Vertical Wave Loads Research Articles

Non-linear wave loads and ship responses by a time-domain strip theory

A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representation. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership and are systematically compared with the experimental results given by Watanabe et al. (1989, J. Soc. Naval Architects Japan, 166) and O’Dea et al. (1992, Proc. 19th Symp. on Naval Hydrodynamics). The agreement between the present predictions and the experiments is very encouraging.

A Practical Method for Estimating Ship Motions of High-speed Crafts in Oblique Waves

In the previous paper, one of the authors and Prof. Fujino, based on a nonlinear strip synthesis, proposed a method to calculate the vertical motions and vertical wave loads of a high-speed craft in head sea. The validity of this method are verified practically through the comparison with model tests data. Furthermore, in this paper, following the similar synthesis scheme, a practical method for predicting the motions of a high-speed craft in oblique waves is presented and applied to an existing craft to clarify its fundamental characteristics of vertical and transverse motions in bow (or beam) sea.In the method presented, the time-varying submerged hull surface and the coupling effect between transverse and vertical motions are considered. Moreover, using the momentum theory, the nonlinear flare impact and dynamic lift are also taken into account. Besides, the equations of motions are described by the body-fixed coordinte, rather than the vehicle-carried vertical frame which is used conventionally.To prevent the numerical divergence due to the drift of sway and/or yaw motions in the time domain simulation, artificial springs in sway and yaw modes are introduced. The effects of the spring constants on the predicted ship motions are also discussed.

Second-harmonic vertical wave loads on arrays of deep-draft circular cylinders in monochromatic uni- and multi-directional waves

The second-harmonic vertical forces on arrays of deep vertical circular cylinders in monochromatic uni- and multi-directional waves are approximately evaluated based on the combined use of analytic first-order diffraction-radiation solutions for multiple columns and asymptotic analyses of the second-harmonic potential at large depths. Particular attention is paid to the qualitative estimation of the effects of the arrangement of columns, body motion, and wave directional spreading on the second-order forces. The asymptotic analysis originally developed by Newman (Newman, J.N., Second-harmonic wave diffraction at large depths. J. fluid mech., 213 (1990) 59–70.) for the mono-directional wave is extended to that for multi-directional waves in order to investigate the effect of wave directional spreading. All the first- and second-order solutions including the diffraction and radiation Kochin functions for multiple columns are obtained in explicit forms. The validity of the present approach is confirmed by comparisons with the numerical results computed from the boundary integral equation methods. The present approach can be used as a tool for PC-based parametric studies in the preliminary design of deep-draft multi-column structures.

R & D of a Displacement-type High Speed Ship

On the R & D of a displacement-type monohull vessel suitable for high speed navigation, seakeeping qualities in rough seas are one of the most important subjects to be investigated.In high speed range up to 50 knots, there still remains uncertainty of the applicability of theoretical prediction methods such as Strip Method. Therefore, seakeeping model tests in head sea condition were carried out in regular and irregular waves for experimental studies. Frequency response functions and short-term responses in irregular waves were obtained about ship motion, acceleration, relative motion, and vertical wave loads.As the results of comparison between theoretical calculations and experimental results, it is revealed that the Strip Method can roughly estimate ship motions and wave loads even at Fn =0.6. For the prediction of short-term responses in irregular waves, however, experimental value of frequency response functions should be used.From the investigation of seaworthiness in irregular head waves of various sea states at various ship speeds, it is estimated that the displacement-type high speed ship has generally a good seakeeping quality on ship motions and vertical wave loads. However, vertical accelerations and relative motions at bow are estimated to be significant in high speed range in long-mean-period irregular waves.

