Local water slamming impact on sandwich composite hulls

The local water slamming refers to the impact of a part of a ship hull on stationary water for a short duration during which high local pressures occur on the hull. We simulate slamming impact of rigid and deformable hull bottom panels by using the coupled Lagrangian and Eulerian formulation included in the commercial software LS-DYNA. We use the Lagrangian formulation to describe plane-strain deformations of the hull panel and consider geometric nonlinearities. The Eulerian formulation is used to analyze deformations of the water. Deformations of the hull panel and of the water are coupled through the hydrodynamic pressure exerted by water on the hull, and the velocity of particles on the hull wetted surface affecting deformations of the water. The continuity of surface tractions and the inter-penetrability of water into the hull are satisfied by using a penalty method. The computer code is verified by showing that the computed pressure distributions for water slamming on rigid panels agree well with those reported in the literature. The pressure distributions computed for deformable panels are found to differ from those obtained by using a plate theory and Wagner's slamming impact theory. We have also delineated jet flows near the edges of the wetted hull, and studied delamination induced in a sandwich composite panel due to the hydroelastic pressure.     

Dynamic buckling and plastic collapse of rectangular strips under axial slamming impact

The dynamic buckling and plastic collapse of elastic-plastic rectangular strips under axial slamming impact are investigated experimentally. The dynamic response of the specimens is measured by several back-to-back paris of strain gages located at different positions. According to the experimental records, the compressive and bending motions of the rectangular strips are analyzed. The strips exhibit three different critical dynamic conditions: buckling, plastic incipience and plastic collapse. Based on the response characters, three criteria are proposed which completely define the elastic-plastic dynamic behavior of rectangular strips under axial slamming impact with loading durations ranging from 14 to 18 milliseconds. These conditions are estimated by introducing three critical axial compressive strains. Moreover, the effect of geometric imperfection on the dynamic behavior of the strips is discussed.     

Comparison of slamming and whipping loads by fully coupled hydroelastic analysis and experimental measurement

This paper proposes a numerical method for analyzing whipping using a fully coupled hydroelastic model. The numerical analysis method utilizes a 3-D Rankine panel method, 1-D/3-D finite element methods, and a 2-D generalized Wagner model, which are strongly coupled in the time domain. The computational results were compared with those of a model test of an 18 000-TEU containership. The slamming pressures and whipping responses to regular waves for bow flare and stern slamming were compared. Furthermore, the slamming pressure was decomposed into its dynamic and static components. The numerical and experimental models produced similar results. In addition, the effects of the discretization and geometric approximation of the 2-D slamming sections were investigated.     

Local slamming impact of sandwich composite hulls

We develop a hydroelastic model based on a {3, 2}-order sandwich composite panel theory and Wagner’s water impact theory for investigating the fluid–structure interaction during the slamming process. The sandwich panel theory incorporates the transverse shear and the transverse normal deformations of the core, while the face sheets are modeled with the Kirchhoff plate theory. The structural model has been validated with the general purpose finite element code ABAQUS^®. The hydrodynamic model, based on Wagner’s theory, considers hull’s elastic deformations. A numerical procedure to solve the nonlinear system of governing equations, from which both the fluid’s and the structure’s deformations can be simultaneously computed, has been developed and verified. The hydroelastic effect on hull’s deformations and the unsteady slamming load have been delineated. This work advances the state of the art of analyzing hydroelastic deformations of composite hulls subjected to slamming impact.     

