Behavior of a Semi-Infinite Ice Cover Under a Uniformly Moving Load

This paper consideres the behavior of a semi-infinite ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a load moving with constant velocity along the edge of the cover at some distance from it. The ice cover is modeled by a thin elastic plate of constant thickness. In a moving coordinate system, the deflection of the plate is assumed to be steady. An analytic solution of the problem is obtained using the Wiener–Hopf technique. The wave forces, the deflection of the plate, and the elevation of the free surface of the fluid at different velocities of the load are investigated.     

Solitary wave packets beneath a compressed ice cover

A family of plane solitary wave packets of a small (but finite) amplitude on the surface of an ideal incompressible fluid of finite depth beneath an ice cover is described. The solitary wave trains correspond to solutions of the two-dimensional system of Euler’s equations of an ideal incompressible fluid of the type of a traveling wave which decreases at infinity and has identical phase and group velocities. The ice cover is simulated by an elastic Kirchhoff-Love plate freely floating on the fluid surface in the compressed state.     

Behavior of a semi-infinite ice cover under periodic dynamic impact

Oscillations of a semi-infinite ice cover in an ideal incompressible liquid of finite depth under local time-periodic axisymmetric load are considered. The ice cover is simulated by a thin elastic plate of constant thickness. An analytical solution of the problem is obtained using the Wiener–Hopf method. The asymptotic behavior of the amplitudes of oscillations of the plate and the liquid in the far field is studied. It is shown that the propagation of waves in the far field is uneven: in some directions, the waves propagate with a significantly greater amplitude.     

Radiation and Diffraction of Water Waves by a Submerged Body with Ice Cover in Finite Depth

This paper presents the three-dimensional Green-function method to predict the radiation and diffraction of water waves by a submerged body in water of uniform finite depth with an ice cover. The fluid is assumed to be perfect and irrotational, the ice is modelled as an elastic plate. The zero-speed Green function of finite depth satisfying the linearized covered-surface condition is derived in three dimensions, the numerical results for the Green function and its derivatives are given. The integral equations are established by distributing the source strength on the body surface, the radiation and diffraction problems are solved. A submerged sphere is taken as an example, the effects of the water depth and the flexural rigidity of ice cover on hydrodynamics are analysed, and the good agreement with the analytical solutions reveals that the present method is correct and reliable.

     

Unsteady gravity-elastic and gravity-capillary ship waves

The development of three-dimensional waves generated by a region of pressures moving uniformly and rectilinearly over the surface of a thin elastic isotropic plate covering an ideal fluid layer of finite depth is investigated. The pressures act starting at a certain instant. A qualitative similarity between the waves occurring and gravity-capillary waves is noted. The calculations are made for an ice cover. This model problem permits examining a number of properties of the oscillations of the ice cover occurring when hauling freight over ice roads, landing and takeoff of aircraft from ice fields, etc. [1]. The development of ship waves in a fluid of finite depth in the absence of a floating plate was investigated in [2, 3] and gravity-capillary waves were studied in [4–6]. Certain properties of steady three-dimensional waves occurring during movement of a load over the surface of a floating elastic plate were established in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 26–32, September–October, 1978.     

Interaction of surface and flexural-gravity waves in ice cover with a vertical wall

The problem of the interaction of surface and flexural-gravity waves with a vertical barrier is solved in a two-dimensional formulation. It is assumed that the fluid is ideal and incompressible, has infinite depth, and is partially covered with ice. The ice cover is modeled by an elastic plate of constant thickness. The eigenfrequencies and eigenmodes of oscillation of the floating elastic ice plate, the deflection and deformation of ice, and the forces acting on the wall are determined.     

Action of periodic surface pressure on an ice cover in the vicinity of a vertical wall

This paper presents the solution of the linear hydroelastic problem for steady forced vibrations of a semi-infinite ice cover under the effect of localized external load. The ice cover is simulated by a viscoelastic thin plate, the thickness of the fluid layer is assumed to be small, and the shallow water theory is used. The fluid is limited by a solid vertical wall, and the rectilinear edge of the elastic plate adjacent to the wall can be both free and clamped. The solution is obtained with the help of the Fourier integral transform. The behavior of the ice cover is studied depending on the frequency of the external load and boundary conditions on the edge of the plate. It is shown that, in the case of a free edge of the plate, there are considerable deflections on the edge, which could be comparable with deflections at the center of the pressure impact region. It is established that, due to the existence of wave movements of the type of edge waves, the external load energy is transferred to larger distances along the free edge, and there are significant bending moments on the edge of the clamped plate, which can lead to fracture of the ice cover with sufficiently great intensity of the external load.     

