Whipping Response Research Articles

Prediction for Global Whipping Responses of a Large Cruise Ship Under Unprecedented Sea Conditions Using an LSTM-Based Encoder–Decoder Model

Abstract Global whipping responses contribute to a significant increase in vertical bending moments (VBM), making their accurate prediction crucial for ship safety. In this study, a long short-term memory (LSTM)-based encoder–decoder model is established to predict the whipping responses under varying sea states. The model is trained on a comprehensive dataset, which includes motion data and VBM history of a cruise ship under various sea conditions. This dataset is established via numerical simulation, ensuring a wide range of scenarios for the model to learn from. The efficacy of the LSTM encoder–decoder model in capturing global whipping responses is initially verified under a single sea condition case. This step confirms the model's ability to accurately predict vertical bending moments under known conditions. Subsequently, the model's performance under unprecedented sea conditions is examined. Given that the distribution of training data significantly influences the model's performance and the data from diverse sea conditions typically exhibit distinct data distribution, a mixed data training strategy is employed during the training process in this scenario. The results indicate that the LSTM encoder–decoder model effectively captures whipping responses. Furthermore, the mixed data training strategy significantly improves the model's prediction accuracy for global whipping responses under unprecedented sea conditions.

Experimental analysis of bow flare slamming and whipping responses in a ship at different sailing speeds

This study conducted an experimental investigation using a segmented model to determine bow flare slamming loads and whipping responses of a ship in regular waves. The model simulated the distribution of the vertical and horizontal bending stiffnesses of the hull. A continuous wavelet transform was employed to capture temporal variations in the harmonic components. The influences of sailing speeds on the temporal and spatial variations in the slamming pressures in the bow flare were analyzed. Subsequently, the time-frequency characteristics and asymmetry of the global responses under different test conditions are discussed. The random errors in the experimental system were investigated through repeated testing. The findings revealed that a higher sailing speed could significantly influence the magnitude and distribution of slamming pressures on the bow flare, while playing an important role in inducing asymmetric slamming loads under oblique waves. The slamming-induced whipping responses under regular waves caused considerable periodic changes in the strengths of the harmonic components around the wet natural frequency of the model. At high sailing speeds, the whipping responses significantly increased the asymmetry of the vertical bending moment (VBM) at midship.

Experimental study of the coupled damage characteristics of a large-scale hull girder subjected to an underwater near-field explosion

This paper presents the design and testing of a 10 m box-shaped hull girder model to investigate the overall response characteristics and damage modes of a warship subjected to an underwater near-field explosion. A 100 g trinitrotoluene (TNT) charge was detonated right below the midspan or quarterspan of the girder. On this basis, the structure strain, shock environment, and displacement of the girder were obtained under varying conditions, including the explosion depths and positions of attack. In the study, the coupling motion and frequency response characteristics between the explosion bubble and the hull girder were analyzed. The basic conditions for the occurrence of a whipping response or sagging damage to the hull girder were proposed. The experimental results showed that the girder and the bubble could easily exhibit a coupled resonance when the frequency of the explosion bubble pulsation is close to the first wet frequency of the girder. Also, a bending deformation or an overall damage is more likely to occur when the underwater explosion (UNDEX) happened directly below the midspan of the girder in comparison to other explosions at different attack positions. It was found that the structural damage is mainly concentrated in the middle of the 1/5 girder length region.

Numerical study of slamming and whipping loads in moderate and large regular waves for different forward speeds

This paper describes the development of a time-domain hydroelastic numerical model for investigating the slamming and whipping loads imposed on a ship traveling at different forward speeds. The numerical model integrates a beam model, the 3-D Rankine panel model, and the 2-D modified Logvinovich model. The tilt angle of the 2-D profile in the slamming model is determined by the direction of relative velocity, which takes the forward sailing speed into account. The computational results are validated against a segmented model test of a large cruise ship. The convergence of the model with different numbers of elastic modes and slamming profiles is studied to ensure that the numerical results are stable. The main contributor to the whipping response is found to be the vibration of the first-order elastic mode. The slamming force is sensitive to the longitudinal interval of the slamming profiles, especially in the stern. The characteristics of the slamming pressure under bow flare and the whipping response at midship are also investigated. The numerical and experimental whipping responses are found to be in good agreement, and the local slamming pressure based on the slamming profile is more accurate when considering the effect of the ship's forward speed.

