom begins to yield, and this state can be regarded to have relation with the leakage of water of double bottom consisted of riveted plates.
(3) After yielding, the neutral axis gradually changes its position with increase of bending moment,
(4) With increase of bending moment, plastic domains spread to longitudinal and vertical directions from decks and bottom of midship. And in plastic domain, principal shearing stress lines are all linear and parallel and directed 45° to sheer line.
Above mentioned results are obtained by neglection of effects of local stresses (effects of local load and water pressure, etc.).Actually local yielding will begin to yield at somewhat larger value of above mentioned bending moment coefficient.

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The Theory of the Longitudinal Strength of Ship has been too classic. The author attempts to modernize and refine it to some extent. This theory is based upon the “Comparative Calculation” at the Standard Condition. But, what does the word “Comparative” mean in case of ships.which are of same size, on the same route and of the same kind but have superstructures of different length? The effects upon the strength due to type, form and structural style are investigated in this paper.
§ Superstructure.
That the superstructrure contributes to the longitudinal strength completely whn its length be over 15% of ship's or 6times of its height, has been the Naval Architect's commonsense, but this is wrong. The effectivity of superstructure chiefly depends upon the sum of its height and half of its breadth. When its length is over 6 times of the sum orl/ (b+h) _??_6, its mid-length becomes completely effective. When l/ (b+h) _??_3, its ability is nearly constant andwhen l/ (b+h) _??_3 the distribution of effectivity is nearly
1-8/π² [exp (-0.973x/ (b+h)) +exp (-0.973 (l-x) / (b+h))]
The reinforcement ot its ends must be increased accoding to its length when l/ (b+h)<2, and when l/ (b+h) >2 this may not be increased.
§ Short longitudinal bulkhead.
Ashort longitudinal bulkhead does not contribute to the longitudinal strength much, but it does not mean that the flow of stress does not exist in it. Especially when it is far from the side plate or continuous longitudinal bulkhead its effectivity is very small.

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In this paper we attempt to find the effect of the rolling of ships on the transverse strength and deformation of ships by the aid of relaxation method. To lighten the labour of calculation, we assume the ship is at the maximum inclination : that is
dθ/dt=0
Then the centrifugal forces vanish and only the inertia forces remain. Calculation is done at 10°, 20° and about 27° inclination : the last one is the angle at which the edge of the bridge deck immerges. On this calculation, we conclude that both statical inclination and inertia forces are not serious on the transverse strength.
The centrifugal forces are conjectured so.
Then as regards to the moment distribution or stresses we do not need the calculation of inclined condition : the one when the ship is upright is sufficient. But as regards to the deformation statical inclination exercises so great influences that we suppose this as one of the serious factors of racking.

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The strength of thin cylindrical shell subjected to external static pressure, has been investigated by Dr. Tokugawa but no research has been made as yet for its strength subjected to impulsive pressure.
The author has commenced with the investigation on the characteristics of the impulsive pressure due to underwater explosion of an explosive and made various experiments with explosives of small charges, and instruments having necessary precisions, formerly not well studied, for measuring the impulsive pressure.
It was found that the impulsive pressure due to underwater explosion of an explosive continues for a brief period forming solitary sine waves proportional to the diameter of the explosive or the cube root of the volume of the charge.
Then the analysis of the indication of a crusher gauge, which was used widely for its simplicity for measuring implusive pressure although of its defect of ambiguity, was made in regard to the problem of deformation of an elastic body subjected to impulsive pressure. It was acertained that the characteristics of the indication of the crusher gauge obtained from experimental results were in consistence with the theoretical researches.
The experiments were further expanded to the study of strength of thin cylindrical shell, making close observation to the fact that the mode “n” of vibration of a cylindrical shell and the number of lobes “n” appearing at the collapsing state of the cylinder subjected to external pressure were a common factor.
Considering for the collapsing state of n-th order, the equation
p_n (s) =p_n (d) ·T_n (t) _max
gives the critical impulsive pressure, where p_n (s) and p_n (d) are statical and impulsive pressures respectively and T_n (t) _max is the magnification factor of impulse depending upon the relation between the frequency of vibration of the cylinder and the impulsive pressure wave form acting on the cylinder externally. Thus the calculation of the critical impulsive pressure can be made by the use of the above equation selecting “n” to minimize p_n (d).
On the other hand, a method of systematic experimental study was made with many model cylinders and explosives of various charges to compensate for the theoretical results by which it was difficult to analyze some complicated conditions in actual case. Hence, it was proved that the experimental results showed the same tendency as the theoretical studies.

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