Hydrodynamic loads acting on an oscillating cylinder submerged in a stratified fluid with ice cover

The two-dimensional problem of steady oscillations of a horizontal cylinder submerged in a linearly stratified fluid layer whose upper boundary is ice cover is considered in a linear treatment using the Boussinesq approximation. The method of mass sources distributed along the body contour is used for the internal wave generation regime, and the integral equation for the disturbed pressure in the fluid is used for the regime of no internal waves. The hydrodynamic load acting on the body was calculated as a function of the oscillation frequency for the case of a continuous ice cover and for special cases (broken ice, free surface, and rigid lid).     

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height circular cylinder

The influence of a wake-mounted splitter plate on the flow around a surface-mounted circular cylinder of finite height was investigated experimentally using a low-speed wind tunnel. The experiments were conducted at a Reynolds number of Re=7.4×10⁴ for cylinder aspect ratios of AR=9, 7, 5 and 3. The thickness of the boundary layer on the ground plane relative to the cylinder diameter was δ/D=1.5. The splitter plates were mounted on the wake centreline with negligible gap between the base of the cylinder and the leading edge of the plate. The lengths of the splitter plates, relative to the cylinder diameter, ranged from L/D=1 to 7, and the plate height was always equal to the cylinder height. Measurements of the mean drag force coefficient were obtained with a force balance, and measurements of the vortex shedding frequency were obtained with a single-component hot-wire probe situated in the wake of the cylinder–plate combination. Compared to the well-studied case involving an infinite circular cylinder, the splitter plate was found to be a less effective drag-reduction device for finite circular cylinders. Significant reduction in the mean drag coefficient was realized only for the finite circular cylinder of AR=9 with intermediate-length splitter plates of L/D=1–3. The mean drag coefficients of the other cylinders were almost unchanged. In terms of its effect on vortex shedding, a splitter plate of sufficient length was able to suppress Kármán vortex shedding for all of the finite circular cylinders tested. For AR=9, vortex shedding suppression occurred for L/D≥5, which is similar to the case of the infinite circular cylinder. For the smaller-aspect-ratio cylinders, however, the splitter plate was more effective than what occurs for the infinite circular cylinder: for AR=3, vortex shedding suppression occurred for all of the splitter plates tested (L/D≥1); for AR=5 and 7, vortex shedding suppression occurred for L/D≥1.5.     

Stress-strain state of ice cover during aircraft takeoff and landing

We consider the linear unsteady motion of an IL-76TD aircraft on ice. Water is treated as an ideal incompressible liquid, and the liquid motion is considered potential. Ice cover is modeled by an initially unstressed uniform isotropic elastic plate, and the load exerted by the aircraft on the ice cover with consideration of the wing lift is modeled by regions of distributed pressure of variable intensity, arranged under the aircraft landing gear. The effect of the thickness and elastic modulus of the ice plate, takeoff and landing regimes on stress-strain state of the ice cover used as a runway.     

圆筒装置内爆炸压力载荷特性实验研究

为了研究密闭环境压力载荷波形特征和分布规律,开展了长径比2∶1圆筒装置的TNT装药内爆炸实验,获取了圆筒壁面、端盖板表面的压力载荷数据,结合仿真计算结果,研究了圆筒壁面、端盖板上压力载荷波形特征和形成机理,建立了压力载荷峰值的表征模型,并开展了模型验证。结果表明,圆筒壁面与盖板压力载荷波形不完全相同,壁面压力载荷按照爆心距由近到远,从显著的单波峰向多峰值变化,在近场区域压力载荷衰减特性与一定炸高自由地面冲击波类似;盖板上压力载荷呈多波峰特点,中心区域压力载荷最大峰值大于首峰值的3倍,角隅区域大于首峰值6倍;圆筒壁面上的压力载荷最大峰呈现凹型分布规律。该研究结果可为密闭环境内爆载荷的特性分析和结构毁伤评估提供参考。     

