Wave scattering by a thin elastic plate floating on a two-layer fluid

The hydroelastic interaction between an incident gravity wave and a thin elastic plate floating on a two-layer fluid of finite depth is analyzed with the aid of the method of matched eigenfunction expansions. The fluid is assumed to be inviscid and incompressible. A two-dimensional problem is formulated within the framework of linear potential theory for small-amplitude waves. The fluid domain is divided into two and three regions for semi-infinite and finite plates, respectively, with the matching relations representing the continuities of the pressure and velocity. A new inner product involving two single integrals is proposed, in which the vertical eigenfunctions in the open water region of the two-layer fluid are orthogonal. Then the orthogonality of the eigenfunctions with respect to the newly defined inner product is used to obtain a set of simultaneous equations for the expansion coefficients of the velocity potentials, and the edge conditions are included as a part of the equation system. The effects of the fluid density ratio and the position of interface on the wave reflection and transmission are discussed. Numerical analysis shows that the method proposed herein is effective with a higher rate of convergence.     

Quarter-plane problem of a floating elastic plate

An investigation is made into the hydro-elastic behavior of a floating elastic plate, which occupies a quarter plane to infinity and is excited by water waves. A boundary-integral equation based on the Green function for this problem is shown for the case of finite water depth, as well as for the case of shallow water. The solution of the quarter-plane problem is composed of the corner effect and the solution of the half-plane problem. The corner effect is divided into two parts. The first part is the end effect of the forcing term of the integral equation, which is analytically estimated and its asymptotic form is derived. The second part is the local contribution whose asymptotic form is also obtained. The asymptotic form of the corner effect is confirmed by a numerical evaluation.     

Wave forces on a submerged vertical plate

Summary A vertical plate of finite length and depth is attacked by gravity waves in water of finite depth. The forces and moments acting on the plate are computed by using the theory of linearized waves. The forces depend on three dimensionless parameters combining the draft, length, water depth and wave length and on the angle of attack. The problem is reduced to the solution of two infinite linear systems of equations. Numerical solutions are presented for different particular combinations of the parameter values. In most of the cases the standing wave approximation yields sufficiently accurate results.     

悬浮隧道动力响应分析方法及模拟的研究进展

为了分析波浪地震耦合作用下悬浮隧道的动力响应,通过Stokes波浪理论和三角级数法计算了波浪荷载和地震荷载,基于D’Alembert原理建立了波浪地震耦合作用下悬浮隧道的管体-锚索模型。结合悬浮隧道待建工程对荷载参数和系统响应进行分析,结果表明：波浪地震耦合作用下悬浮隧道管体-锚索模型与锚索振动模型具有较好的一致性,但后者无法考虑系统的参数振动;地震的方向对悬浮隧道系统的响应具有显著影响,相同地震峰值加速度下水平地震作用所产生系统的响应要大于竖向地震作用,且锚索的响应大于管体;地震的峰值加速度与系统响应之间具有一定的函数关系,随地震荷载峰值加速度的增加系统的最大位移响应约呈线性增加趋势;在地震荷载的基础上考虑波浪荷载后系统的响应有所增大。随波浪波高和波长增加系统响应约呈线性增大,且较小波浪的周期(小于10 s)易引发系统的共振。     

Generalized analytical solution to wave interaction with submerged multi-layer horizontal porous plate breakwaters

This study deals with the flow induced by a rigid flat plate of finite length, initially touching a horizontal water surface, when it starts to move upwards with constant acceleration. In the present model, negative hydrodynamic pressures on the lower (wetted) surface of the plate are allowed, and thus, the water follows the plate due to the resulting suction force. The acceleration of the plate and the plate length are such that gravity, surface tension and viscous effects can be neglected during the early stages of the motion. Under these assumptions, the initial two-dimensional, potential flow caused by the plate lifting is obtained by using the small-time expansion of the velocity potential. This small-time solution is not valid close to the plate edges, as it predicts there singular flow velocities and unbounded displacements of the water-free surface. It is shown that close to the plate edges the flow is nonlinear and self-similar to leading order. This nonlinear flow is computed by the boundary-element method combined with a time-marching scheme. The numerical time-dependent solution approaches the self-similar local solution with time.     

Penetration of flexural waves through a periodically constrained thin elastic plate in vacuo and floating on water

The subject of this paper, the scattering of flexural waves by constrained elastic plates floating on water is relatively new and not an area that Professor Newman has worked in, as far as the authors are aware. However, in two respects there are connections to his own work. The first is the reference to his work with H. Maniar on the exciting forces on the elements of a long line of fixed vertical bottom-mounted cylinders in waves. In their paper (J Fluid Mech 339 (1997) 309–329) they pointed out the remarkable connection between the large forces on cylinders near the centre of the array at frequencies close to certain trapped-mode frequencies, which had been discovered earlier, and showed that there was another type of previously unknown trapped mode, which gave rise to large forces. In Sect. 6 of this paper the ideas described by Maniar and Newman are returned to and it is shown how the phenomenon of large forces is related to trapped, or standing Rayleigh–Bloch waves, in the present context of elastic waves. But there is a more general way in which the paper relates to Professor Newman and that is in the flavour and style of the mathematics that are employed. Thus extensive use has been made of classical mathematical methods including integral-transform techniques, complex-function theory and the use of special functions in a manner which reflects that used by Professor Newman in many of his important papers on ship hydrodynamics and related fields.     

