Forced vibrations of a beam elastically restrained against rotation and carrying a spring–mass system

An exact solution for the title problem is obtained in closed form fashion in the case of a Bernoulli–Euler beam. It is assumed that the exciting force is applied to the mass which is elastically mounted on the beam. The mathematical model constitutes a first order approximation to a motor or engine elastically mounted on a structural element. The operation of the machine generates a transverse, sinusoidally varying force. The problem is of basic interest in mechanical, naval and ocean engineering systems from the point of view of the determination of dynamic displacements and stresses; sound radiation calculations, etc. The present problem arose in connection with the mounting of an engine on a structural beam in a small naval vessel and when excessive vibrational level was noted. This study was undertaken in order to understand the physical problem and to correct the mechanical situation     

Simulation of Random Waves and Associated Laminar Bottom Shear Stresses

This work presents a new approach for simulating the random waves in viscous fluids and the associated bottom shear stresses. By generating the incident random waves in a numerical wave flume and solving the unsteady two-dimensional Navier-Stokes equations and the fully nonlinear free surface boundaiy conditions for the fluid flows in the flume, the viscous flows and laminar bottom shear stresses induced by random waves axe determined. The deterministic spectral amplitude method implemented by use of the fast Fourier transform algorithm was adopted to generate the incident random waves. The accuracy of the numerical scheme is confirmed by comparing the predicted wave spectrum with the target spectrum and by comparing the nanlerical transfer function between the shear stress and the surface elevation with the theoretical transfer function. The maximum bottom shear stress caused by random waves, computed by this wave model, is compared with that obtained by Myrhaug＇ s model （1995）. The transfer function method is also employed to determine the maximum shear stress, and is proved accurate.     

An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: II. Breaking waves

The evaluation of the wave-induced liquefaction potential is particularly important for coastal engineers involved in the design of marine structures. Most previous investigations of the wave-induced liquefaction have been limited to two-dimensional non-breaking waves. In this paper, the integrated three-dimensional poro-elastic model for the wave-seabed interaction proposed by [Zhang, H., Jeng, D.-S., 2005. An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: I. A sloping seabed. Ocean Engineering 32(5/6), 701–729.] is further extended to simulate the seabed liquefaction potential with breaking wave loading. Based on the parametric study, we conclude: (1) the liquefaction depth due to breaking waves is smaller than that of due to non-breaking waves; (2) the degree of saturation significantly affects the wave-induced liquefaction depth, and no liquefaction occurs in full saturated seabed, and (3) soil permeability does not only significantly affect the pore pressure, but also the shear stresses distribution.     

Long-term distribution of seabed shear stresses beneath random waves

The long-term distribution of seabed shear stresses under random waves is presented. The approach combines short-term distribution of maximum bottom shear stresses with a joint frequency table of significant wave height and peak period. An example of application is given where the long-term probability of exceeding a given level of the maximum bottom shear stress in the central North Sea is presented. The example includes estimation of the return period of the critical shear stress for sheet flow conditions, as well as the bottom shear stresses associated with the 1, 10 and 100 years return periods.     

磨刀门拦门沙区域枯季波流共同作用近底切应力和泥沙运动研究

On the basis of the measurement data pertaining to waves, current, and sediment in February 2012 in the mouth bar of the Modaomen Estuary, the Soulsby formulae with an iterative method are applied to calculating bottom shear stresses （BSS） and their effect on a sediment resuspension. Swell induced BSS have been found to be the most important part of the BSS. In this study, the correlation coefficient between a wavecurrent shear stress and SSC is 0.86, and that between current shear stresses and SSC is only 0.40. The peaks of the SSC are consistent with the height and the BSS of the swell. The swell is the main mechanism for the sediment re-suspension, and the tidal current effect on sediment re-suspension is small. The peaks of the SSC are centered on the high tidal level, and the flood tide enhances the wave shear stresses and the SSC near the bottom. The critical shear stress for sediment re-suspension at the observation station is between 0.20 and 0.30 N/m2. Tidal currents are too weak to stir up the bottom sediment into the flow, but a WCI （wave-current interaction） is strong enough to re-suspend the coarse sediment.     