基于S-ALE方法的圆柱体垂直出水破冰研究

以往针对结构物垂直贯穿冰层破裂的研究多不考虑水的作用, 与实际应用场景不符. 本文应用 LS-DYNA 有限元软件建立了基于结构化-任意拉格朗日欧拉(S-ALE)流固耦合方法及罚函数接触算法的冰?水?结构物耦合作用数值模拟方法. 采用欧拉算法描述空气域和水域, 采用拉格朗日算法描述圆柱体结构和冰层结构, 使用弹塑性应变率模型表征冰材料力学性质. 自主搭建了圆柱体垂直贯穿冰层试验台架, 验证了有限元方法计算结构物?冰层相互作用问题的可行性. 通过模拟圆柱体垂直出水破冰过程, 并与无水环境下圆柱体垂直贯穿冰层破裂过程进行对比. 结果表明: 有水环境下结构物?冰层间作用存在“水垫效应”; 冰层突破载荷极值大小与有、无水环境无显著变化; 有水环境下的结构物突破冰层冰载荷持续时间明显长于无水环境下持续时间; 有水环境冰层弹性变形阶段更长, 且有水环境冰层挠度变化大于无水环境下的挠度变化. 本文研究成果为极地冰区环境下结构物垂直出水破冰的结构强度计算及优化设计提供了研究基础.      

Surface wave diffraction at a crack in sheet ice

The time-periodic motions of a liquid layer of finite depth beneath an ice sheet with a straight infinite crack having a periodic dependence on the horizontal coordinate in the direction of the crack are considered. The ice sheet is simulated by a thin elastic plate. It is assumed that the thickness of the plate changes abruptly across the crack. The problems of plane-wave diffraction at a crack, plane-wave diffraction atN cracks in a uniform ice sheet, and plane-wave reflection from a rigid wall are solved. The effect of the pre-existing state of stress of the ice sheet on the properties of the reflected waves is investigated. The condition of nontransmission of fix-frequency waves beneath the edge of the ice is obtained.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 93–102, March–April, 1993.     

Off-plane concentric penny-shaped crack in a finite cylinder under arbitrary torsion

The Hankel transform and Fourier series are employed to obtain the stress intensity factor for a penny-shaped crack situated away from the mid-plane of a finite radius cylinder under torsion. Results for the case of a concentric penny-shaped crack off the mid-plane of a circular plate with infinite radius can be derived. Another special case is the Mode III deformation of a concentric penny-shaped crack in the mid-plane of a finite cylinder.     

Action of a Local Time-Periodic Load on an Ice Sheet with a Crack

The problem of vibrations of an ice sheet with a rectilinear crack on the surface of an ideal incompressible fluid of finite depth under the action of a time-periodic local load is solved analytically using the Wiener–Hopf technique. Ice cover is simulated by two thin elastic semi-infinite plates of constant thickness. The thickness of the plates may be different on the opposite sides of the crack. Various boundary conditions on the edges of the plates are considered. For the case of contact of plates of the same thickness, a solution in explicit form is obtained. The asymptotics of the deflection of the plates in the far field is studied. It is shown that in the case of contact of two plates of different thickness, predominant directions of wave propagation at an angle to the crack can be identified in the far field. In the case of contact of plates of the same thickness with free edges and with free overlap, an edge waveguide mode propagating along the crack is excited. It is shown that the edge mode propagates with maximum amplitude if the vertical wall is in contact with the plate. Examples of calculations are given.     

水下成组药包爆炸作用下冰盖动态响应数值模拟

利用大型有限元软件ANSYS/LS-DYNA建立了成组药包水下爆炸冰盖动态响应模型,通过数值计算,得到了冲击波峰值压力变化规律,峰值压力与理论计算结果基本吻合。本文分析了冰盖在成组药包水下爆炸冲击载荷下的应力分布及垂直位移响应特征。结果表明,冰盖迎爆面为压缩破坏,背爆面为拉伸破坏,两者数值均十分接近,其中迎爆面最大压力值可达18.12MPa,冰盖近爆炸点最大垂直位移为1.211cm,两药包连线中点最小位移为0.15cm,达到脆性冰盖形成贯通裂隙的基本条件,从而确定了冰盖在水下成组药包大间距布设条件下,其动态破坏形式是以产生裂隙为主要特征。     