Numerical method for whipping response of ultra large container ships under asymmetric slamming in regular waves

In this paper, a 3-D nonlinear time-domain hydroelastic analysis method for ship wave loads considering asymmetric slamming is proposed, and a 3-D Rankine panel method is used to solve the seakeeping problem. To accurately predict the hydroelastic response of the hull girder, the interaction between the hull structure and the flow field is considered in the body boundary condition. The motions and sectional loads of the ship are expressed by the superposition of the modal, which is obtained by modal analysis on a 3-D finite element model of the hull. After calculating asymmetric slamming loads using the Modified Logvinovich Model (MLM), the hydroelastic response of a 21,000-TEU container ship is analyzed, which incorporates the horizontal bending-torsional coupling vibration. Furthermore, the hull motion, slamming force, and section load are analyzed in detail to properly identify the mechanism of the slamming-whipping phenomenon. The results show that asymmetric slamming significantly affects the horizontal-torsional whipping response of the hull, especially when the wave encounter frequency matches the natural frequency.

Reconstruction and prediction of global whipping responses on a large cruise ship based on LSTM neural networks

This study presents a model based on Long Short-Term Memory (LSTM) neural networks for the reconstruction and prediction of global whipping responses using ship motion data. The model is fine-tuned and trained based on a dataset of heave, pitch, surge motion data, vertical acceleration data, and vertical bending moments (VBM) from a large cruise ship model experiment by utilizing 5-fold cross-validation. The established model is tested with a pre-split test dataset and used to carry out reconstruction and multi-step prediction of the VBM amidship in following and head seas. The reconstructed results demonstrate a high degree of fit with the measured VBM amidship under both regular and irregular wave cases, indicating the model's ability to capture whipping responses. The findings of multi-step prediction indicate that the prediction accuracy and the model's ability to capture whipping responses decrease as the horizon increases, and the model is more accurate in predicting whipping responses when they are stronger.

Experimental study of stern slamming and global response of a large cruise ship in regular waves

This paper presents an experimental investigation of stern slamming and global responses using a segmented model test. A model of large cruise ship with a long and flat stern is selected for the test, with a scale ratio of 1:60. Experimental random uncertainty is analyzed by considering the model responses in a series of regular waves. It is found that different types of response have different levels of dispersion. A calculation model that can reproduce ship–wave relative motions during stern slamming is established based on the experimental data. The influences of the instantaneous impact velocity and longitudinal deadrise angle on the distribution of local slamming pressure are analyzed. Finally, the effect of stern slamming on global responses is discussed. This investigation shows that the longitudinal deadrise angles are usually small in following waves, and this results in a large slamming force loaded on the stern in a short time. In addition, a whipping response of the hull girder will be excited.

Effect of hull inelasticity on whipping responses by underwater explosions

ABSTRACT This paper aims to verify why the inelastic hull responses of buckling and plastic deformation should be considered in the underwater explosion (UNDEX) simulations. A battleship was discretized into the five longitudinal segments that were composed of Timoshenko beam elements. The number of elements was determined through convergence simulations of natural frequency. The inelastic nonlinear moment-curvature curves using Smith’s method were applied to the UNDEX models. The incompressible gas bubble model was chosen for the UNDEX simulations because the compressible one produced acceleration less conservatively than the incompressible one. The UNDEX simulations were performed for the far and less far stand-off distances. The bending moment in the inelastic model was less developed than those in the elastic model for two stand-off distances. More evident Inelastic effects were observed for the reduced stand-off distance. The inelastic effect should be considered in the UNDEX analyses for even far-field UNDEX cases.