Strength design method for tubing hanger of subsea christmas tree against big temperature difference

The tubing hanger is an important component of the subsea Christmas tree, experiencing big temperature difference which will lead to very high thermal stresses. On the basis of API 17D/ISO 13628-4 and ASME VIII-1, and by comprehensively considering the erosion of oil and the gravity load of the tubing, a calculation model is established by regarding design pressure and thermal stress, and the method for designing the tubing hanger of the horizontal Christmas tree under big temperature difference condition is developed from the fourth strength theory. The proposed theory for strength design of the tubing hanger in big temperature difference is verified by numerical results from ABAQUS.     

Calculation of stresses in concrete ocean structures subjected to steady and time-varying temperatures,as influenced by creep

The stress redistribution brought about by differential thermal creep in non-uniformly heated concrete structures is considered. Theory is presented which permits stresses to be evaluated in both the transient creep phase and in the limiting steady-state condition, from direct procedures, when temperatures are either time-invariant or vary cyclically in time. Illustrative numerical examples are presented and these reflect the dominant behaviour of flexurally restrained sections as occur in the walls of concrete oil containment structures. They are used also, to highlight some of the influential parameters on the stresses, e.g. magnitude of temperature crossfall through wall, ratio of maximum to minimum temperatures, and the nature of the cyclic variations of temperature with time.It is concluded that creep, coupled with non-uniform temperature, causes significant time-dependent variations of the stresses to occur. The theory presented forms a useful means of making stress predictions for specified states of temperature and helps to assess the probability of possible cracking in sections which might otherwise be assumed to be ‘safe’ from a conventional elastic calculation.The analyses relate to prestressed sections where cracking does not dominate, and to stress levels in the ‘working’ range for which creep is linearly related to stress.     

Seabed shear stresses under irregular waves plus current from Monte Carlo simulations of parameterized models

Shear stresses on a rough seabed under irregular waves plus current are calculated. Parameterized models valid for regular waves plus current have been used in Monte Carlo simulations, assuming the wave amplitudes to be Rayleigh-distributed. Numerical estimates of the probability distribution functions are presented. For waves only, the shear stress maxima follow a Weibull distribution, while for waves plus current, both the maximum and time-averaged shear stresses are well represented by a three-parameter Weibull distribution. The behaviour of the maximum shear stresses under a wide range of wave-current conditions has been investigated, and it appears that under certain conditions, the current has a significant influence on the maximum shear stresses. Results of comparison between predictions and measurements of the maximum bottom shear stresses from laboratory and field experiments are presented.     

Application of a BEM time stepping algorithm in understanding complex unsteady propulsion hydrodynamic phenomena

We solve the problem of unsteady potential flow around a system of arbitrarily moving rigid or flexible, lifting or non-lifting bodies, in an infinite fluid free of distributed vorticity. For the solution we use a time stepping algorithm and a potential based formulation of the corresponding free BVP. Nonlinear free shear layer dynamics are included in our modeling. This is a major innovation in treating complex unsteady propulsion problems since no simplifying assumptions (like that of a helicoidal wake) are used regarding the wake model. Bilinear quadrilateral elements are used to describe body and shear layer geometry at each time t. Three types of Kutta conditions can be alternatively applied for the determination of the shed vorticity from lifting bodies. The theoretical and numerical aspects of the method are presented followed by a number of applications, elucidating the qualitative and quantitative physical characteristics of a number of complex unsteady propulsion problems.     

On the fluid structure interaction of a marine cycloidal propeller

Marine cycloidal propulsion system is efficient in maneuvering ships like tugs, ferries, etc. It is capable of vectoring thrust in all direction in a horizontal plane. When used in pair, the system enables a vessel to perform maneuvers like moving sideways, perform rotation about a point, i.e. turning diameter of its own length, etc. In this system, the propeller blades have to change their angle of attack at different angular position of the disc. Due to this reason, the inflow velocity vector to propeller blades changes continuously. The propeller blade oscillates about a vertical axis passing through its body and at the same time rotates about a point. Superposed on these motions is the dynamics of the ship on which the propulsion system is installed. This results in a formidable and challenging hydrodynamics problem. Each of the propeller blade sections could be considered as an aerofoil operating in combined heave and pitch oscillation mode. Due to the constantly varying inflow velocity, the hydrodynamic flow is unsteady. The unsteady hydrodynamic flow is simulated by incorporating the effect of shed vortices at different time instant behind the trailing edge. Due to the kinematics of the problem, the blade is subjected to higher structural deformation and vibration load. The structural deformation and vibration when coupled with the hydrodynamic loading add another level of complexity to the problem. In this paper, the variation of hydrodynamic load on the propeller blade due to steady and unsteady flow is compared. We also model the structural dynamics of the blade and study its effect on the hydrodynamic loading. Finally, we couple the structural dynamics with hydrodynamics loading and study its influence on the propeller blade for different operating regimes.     