Finite Oscillations of a Cylinder in a Coaxial Duct Subjected to Annular Compressible Flow

As a generalization considering small fluid-structural vibrations, the present paper examines the finite magnitude oscillatory motion of an elastically supported rigid cylinder in a cylindrical rigid duct conveying a compressible flow. The fluid is assumed to be inviscid and irrotational and free purely transverse vibrations of the body are dealt with. The governing equations of motion are the fully nonlinear Euler equations together with the continuity equation and a state equation (here for an ideal gas), the ordinary differential equation for the vibrating cylinder, and the kinematical transition and boundary conditions at the moving contact interface between fluid and body and the outside fluid border, respectively. A pertubation analysis is performed to calculate not only the dynamic characteristics for small coupled oscillations but also the corrections due to the inherent nonlinearities of the vibroacoustic problem. To make the calculation steps more transparent, the simpler problem of a two-dimensional channel flow between a rigid wall and an elastically supported rigid plate is also included in the present study. As an outlook, the influence of flexibility of the cylinder (or the plate) is addressed and the problem of forced vibrations is touched. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling ocean wave propagation under sea ice covers

Operational ocean wave models need to work globally, yet current ocean wave models can only treat ice covered regions crudely. The purpose of this paper is to provide a brief overview of ice effects on wave propagation and different research methodology used in studying these effects. Based on its proximity to land or sea, sea ice can be classified as: landfast ice zone, shear zone, and the marginal ice zone. All ice covers attenuate wave energy. Only long swells can penetrate deep into an ice cover. Being closest to open water, wave propagation in the marginal ice zone is the most complex to model. The physical appearance of sea ice in the marginal ice zone varies. Grease ice, pancake ice,brash ice, floe aggregates, and continuous ice sheet may be found in this zone at different times and locations. These types of ice are formed under different thermal-mechanical forcing. There are three classic models that describe wave propagation through an idealized ice cover: mass loading,thin elastic plate, and viscous layer models. From physical arguments we may conjecture that mass loading model is suitable for disjoint aggregates of ice floes much smaller than the wavelength, thin elastic plate model is suitable for a continuous ice sheet, and the viscous layer model is suitable for grease ice. For different sea ice types we may need different wave ice interaction models. A recently proposed viscoelastic model is able to synthesize all three classic models into one. Under suitable limiting conditions it converges to the three previous models. The complete theoretical framework for evaluating wave propagation through various ice covers need to be implemented in the operational ocean wave models. In this review, we introduce the sea ice types, previous wave ice interaction models, wave attenuation mechanisms,the methods to calculate wave reflection and transmission between different ice covers, and the effect of ice floe breaking on shaping the sea ice morphology. Laboratory experiments,field measurements and numerical simulations supporting the fundamental research in wave-ice interaction models are discussed. We conclude with some outlook of future research needs in this field.     

Initial-Value Problem on the Behavior of an Ice Cover under the Load in the Presence of Shear Current

Fluid Dynamics - The solution to the problem on the behavior of an ice cover on the surface of an ideal incompressible fluid of finite depth under a local pressure domain in the presence of a shear...     

Uni-modal destabilization of a visco-elastic floating ice layer by wind stress

A destabilization by wind stress of a homogeneous visco-elastic ice layer of infinite horizontal extent and finite thickness floating on a water layer of finite depth is studied. The water is assumed to be weakly compressible; the viscous dissipation in the water layer is shown to be negligible compared to that in the ice layer. In the model, we assume that a homogeneous wind shear stress is applied to the upper surface of the ice layer at near field and the compression within the ice layer is fixed below the maximum admissible value, i.e. below the value above which ice can no longer be treated as an elastic material. The effect of viscosity is shown to stabilize the acoustic mode and all the unstable seismic modes that in a purely elastic model, treated by Brevdo and Il'ichev [Brevdo, L., Il'ichev, A., 2001. Multi-modal destabilization of a floating ice layer by wind stress. Cold Reg. Sci. Technol. 33, 77–89], possess unbounded growth rates for a growing wave number. The buckling mode is unstable in the domain of parameters considered. In all the cases treated, the model is marginally absolutely stable. The localized unstable disturbances propagate against the wind. The spatially amplifying waves in the model amplify in the direction opposite to the wind direction. The stability results are well approximated by those in a Kirchoff–Love thin ice plate model.