Nonlinear Prediction of Vertical Motions of a Fishing Vessel in Head Sea

Several years ago the authors developed a practical method for calculating vertical motions and wave loads of a high-speed craft which travels in regular head sea, and verified its validity by comparing the computed motions and wave loads with the results of model tests. In order to clarify further its validity, the method is applied herein to compute the vertical motions of a fishing vessel, and the computed motions are compared with the results of experiments conducted by Bales and others at the David W. Taylor Naval Ship Research and Development Center (DTNSRDC). Also, the vertical motions and shipto-wave relative motions predicted by the method are compared with the numerical results of conventional linear strip theory computations performed at DTNSRDC. As a result, it is found that the present method, which in principle is based on the conventional Ordinary Strip Method synthesis but modified to be able to evaluate nonlinear hydrodynamic impact forces as well as dynamic lift in waves, can be applied to estimate vertical motions and ship-to-wave relative motions of fishing vessels traveling in head sea with enough accuracy for practical use.

Effect of Hull Form Parameters on Ship Motions of High-speed Crafts

In order to provide a tool, which is useful for synthesizing hull forms leading to superior seakeeping performance in the early stages of high-speed craft design, the authors propose some regression equations to evaluate the seakeeping performance of high-speed crafts of a hard-chine type, by means of some simple hull form parameters.Several years ago, one of the authors and Prof. M. Fujino developed a practical method for calculating vertical motions and wave loads of a high-speed craft travelling in head sea, and verified its validity by comparing the computed results with those of model tests. In this paper, the above-stated method is applied to calculate the vertical motions of 20 hard-chine-type data base hulls in head sea, and the obtained motion responses are classified into several groups by using correlation analysis. Then following Bales' procedure, a number of seakeeping performance ranks connected with these groups of motion responses are found. Finally, the relations between these performance ranks and hull form parameters are established by using regression analysis. Through the present rank equations, the effect of hull form parameters are clarified and the guidelines for improvement of seakeeping performance are also presented. Furthermore, the influence of ship speeds are also discussed.

A Consideration on Vertical Wave Loads Acting on a Large-sized High-speed Craft

In previous papers, the authors presented a method for calculating vertical motions and vertical wave loads for a high-speed craft of medium size by treating the craft as a rigid body. In this paper, calculations for both rigid and elastic representations are presented for an existing large-sized high speed craft. Tests were performed to measure the vertical motions of two differently-scaled wood models. Still other tests measured the distribution of vertical bending moment along the ship's length of an elastic backbone model. The theoretical predictions are compared with the experimental results and with the experimental conclusions of other researchers. The comparison shows the two theoretical methods to be accurate enough for practical application.

A Consideration on Vertical Wave Loads Acting on a High-speed Craft of Medium Size

In the previous paper, the authors presented a method for calculating vertical motions and vertical wave loads of a high-speed craft which travels in regular head sea, and verified its validity comparing the computed motions and wave loads with the results of model tests. Furthermore in this paper, the above-stated method is applied to an existing high-speed craft of medium size in order to clarify the fundamental characteristics of vertical motions and wave loads of the medium-sized craft. The illustrative calculation is performed extensively for various cases of wave length, wave height and advance speed.As a result, it is found that the magnitudes of the vertical acceleration at the bow and the vertical bending moment correlate definitely to each other. This fact approves the propriety of the current design practice : the highest possible bending moment that is required to be predetermined for structural design of the hull is prescribed well as a function of the vertical acceleration at the bow.Besides, remarkable dependence of the maximum bending moment on the advance speed of a craft is demonstrated successfully by dividing the vertical bending moment into three parts and then clarifying the effects of advance speed on each part.

Vertical Motions of High-speed Boats in Head Sea and Wave Loads

In this paper, the authors investigate into vertical motions of a high-speed boat travelling in head sea and wave loads acting on it, taking account of the effects of non-linear hydrodynamic forces and dynamic lift in waves. A series of tests was carried out to measure heave and pitch, bow acceleration, vertical bending moment and shearing force at the midship section of a segmented model. The experimental results were compared with theoretical values predicted in the following three different ways : (A) linear calculation, that is to say, the Ordinary Strip Method applied to the running condition at travelling in a calm water, (B) non-linear calculation in which the effects of time-varying sectional hydrodynamic forces were taken into account, and (C) non-linear calculation taking account of the effects of planing at a high-speed as well as the effects of time-varying sectional hydrodynamic forces. As the result of comparison, it was shown that vertical motions and wave loads of high-speed boats can be evaluated by the method presented in this paper with accuracy enough for practical use, and that the method may be applied to the case of travelling at a higher speed than that considered in this paper if the sectional hydrodynamic forces will be appropriately evaluated when travelling at that speed.