Delamination in sandwich panels due to local water slamming loads

We study delamination in a sandwich panel due to transient finite plane strain elastic deformations caused by local water slamming loads and use the boundary element method to analyze motion of water and the finite element method to determine deformations of the panel. The cohesive zone model is used to study delamination initiation and propagation. The fluid is assumed to be incompressible and inviscid, and undergo irrotational motion. A layer-wise third order shear and normal deformable plate/shell theory is employed to simulate deformations of the panel by considering all geometric nonlinearities (i.e., all non-linear terms in strain–displacement relations) and taking the panel material to be St. Venant–Kirchhoff (i.e., the second Piola–Kirchhoff stress tensor is a linear function of the Green–St. Venant strain tensor). The Rayleigh damping is introduced to account for structural damping that reduces oscillations in the pressure acting on the panel/water interface. Results have been computed for water entry of (i) straight and circular sandwich panels made of Hookean materials with and without consideration of delamination failure, and (ii) flat sandwich panels made of the St. Venant–Kirchhoff materials. The face sheets and the core of sandwich panels are made, respectively, of fiber reinforced composites and soft materials. It is found that for the same entry speed (i) the peak pressure for a curved panel is less than that for a straight panel, (ii) the consideration of geometric nonlinearities significantly increases the peak hydrodynamic pressure, (iii) delamination occurs in mode-II, and (iv) the delamination reduces the hydroelastic pressure acting on the panel surface and hence alters deformations of the panel.     

Servo-hydraulic System for Controlled Velocity Water Impact of Marine Sandwich Panels

Slamming, the impact between a marine craft’s hull and the water surface is a critical load case for structural design of marine vessels. The importance of hull slamming has led to a significant body of work to understand, predict and model these impacts. There is however, a lack of experimental data for validation, particularly for deformable panels and sandwich structures. This paper describes a high-velocity panel slamming test system that enables the generation of comprehensive and reliable experimental data on slamming impacts for both rigid and flexible panel structures. The pressure magnitudes, time-histories and spatial distributions resulting from testing of a nominally rigid panel have been compared with previous analytical, semi-empirical and experimental studies. Slamming impacts of a deformable sandwich panel are shown to cause different pressures to those from a rigid panel impact, resulting in increased transverse shear loading at the panel edge.     

Sloshing

本文列举了诸多工程领域中的液体共振运动现象,详细探讨了船舱中伴有剧烈流动的晃荡问题.描述了基于理论分析的非线性多模态方法,该方法便于波动稳定性分区、多分支解和物理稳定性的研究.强调了方形舱、垂向圆柱舱以及球形舱内伴有旋转和混沌（不规则波动）的三维流动的重要性.晃荡引起的砰击涉及到各种各样的内流条件,这些条件随液体深度与舱体长度之比而变化.针对棱柱状LNG舱,讨论了许多与流体力学和热力学参数、影响砰击载荷效应的水弹性以及模型实验缩尺比的物理现象.     

晃荡

本文列举了诸多工程领域中的液体共振运动现象,详细探讨了船舱中伴有剧烈流动的晃荡问题.描述了基于理论分析的非线性多模态方法,该方法便于波动稳定性分区、多分支解和物理稳定性的研究.强调了方形舱、垂向圆柱舱以及球形舱内伴有旋转和混沌(不规则波动)的三维流动的重要性.晃荡引起的砰击涉及到各种各样的内流条件,这些条件随液体深度与舱体长度之比而变化.针对棱柱状LNG舱,讨论了许多与流体力学和热力学参数、影响砰击载荷效应的水弹性以及模型实验缩尺比的物理现象.     

Coupled MPS-modal superposition method for 2D nonlinear fluid-structure interaction problems with free surface

In this paper, a coupled MPS-modal superposition method is developed for 2D nonlinear fluid-structure interaction problems. In this method, the rigid-body and relatively small elastic deformation are coupled together, which considers the mutual effect between them. The elastic deformation of the structure is represented by a mode superposition formulation, which is more efficient compared with FEM, regardless of the size of the structure. For 2D cases, if the first three modes are chosen to represent the flexible deformation of the structure, it only results in a 6×6 matrix equation to be solved. For the fluid motion, the modified Moving Particle Semi-implicit (MPS) method, which significantly reduces the fluctuation of pressure calculation of the original MPS method, is used.Two nonlinear problems, i.e. breaking-water-dam impacting a floating beam and flexible wedge slamming into the water are simulated to demonstrate the performance of the developed method. The numerical simulations show that this coupling model is capable of providing stable results that are generally in good agreement with the available experimental data. For the highly nonlinear case with very large rigid motions, the mutual effect between elastic deformation and rigid motions could accumulate to a relatively remarkable level shown by the curves of trajectories or acceleration history of the body mass centre. This also indicates the importance of mutual effect to analyse highly nonlinear FSI problems with large rigid-body motions and relatively small flexible deformation.     