结合抛物型缓坡方程计算波浪辐射应力

将波浪辐射应力与抛物型缓坡方程中的待求变量联系起来,提出了一种计算辐射应力的新方法,并用有限差分法对控制方程进行了数值求解。数值结果表明这种方法精度高、编程简单、求解快速,可用于实际大区域波浪辐射应力的计算。     

Downward transfer of momentum by wind-driven waves

A model for the downward transfer of wind momentum is derived for growing waves. It is shown that waves, which grow due to an uneven pressure distribution on the water surface or a wave-coherent surface shear stress have horizontal velocities out of phase with the surface elevation. Further, if the waves grow in the x-direction, while the motion is perhaps time-periodic at any fixed point, the Reynolds stresses associated with the organized motion are positive. This is in agreement with several field and laboratory measurements which were previously unexplained, and the new theory successfully links measured wave growth rates and measured sub-surface Reynolds stresses. Wave coherent air pressure (and/or surface shear stress) is shown to change the speed of wave propagation as well as inducing growth or decay. From air pressure variations that are in phase with the surface elevation, the influence on the waves is simply a phase speed increase. For pressure variations out of phase with surface elevation, both growth (or decay) and phase speed changes occur. The theory is initially developed for long waves, after which the velocity potential and dispersion relation for linear waves in arbitrary depth are given. The model enables a sounder model for the transfer to storm surges or currents of momentum from breaking waves in that it does not rely entirely on ad-hoc turbulent diffusion. Future models of atmosphere-ocean exchanges should also acknowledge that momentum is transferred partly by the organized wave motion, while other species, like heat and gasses, may rely totally on turbulent diffusion. The fact that growing wind waves do in fact not generally obey the dispersion relation for free waves may need to be considered in future wind wave development models.     

A numerical method for the solution of a line source under a free surface

A modified source-and-dipole type singularity panel method is proposed to calculate the flow properties for an oscillating arbitrary body in the presence of a free surface. The technique is based on Green's identity whereby the boundary value problem is expressed as a boundary integral equation which is solved numerically. The free-space Green function is used in the integral equation. To demonstrate the feasibility of the method, the problem of a pulsating submerged line source under a free surface is treated and results are compared with the exact solution.An excellent agreement with the theory is obtained for panel density of about ten panels per wavelength and paneled water surface length of two wavelengths with very low computing times, indicating the feasibility of the method for unsteady water wave problems.     

Propagation of internal Airy and Fresnel waves in unsteady media

A problem on the propagation of internal Airy and Fresnel waves in unsteady stratified media is solved by the running wave method. An eikonal equation is derived for the determination of the location of wave fronts. Conservation laws are obtained which allow us to determine the evolution of the wave width and amplitude with time. A problem on the propagation of an Airy wave from a pointwise mass source moving in unsteady media is solved numerically.Translated by Mikhail M. Trufanov.     

On a translating and transversely oscillating cylinder. Part 1—The effect of the strouhal number on the hydrodynamic forces and the near-wake structure

The problem of unsteady, laminar flow past a circular cylinder which starts translating and oscillating impulsively from rest in a viscous fluid is numerically investigated at a Reynolds number of R = 10³. The flow is incompressible and two-dimensional, and the cylinder oscillations are harmonic. The transverse oscillations are only allowed when the maximum oscillatory-to-translational velocity ratio is 0.5. The investigation is based on an implicit finite difference scheme for integrating the unsteady Navier-Stokes equations together with the mass-conservation equation in their vorticity stream function formulation. A non-inertial coordinate transformation is used so that the grid mesh remains fixed relative to the accelerating cylinder. Present calculations are performed within the range of sufficiently large oscillation amplitude to induce separation. The time variation of the in-line and transverse force coefficients are presented. The study also focuses on the laminar asymmetric flow structure in the near-wake region. In this flow regime, it is found that there is alternate shedding of vortices from either side of the cylinder over an oscillation cycle (as predicted experimentally); this is the classical mode of vortex shedding leading to formation of the Kármán street.     