Experimental and Theoretical Approach to the Estimation of Non-Linear Vertical Wave Loads

Accurate estimation of wave loads acting on a ship is a long-lasting task for naval architects. Recently, a new approach for the investigation of non-linear characteristics of wave loads was introduced; namely, combination of experiments using “elastic model” and non-linear digital simulation.In this paper, at first, possible construction techniques of “elastic model” are examined. Adopting “backbone model” composed of segmented hulls and a metal backbone representing ship's longitudinal rigidity, two series of model experiments were carried out for a high-speed cargo vessel with different values of backbone's rigidity.Application of “backbone model” makes it easy to change model's longitudinal rigidity. Using as high rigidity backbone as possible, vibration response components can be reduced and responses almost as a rigid body can be measured. Replacing the backbone with the one having corresponding rigidity to the full scale ship, approximate responses of the ship can be measured.By the examination of dynamic characteristics of the model, vibration modes and modal damping coefficients were obtained, and the damping coefficients were found to be very close to those of full scale ships. It means that close correspondence between model experiments and full scale phenomena can be obtained.A digital simulation program was developed for the estimation of nonlinear heave and pitch motions, vertical bending moment and shearing force. Compared with the results measured through the model test, calculated results seem to predict non-linear characteristics fairly well.

A Study on Longitudinal Motions and Wave Loads of a Container Ship in Waves

In the first and second report, comparisons between tank experiments and theoretical calculations were carried out mainly in following waves where encounter frequency is very low. At ωe_??_0 transfer functions of vertical wave load from experiment showed a considerable difference compared with results of theoretical calculation methods. And this difference is understood that there was certain problem in calculation of diffraction force and radiation force, especially in following waves.In this paper, we made a reconsideration of accurate estimation on longitudinal ship motions and vertical wave loads taking account Mizoguchi's method for diffraction force and moment and using Maruo's three dimensional correction for only added-mass in radiation component. This calculation method for diffraction force and moment is a complementary approach in Newman's diffraction solution, considering no effect of the forward velocity on the hydrodynamic coefficients mentioned in our second report. By applying this method, experimental values of longitudinal ship motions and vertical wave loads can be explained satisfactorily not only in following sea, but in all the wave directions and all Froude numbers within the range for practical use.

On the Prediction of Longitudinal Motions and Vertical Wave Loads of a Ship in Following Sea

As a sequel to Ref 1, comparison between results of theoretical calculation and tank experiment was mainly carried out at the zone where encounter frequency approaches zero in following waves. Vertical shearing force, which was not dealt with previously, is included in this paper. Meanwhile, problem on following long crested irregular waves are also dealt with. The following are outlines of conclusions.1) Calculated results by the widely used New Strip Method (NSM) or Ordinary Strip Method (OSM) for transfer function of vertical shearing force in following waves were compared to experimental results. This comparison shows bad agreement, worse than that in the case of vertical bending moment. Hence, these methods are regarded to be impracticable in following waves.2) Transfer function of vertical shearing force by N (A), recommended in the previous paper to be a new practical method for vertical bending moment, shows a considerable difference from experimental results. Therefore, it can not be regarded as having practical precision of prediction on vertical shearing force.3) In following waves, results of theoretical calculation of vertical wave loads transfer function at Fn=0 express experimental ones the best quantitatively in any ship speed. Hence, this approximate calculation can be recommended as a practical tentative one.4) It is understood that there is still certain problem in calculation of diffraction forces and Froude Krylov forces in following waves by presently used theoretical methods.5) By applying transfer function obtained from experiment, characteristics in long crested irregular following waves can be precisely predicted. In other words, despite the singular form of spectra in the encounter phenomena in following waves, the popular method of short term prediction based on the principle of linear superposition is proved with experimental evidence.6) Encounter mean period, both obtained from estimated encounter spectra and measured directly from encounter time history, appear to be nearly identical. This means that it is possible to predict encounter mean period in long crested waves from encounter spectrum.