Experimental investigation of hydrodynamic loads and pressure distribution during a pyramid water entry

In the maritime environment slamming is a phenomenon known as short duration impact of water on a floating or sailing structure. Slamming loads are local and could induce very high local stresses. This paper reports a series of impact test results and investigate the slamming loads and pressures acting on a square based pyramid. In this study the slamming tests have been conducted at constant velocity impact with a hydraulic high speed shock machine. This specific experimental equipment avoids the deceleration of the structure observed usually during water entry with drop tests. Three velocities of the rigid pyramid have been used (10, 13 and 15 m s⁻¹). Time-histories of local pressures, accelerations and slamming loads were successfully measured. The relationship between the pressure magnitude and the impact velocity is obtained and the spatial distribution of pressures on pyramid sides is characterized. The impact velocity was found to have a negligible influence in predicting the maximum pressure coefficient.     

Cross-well chaos and escape phenomena in driven oscillators

The paper is devoted to the study of common features in regular and strange behavior of the three classic dissipative softening type driven oscillators: (a) twin-well potential system, (b) single-well potential unsymmetric system and (c) single-well potential symmetric system.Computer simulations are followed by analytical approximations. It is shown that the mathematical techniques and physical concepts related to the theory of nonlinear oscillations are very useful in predicting bifurcations from regular, periodic responses to cross-well chaotic motions or to escape phenomena. The approximate analysis of periodic, resonant solutions and of period doubling or symmetry breaking instabilities in the Hill's type variational equation provides us with closed-form algebraic simple formulae; that is, the relationship between critical system parameter values, for which strange phenomena can be expected.     

Global Dynamics of a Rapidly Forced Cart and Pendulum

In this paper, we study emergent behaviors elicited by applying open-loop, high-frequency oscillatory forcing to nonlinear control systems. First, we study hovering motions, which are periodic orbits associated with stable fixed points of the averaged system which are not fixed points of the forced system. We use the method of successive approximations to establish the existence of hovering motions, as well as compute analytical approximations of their locations, for the cart and pendulum on an inclined plane. Moreover, when small-amplitude dissipation is added, we show that the hovering motions are asymptotically stable. We compare the results for all of the local analysis with results of simulating Poincaré maps. Second, we perform a complete global analysis on this cart and pendulum system. Toward this end, the same iteration scheme we use to establish the existence of the hovering periodic orbits also yields the existence of periodic orbits near saddle equilibria of the averaged system. These latter periodic orbits are shown to be saddle periodic orbits, and in turn they have stable and unstable manifolds that form homoclinic tangles. A quantitative global analysis of these tangles is carried out. Three distinguished limiting cases are analyzed. Melnikov theory is applied in one case, and an extension of a recent result about exponentially small splitting of separatrices is developed and applied in another case. Finally, the influence of small damping is studied. This global analysis is useful in the design of open-loop control laws.     

Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation

The global bifurcations in mode interaction of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation are investigated with the case of the 1:1 internal resonance, the average equations representing the evolution of the amplitudes and phases of the interacting normal modes exhibiting complex dynamics. A global perturbation method, i.e., the higher-dimensional Melnikov method and its extensions proposed by Kova?i? and Wiggins, is utilized to analyze the global bifurcations for the rectangular metallic plate. A sufficient condition for the existence of a Silnikov-type homoclinic orbit is obtained, which implies that chaotic motions may occur for this class of rectangular metallic plates. Finally, numerical results are presented to confirm these analytical predictions.     