수중 폭발에 의한 함체의 비탄성 휘핑 응답에 관한 연구

The primary effect of the far-field underwater explosion (UNDEX) is the whipping of the ship hull girder. This paper aims to verify why inelastic effects should be considered in the whipping response estimations from the UNDEX simulations. A navy ship was modeled using Timoshenko beam elements over the ship length uniformly keeping the constant midship section modulus. The transient UNDEX pressure was produced using two types of the Geers-Hunter doubly-asymptotic models: compressible and incompressible fluids. Because the UNDEX model based on incompressible fluid assumption provided more increased fluid volume acceleration in the bubble phase, the incompressible fluid-based UNDEX model was adopted for the inelastic whipping response analyses. The non-linear hull girder bending moment-curvature curve was used to embed inelastic effects in the UNDEX analyses where the Smith method was applied to derive the non-linear stiffness. We assumed two stand-off distances to see more apparent inelastic effects: 40.5 m and 35.5 m. In the case of the 35.5 m stand-off distance, there was a statistically significant inelastic effect in terms of the average of peak moments and the average exceeding proportional limit moments. For the conservative design of a naval ship under UNDEX, it is recommended to use incompressible fluid. In the viewpoint of cost-effective naval ship design, the inelastic effects should be taken into account.

A simplified theoretical model of the whipping response of a hull girder subjected to underwater explosion considering the damping effect

This paper presents a simplified hull girder model to quickly and accurately predict the overall whipping response of a vessel subjected to an underwater explosion. The effects of structural damping and fluid damping on the vessel dynamic response to an explosion directly below the midspan of a hull girder of uniform cross-section were analyzed. The load profile of an underwater explosion was first divided into five phases, and a theoretical model of fully elastic response and elastic-plastic response of the hull girder under the combined effects of an explosion shock wave and pulsating bubble was established and verified using experimental data. Finally, the effects of damping on the overall mode, period, and amplitude of the deformation, as well as the plastic hinge of the girder were investigated. When the damping effect is considered, the proposed model can capture the repetitive loading and unloading processes leading to plastic deformation of the girder and accurately forecast the period and amplitude of the overall periodic deformation of the hull girder with an error of less than 10%. Damping suppresses the whipping response, and the suppression effects were found to increase as the distance from the explosion decreases. Moreover, damping is an important factor affecting the plastic hinge rotation angle of the girder, and therefore, cannot be ignored.

Investigation of the nonlinear slamming-induced whipping response of ships using a fully-coupled hydroelastoplastic method

Slamming-induced whipping is traditionally computed as the response of a linear-elastic structural model. However, in order to investigate the consequence of whipping on the hull girder’s collapse, the hydro-structure interaction must be performed in a fully-coupled approach where the nonlinearities of both domains are considered. Therefore, this paper presents a new approach developed for solving the fully-coupled hydroelastoplastic problem. The structural part is modeled as two non-uniform Timoshenko beams, connected with a nonlinear hinge, described by the nonlinear relation between the internal bending moment and the relative rotation angle. The hydrodynamic problem is solved using the 3D boundary element method, and the exact coupling between the structural and the 3D hydrodynamic models is achieved by constructing the hydrodynamic boundary value problem for each shape function of the finite element beam model. The hydroelastoplastic response is calculated using a hybrid nonlinear time-domain approach, allowing for very fast computation of the nonlinear whipping response. Finally, the nonlinear whipping response is calculated on a broad range of ships and it is compared to the linear whipping response in order to derive the whipping effectiveness coefficients. It is shown that the nonlinear structural behavior has a very small influence on the whipping response, and thus, the effectiveness of whipping should not be reduced.

Viscous fluid–flexible structure interaction analysis on ship springing and whipping responses in regular waves

A two-way fluid structure interaction (FSI) of CFD–FEA numerical method is adopted to predict ship motions, wave loads and hydroelastic responses in regular waves. In the FSI algorithm, the external fluid loads obtained from the CFD model and the motions and structural deformations obtained from the FEA model are exchanged between each other in an iteratively staggered implicit coupling regime in time domain. The motions, vertical accelerations and wave loads including springing and whipping responses of a flexible S175 container ship under different regular wave conditions predicted by the FSI co-simulation method are systematically analyzed. High order hull girder vertical vibrations of up to 12th order harmonic springing and up to 4-node whipping responses have been successfully reproduced, which indicates that the CFD–FEA co-simulation method is reliable and capable in simulating ship nonlinear hydroelastic responses in waves. Moreover, some complex flow phenomena such as slamming, green water on deck, wave breaking and splashing have also been well reproduced from the CFD simulation. It is believed that the present FSI method will exhibit significant advantage over the traditional ways used for ship seakeeping and hydroelasticity analyses.