Generation of waves in a bounded basin by a traveling front of atmospheric pressure and the field of wind stresses induced by this front

A plane problem of generation of barotropic seiches in a bounded rotating basin by traveling atmospheric fronts is studied within the framework of the linear theory of long waves. The front is characterized by disturbances of the baric field and the corresponding field of tangential wind stresses. We deduce the modified Ackerblom formulas for the wind stresses according to the given anomalies of atmospheric pressure in which the uniform transport of disturbances of the baric field is taken into account. We perform the numerical analyses of the dependences of the amplitudes of oscillations of fluid in the basin on the parameters of the atmospheric front and the choice of the formulas for the tangential wind stresses. The influence of the wind stresses leads to significant quantitative and qualitative changes in the oscillations of fluid in the basin as compared with the case of pure baric action.     

Simulation for the propulsion of a micro-hydro robot with an unstructured grid

The flow mechanism of contractive and dilative motion was numerically investigated to obtain a propulsive force in a highly viscous fluid. The computing program for the analysis of complicated motions was numerically developed with a cell-centered, unstructured grid scheme. The developed program was validated by the well-known equation of an oscillating plane below viscous fluid for an unsteady problem, which is known as Stokes’ second problem. Validation has continued through comparison with the experimental results.In this case, sinusoidal motion was applied to the validation, instead of trochoidal motion, because it was very difficult to actually simulate trochoidal motion in this experiment. Finally, the validation and comparison with the nodal-point scheme was accomplished by Stokes’ problem, which is the famous problem at a low Reynolds number. The validated code was applied to contractive and dilative motion in a narrow tube, whose motion was embodied by trochoidal movement. In a highly viscous fluid, such as a very sticky honey or a swamp, the computed results show that a viscous force can be used for propulsion instead of a dynamic force.From the present results, it was found that a propulsive force can be obtained by contractive and dilative motion at a low Reynolds number, which can be applied to the propulsion of micro-robots in a highly viscous fluid such as a blood vessel or a swamp. This research could also be considered fundamental research for the propulsion of micro-hydro robots, which are expected to be actively studied in the future in accord with further development of nanotechnology.     

Laboratory modeling of the structure of a thermal bar and related circulation in a basin with a sloping bottom

Development of a thermal bar in a laboratory flume with an inclined bottom (3.7°–12°) under the conditions of cooling/heating of the water with a temperature close to that of the maximal density is studied. The structure of the temperature field and currents during different stages of the circulation is examined: (i) formation of an along-slope gravity current, (ii) generation of a subsurface jet, and (iii) transformation of one type of the circulation into another at passing the temperature of the maximum density. The “fall” and “spring” types of the thermal bar are shown to be dynamically equivalent: the transport of the near-shore waters to the deepwater part, which is driven by the buoyancy flux rather than by the heat flux across the surface, transforms stage (i) into stage (ii), while the opposite (on-shore) flow is generated in the intermediate layers. A comparison of the results with the field and laboratory data published allows us to suggest that the propagation of the thermal bar front in the “fast” stage can be considered as the development of a convective jet with its velocity U ～ h ^3/4, which is proportional to the growing thickness of the upper layer h affected by the heating/cooling processes     

Potential vorticity estimates of absolute velocities on the Ross Sea shelf

We analyze absolute velocities on the continental shelf off Cape Adare, in the western sector of the Ross Sea (Antarctica). Such a velocity field is here inferred by using a novel inverse method of absolute velocity determination, namely the tracer PV method, related to potential vorticities of temperature and salinity. This theoretical choice allows us to directly use in situ temperature and salinity data. Moreover, it avoids high-order derivatives, which can give large uncertainties that affect estimates made using previous approaches. The tracer PV method also allows us to separately estimate the steady and non-diffusive component and the unsteady and diffusive components of the flow. The western sector of the Ross Sea is characterized by a surface layer of Antarctic Surface Water over layers of Low Salinity Shelf Water and High Salinity Shelf Water, flowing northward with average velocities ～6–7 cm/s. At ～200 m depth an intrusion of warmer and saltier Circumpolar Deep Water is also evident in our data. The steady absolute velocities are in good agreement with those obtained from the classical Margules equation, in particular regarding the northward flux of the High Salinity Shelf Water. Furthermore, velocities due to diffusive processes and mesoscale activity are discussed. Finally, a steady “thermal” approximation is discussed; it allows for a qualitative check of the results by means of temperature horizontal sections only.