Dual mode vibration isolation based on non-linear mode localization

We study a non-linear vibration isolation system capable of (a) isolating its upper part (the ‘machine’) from periodic disturbances generated at its base; and (b) simultaneously isolating its base from periodic disturbances generated at the level of the machine. By making use of essentially non-linear (e.g. non-linearizable) stiffness elements we completely eliminate resonances close to linearized modes, thus achieving vibration isolation over an extended frequency range. Instead, we prove the existence of branches of localized steady state motions in the frequency domain. Indeed, these localized forced motions are principally responsible for fulfilling the dual mode vibration isolation objective of this work. The method of analysis followed is based on complexification and separation of the dynamics into ‘slow’ varying and ‘fast’-varying parts. Direct numerical simulations confirm the analytical predictions. An analytical method is then developed for determining the placement of the localized branches in the frequency domain as the system parameters vary; this permits the design of the vibration isolation system for best performance in a specified frequency range. The vibration isolation performance achieved by the non-linear system considered has no counterpart in linear theory.     

Analytical solution for squeeze film damping of MEMS perforated circular plates using Green’s function

Squeezed air film between two closely spaced vibrating microstructures is the important source of energy dissipation and has profound effects on the dynamics of microelectromechanical systems (MEMS). Perforations in the design are one of the methods to model these damping effects. The literature reveals that the analytical modeling of squeeze film damping of perforated circular microplates is less explored; however, these microplates are also an imperative part of the numerous MEMS devices. Here, we derive an analytical model of transverse and rocking motions of a perforated circular microplate. A modified Reynolds equation that incorporates compressibility and rarefaction effects is utilized in the analysis. Pressure distribution under the vibrating microplate is derived by using Green’s function and also derived by finite element method (FEM) to visualize the pressure distribution under perforated and non-perforated areas of the microplate. The analytical damping results are validated with previous renowned analytical models and also with the FEM results. The outcomes confirm the potential of the present analytical model to accurately predict the squeeze film damping parameters.     

基于SPH法的返回舱入水载荷模拟分析

返回舱水上着落前期面临较大砰击,为研究过程中受到的砰击载荷,基于光滑粒子流体动力学(SPH)气-液两相流算法,首先通过模拟平板和楔形体两种算例模型的入水过程,并与相关文献的试验结果进行对比,验证算法的有效性。在此基础上,对返回舱的入水过程进行模拟。结果显示,两种算例模型的计算结果与相关文献试验结果吻合良好。返回舱入水速度和倾角对砰击有较大影响并且过程中存在二次砰击现象。砰击载荷随入水速度增大而增加。第一次砰击载荷峰值随倾角增大而减小,第二次砰击载荷峰值随倾角增大先增后减。结果表明,SPH气-液两相流算法能够较好地模拟返回舱入水过程。     

Chaos and instability in a power system: Subharmonic-resonant case

The response of a single-machine quasi-infinite busbar system to the simultaneous occurrence of principal parametric resonance and subharmonic resonance of order one-half is investigated. By numerical simulations we show the existence of oscillatory solutions (limit cycles), period-doubling bifurcations, chaos, and unbounded motions (loss of synchronism). The method of multiple scales is used to derive a second-order analytical solution that predicts (a) the onset of period-doubling bifurcations, which is a precursor to chaos and unbounded motions (loss of synchronism), and (b) saddle-node bifurcations, which may be precursors to loss of synchronism.     

On Modal Interaction,Stability and Nonlinear Dynamics of a Model Two D.O.F. Mechanical System Performing Snap-Through Motion

Dynamics of a simple two degrees of freedom (d.o.f.) mechanical system is considered, to illustrate the phenomena of modal interaction. The system has a natural symmetry of shape and is subjected to symmetric loading. Two stable equilibrium configurations are separated by an unstable one, so that the model system can perform cross-well oscillations. Nonlinear statics and dynamics are considered, with the emphasis on detecting conditions for instability of symmetric configurations and analysis of bi-modal non-symmetric motions. Nonlinear local dynamics is analyzed by multiple scales method. Direct numerical integration of original equations of motions is carried out to validate analysis of modulation equations. In global dynamics (analysis of cross-well oscillations) Lyapunov exponents are used to estimate qualitatively a type of motion exhibited by the mechanical system. Modal interactions are demonstrated both in the local dynamics and for snap-through oscillations, including chaotic motions. This mechanical system may be looked upon as a lumped parameters model of continuous elastic structures (spherical segments, cylindrical panels, buckled plates, etc.). Analyses performed in the paper qualitatively describe complicated phenomena in local and global dynamics of original structures.