The use of operational modal analysis and mode tracking for insight into polar vessel operations

Accurate dynamic models of flexible ship structures are required to predict structural vibration caused by environmental loads. Knowledge of dynamic or modal properties are important, for example, to study fatigue damage. In this paper, operational modal analysis (OMA) is used to identify the vibration characteristics of a polar vessel from full-scale acceleration measurements. Five modes are tracked over a range of different operating and environmental conditions, including calm, open water, two ice cases and an open water storm. Compared to the calm, open water conditions, vertical bending modes were generally affected the most by the operating environment, with natural frequency and damping increasing up to 3.7 and 349 %, respectively, in ice. Severity of two-node and three-node vertical bending responses, quantified using a root-mean-square value, were found to be especially large during the open water storm case. Temporal behaviour of two-node and three-node vertical bending due to wave-slamming further contained multiple whipping responses, pointing towards possible cumulative damage over a large number of stress cycles occurring at the midship. Higher damping in ice resulted in responses with lower magnitudes and shorter durations.

A study on whipping related double bottom response as well as its statistical characteristics based on full-scale measurements

Recently, the great enlargement of container ships has brought broad concern on the effect of whipping response. Meanwhile, the accompanying wider width of double bottom may cause more flexible responses of the double bottom structures. The numerical simulation studies have shown that the longitudinal stresses of the hold central bottom of a container ship due to the double bottom bending superimpose on the longitudinal stresses due to hull girder bending in both wave response component and vibrational response component. In this research, the authors firstly extract the full scale measurements data whose sea states are closest to that of numerical simulation among existing time series, with the purpose of analyzing correlation between double bottom bending and hull girder bending in wave response and vibrational response. As a result, studies from full scale measurements well verified the phenomenon that double bottom of larger container ship responds to forced vibration due to whipping excitation as observed in theoretical studies. Then, the statistical characteristics of correlation factor between hull girder bending stress and double bottom bending stress were investigated, based on relatively large number of data with regard to wave height and relative wave direction, as well as the classification between low- and high-frequency-dominant response cases. All these studies may contribute to future optimized operation, maintenance and design of ship.

Investigation on effects of springing and whipping on fatigue damages of ultra-large container ships in irregular seas

Springing and whipping play an important role in determining the fatigue damages of ultra-large container ships in waves, and it is widely acknowledged that the separation of the contributions of springing and whipping on fatigue damages is difficult. In this paper, the effects of springing and whipping on a targeted 21,000 TEU container ship are numerically investigated. The springing responses are calculated based on the linear 3D frequency domain hydroelasticity theory, while a 3D nonlinear time domain hydroelasticity formulation which couples the 3D hydrodynamic theory, 1D Timoshenko beam theory, 2D generalized Wagner method and 1D green water theory, is adopted to obtain the slamming-induced whipping response. Spectral analysis method is analyzed and compared with an indirect time domain method. Through investigating the characteristics of the accumulated fatigue damages with respect to the significant wave heights and characteristic wave periods of short-term sea states, the contributions from springing and whipping to the accumulated fatigue damages are generally separated for most short-term sea states. In addition, several short-term sea states are chosen to present detailed information on the extents to which springing and whipping increase the fatigue damages relative to the low-frequency structural responses counterpart.

Statistical Analysis of Vertical and Torsional Whipping Response Based on Full-Scale Measurement of a Large Container Ship

In this study, as a preliminary attempt to reveal the whipping response of large container ships in actual seaways, the stress monitoring data of an 8600 TEU large container ship were analyzed. The measurement lasted approximately five years, and using a large amount of data, we investigated how the sea state and operational conditions affected the whipping response. In addition, the midship longitudinal stresses were decomposed into hull girder vertical bending, horizontal bending, and torsional and axial components. Thereafter, we found that the whipping magnitude on the torsional and horizontal bending components is much smaller than that on the vertical bending component. Future research would include the analysis of a larger amount of data, analysis of other sensor data, and effects of various patterns of vibrational response on the ultimate strength and fatigue strength. The obtained results will benefit the future design and operation of large container ships for safer navigation.