弹性限位浮筏系统的随机振动建模与算法

对具有弹性限位的浮筏隔振系统,采用单边约束动力学方程,引入接触力,建立系统的确定性方程。再设系统的激励受随机因素的影响,导出系统的随机离散动力学模型,给出离散的计算格式。由于浮筏系统中限位器的个数很多,系统受冲击后,限位器接触状态的可能性非常多,因此对于限位器的接触状态的判别采用了人工神经网络,使得接触计算得以实现。最后通过实例分析对系统的随机动力学特性进行分析,给出噪声对系统振动周期性的影响,以及限位器间隙与位移方差之间的关系。     

Frequency- and time-domain analysis of the transient resonance scattering resulting from the interaction of a sound pulse with submerged elastic shells

The authors present a resonance scattering analysis of the echoes returned by a submerged, air-filled, elastic spherical shell, and also from a rigid sphere, when they are insonified by sound pulses. They consider arbitrary pulsed incidences of any duration, carrier frequency, envelope and shape. The approach is equally effective in the frequency and the time domains. They compare backscattered echoes returned by the structures under study in various instances, which are predicted by exact modal approaches, and by the approximate Kirchhoff method. The effects of pulse duration are examined, and so are the various kinds of resonances that develop when a shell is insonified by extremely narrowband pulses. Also examined is the concept of an impulse sonar, for incident pulses that are short- and broadbanded. An inverse scattering analysis shows how and how well physical target characteristics extracted in situ from the remotely sensed echoes can be used for target identification. Various sample cases are constructed and solved and the results interpreted.     

Second-order wave interaction with a vertical plate

The second-order interaction of monochromatic water waves with a rigid vertical plate is investigated numerically and experimentally. The plate has a finite width and is projected from one of the side-walls of a wave-tank. This geometry reduces the wave cases to normal incidence but permits a semi-analytical resolution based on eigenfunction expansions. Obtained numerical results are shown to be insensitive to the width of the tank beyond some value, and to converge quickly with the truncation orders of the expansions, in spite of the second-order potential having a logarithmic singularity at the plate edge. Second-order free-surface elevations are compared with values derived from experimental measurements at the BGO-First offshore wave-tank. Good agreement is reported. It is with much pleasure and admiration for his achievements that we dedicate this work to Nick Newman.     

Wave propagation passing over a submerged porous breakwater

A linear model of waves propagating over a submerged porous breakwater is derived from two coupled boundary-value problems, each of which represents the governing equation in a different medium. The model is similar to the shallow-water equations (SWE), with a damping term proportional to the character of the porous breakwater. Therefore, waves traveling above the breakwater will be absorbed, and the amplitude decreases. The wave propagation passing over the submerged breakwater for monochromatic and solitary waves is analyzed. For monochromatic waves, the numerical solution agrees with the analytical. The amplitude decreases exponentially with respect to the space variable in the region above the breakwater. The reflected wave is also analyzed when the model is combined with a model using the shallow-water equations.     

Applicability of the method of fundamental solutions to interaction of fully nonlinear water waves with a semi-infinite floating ice plate

In this research effort, a meshless numerical model was developed to study the hydroelastic interaction of an incident wave with a semi-infinite horizontal floating plate. It is assumed that the fluid is homogenous, inviscid and incompressible. Fundamental solution of the governing Laplace equation is considered to be radial basis functions. In this method, only a few boundary points are located on the boundary. Moreover, there are a few source points that are located outside the computational domain. Two additional source points are introduced to deal with the plate's edge conditions. The problem is solved using collocations at only a few boundary points. When density and thickness of the plate are reduced to zero, good agreements with other numerical works are observed.     

Analysis of oblique wave interaction with a submerged perforated semicircular breakwater

This study examines oblique wave interaction with a submerged perforated semicircular breakwater based on the linear potential theory. The fluid domain is divided into inner and outer regions by a perforated semicircular arc. The velocity potentials in the inner and outer regions are constructed by eigenfunction expansions and multipole expansions, respectively. The unknown constants in the velocity potentials are determined by matching the boundary conditions on the perforated arc. The convergence of the solution method we have developed is rapid. The reflection and transmission coefficients and the wave forces acting on the breakwater are calculated and examined. Some useful results are presented for practical engineering.     

Interaction of a turbulent boundary layer with an elastic plate

An approximate method is presented for the determination of the efficiency with which an elastic plate reduces turbulent friction, and experimental results are also presented.Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 2, pp. 220–225, February, 1989.     

Transient SH-waves in an elastic plate with a moving edge

The propagation of transient SH-waves in a plate is discussed. An SH-wave source is placed on a fixed edge of the plate and the other edge moves outward with uniform velocity. Two Laplace transforms in fixed and moving coordinate systems are employed. Developing an exchange formula between two Laplace transforms, a coupled functional equation for two unknown coefficients is derived and solved by iteration. The solution obtained here is exact up to three reflection times of an incident (source) wave, and the time-development of the wave front shape is also discussed.     

Stability of a compressed elastic plate with nonlinear supporting elements

An approach for studying the critical loading parameters of stability of an elastic plate with nonlinear supporting elements is developed. A general potential function of the system depending on state variables and control parameters is constructed. Classical methods of catastrophe theory including a determination of the different bifurcational sets and an analysis of the physical meaning of the corresponding stability criteria are used. The influence of the supporting elements on the behaviour of the plate under the loading is determined     

The interaction of shock waves with a boundary layer on a sharp plate and a blunted plate

The interaction of shock waves with a turbulent boundary layer on a sharp plate and a blunted plate is numerically investigated. The shock waves in the flow are generated by wedges installed on the flat plate. The flow is simulated by the dynamic equations of a viscous perfect gas. The effect of the blunting radius of the plate’s leading edge and the wedge angle on the flow field and the local aerodynamic coefficients is shown. The calculated results are in agreement with the experimental data.