Reliability analysis of hull girder ultimate strength for large container ships under whipping loads

The two incident reports for MSC (Mediterranean Shipping Company) Napoli in 2008 and MOL (Mitsui O.S.K. Lines) Comfort in 2015 both pointed out that whipping response was one main reason for inducing the catastrophes. Subsequently, International Association of Classification Societies (IACS) proposed a Unified Requirement (UR) S11A for ultimate strength evaluation of container ships, and main classification societies also updated their guidelines for whipping response. However, there are big differences in these requirements, and the safety level of ultimate strength under whipping loads is still unclear. This article is to find the effect of the whipping loads on hull girder reliability. Two large container ships 14500TEU and 19000TEU designed by China Classification Society (CCS) Rules are selected as case studies. Hull girder ultimate capacity in mid-ship section under hogging conditions is adopted as the dangerous failure mode, which is predicted by the increment-iterative method in IACS Common Structural Rules (CSR). The whipping effect on hull girder reliability is accounted for by a factor attaching on wave-induced moment. Then, a new evaluation criterion is proposed to evaluate hull girder ultimate strength for container ships under whipping loads, and sensitivity analysis of whipping effect is carried out. The conclusions in this article can provide a guidance for revising rule requirements in classification societies and optimising container ship structural design.

A study on prediction of whipping effect of very large container ship considering multiple sea states

In the design stage of the very large container ships, some methodologies for the whipping effects have been developed, but most of them are based on single sea state. We developed a methodology that considers multiple sea states. Fluid-structure Interaction (FSI) analyses with one dimensional structural model were carried out to capture slamming-induced transient whipping behaviors. Because of the nature of random phases of the applied wave spectra, the required period for entire FSI analyses was determined from the convergence study where the whipping effect became stable. Low pass filtering was applied to the transient whipping responses to obtain the hull girder bending moment processes. Peak counting method for the filtered whipping responses was used to obtain collection of the vertical bending moment peaks. The whipping effect from this new method is compared with that from based on single sea state approach. The efficiency and advantage of the new methodology are presented.

Dynamic and whipping response of the surface ship subjected to underwater explosion: experiment and simulation

ABSTRACT The dynamic and the whipping phenomena through an underwater explosion (UNDEX) experiments and simulations were verified. Furthermore, the comparison of the simulation and experimental results were conducted. The experiment was conducted at a reservoir and the MegaMEX was used as an explosive. The simulation was performed by combining the DAA-based USA code with the LS-Dyna which is a finite element analysis code, and for the gas bubble, the second-generation Geers–Hunter model was used. For the experiment, the natural frequency analysis of the structure was carried out to establish the explosion condition and four underwater explosion tests were carried out. Acceleration, velocity, strain and underwater pressures were measured by underwater explosion experiments, and acceleration, velocity and strain were compared. In this research, the whipping phenomenon by underwater explosion was confirmed through experiments and simulation. The results of this study are expected to contribute to the improvement of UNDEX simulation technique.

Experimental study on the asymmetric impact loads and hydroelastic responses of a very large container ship

This paper presents an experimental investigation of asymmetric impact effects on hydroelastic responses. A 1:64 scaled segmented ship model with U-shape open cross-section backbone was newly designed to meet elastic similarity conditions of vertical, horizontal and torsional stiffness simultaneously. Different wave heading angles and wavelengths were adopted in regular wave test. In head wave condition, parametric rolling phenomena happened along with asymmetric slamming forces, the relationship between them was disclosed at first time. The impact forces on starboard and port sides showed alternating asymmetric periodic changes. In oblique wave condition, nonlinear springing and whipping responses were found. Since slamming phenomena occurred, high-frequency bending moments became an important part in total bending moments and whipping responses were found in small wavelength. The wavelength and head angle are varied to elucidate the relationship of springing/whipping loads and asymmetric impact. The distributions of peaks of horizontal and torsional loads show highly asymmetric property.