Drift of an inclined plate counter oncoming waves

The dependence of the velocity of the motion of a tow with an inclined plate mounted in a wave water channel on the wave parameters, the submergence depth, and the angle of inclination and dimensions of the plate is experimentally investigated. The effect of tow motion counter to the waves is detected and theoretically justified. The free surface profiles for periodic waves above an inclined plate obtained using the elolutionary system of the Boussinesq approximation equations correspond to the measured ones. The pulse generated as a result of wave breakup is estimated.     

Wave-induced dynamics of a particle on a thin circular plate

In this paper, the dynamics of a particle placed on a thin circular plate carrying circumferential harmonic travelling wave is studied. Coulomb friction is used to model the particle–surface interaction. Distinct regions on the plate surface are identified where either of the three phases of particle motion, namely jumping, sliding and sticking, occurs. Also, the effect of wave frequency and the plate geometry on these regions is studied. Interestingly, there exists an optimum plate thickness for which the region of sliding is maximum. At certain wave frequencies, from the numerical simulations within sticking and sliding regions, it is observed that the average particle motion spirals inwards towards the plate centre. Such an average motion is observed whenever the particle is placed initially with a zero velocity relative to the plate surface. The Gedanken experiments discussed herein provide cogent explanations to all the observed average (slow) dynamics and are also found to be useful in predicting the slow dynamics of the particle a priori, that is, before the actual numerical simulations. The particle’s velocity couples the radial and tangential sliding friction components and is found to be the key physical feature that explains the observed behaviour. Also, it is observed that the plate surface excited by circumferential travelling waves can provide acoustic lubrication to a particle by reducing the limiting force required to move it relative to the surface. The methods discussed in this paper can be extended to study the dynamics of a group of particles (granular materials) and extended rigid bodies, interacting with such surface waves.

     

Rayleigh-type waves in a water-saturated porous half-space with an elastic plate on its surface

The paper deals with the plane problem of steady-state time harmonic vibrations of an infinite elastic plate resting on a water-saturated porous solid. The displacements of the plate are described by means of the linear theory of small elastic oscillations. The motion of the two-phase medium is studied within the framework of Biot's linear theory of consolidation. The main interest is focused on the investigation of properties of the Rayleigh-type waves propagating alongside of the contact surface between the plate and the porous half-space. In particular, the dependence of the phase velocity and attenuation of the waves on the plate stiffness, mass coupling coefficient, and degree of saturation of the medium is studied. Besides, for the limiting case of an infinitely thin plate, the comparison of the wave characteristics is carried out with those of the pure Rayleigh waves.     

Testing and calculations of the motion of a model ship with a direct-flow wave propulsor

A new design of the wave propulsor is presented. In this design the thrust mechanism is due to the interaction between the waves and the ship structure elements rather than to ship’s motions. To verify the possibility of using a rigidly fixed inclined plate as the ship wave propulsor a model catamaran was constructed in the Institute of Mechanics of Moscow State University. The effect of the upwave motion of the ship, whose mean velocity is a nonmonotonic function of the wavelength, is studied. As the plate edge pierces the water surface, the ship starts to move in the opposite direction, that is, downwave. The experimentally observable effects are also revealed in the numerical simulation using the XFlow software package which involves the meshless lattice Boltzmann method. On the basis of the calculated results it is shown that the upwave motion effect is due to a variation in the hydrostatic force component in the case of wave breakdown.     

Effect of a biasing electric field on the propagation of antisymmetric Lamb waves in piezoelectric plates

Based on the theories of anisotropic elasticity, piezoelectricity and elastic waves in solids, the propagation of antisymmetric Lamb waves in a biasing electric field is investigated in this paper. By solving the coupled differential equations of motion under a biasing electric field, the phase velocity equations of antisymmetric Lamb wave modes for electrically open and shorted cases are obtained, respectively. The beating effect arising from the difference between the phase velocity of the zero-order symmetric mode and antisymmetric mode exists in the plate when the plate has a thickness comparable to or slightly larger than the wavelength. The influence of the biasing electric field on the phase velocity, beat wavelength, mechanical displacement and stress fields for the lowest two antisymmetric modes of Lamb waves are discussed in detail. From the calculated results, it is seen that the phase velocity of the fundamental antisymmetric mode is especially sensitive to the applied biasing electric field.     

On waves due to rolling of a ship in water of finite depth

Summary The problem of the generation of waves due to small rolling oscillations of a thin vertical plate partially immersed in uniform finite-depth water is investigated here by utilizing two mathematical methods assuming the linearised theory of water waves. In the first method, the use of eigenfunction expansion of the velocity potentials on the two sides of the plate produces the amplitude of wave motion at infinity in terms of an integral involving the unknown horizontal velocity across the gap, and also in terms of another integral involving the unknown difference of the potential across the plate. These unknown functions satisfy two integral equations. Any one of these, when solved numerically, can be used to compute the amplitude of the wave motion set up at either infinity on the two sides of the plate for various values of the wave number.In the second method, the problem is formulated in terms of a hypersingular integral equation involving the difference of the potential function across the plate. The hypersingular integral equation is solved numerically, and its numerical solution is used to compute the wave amplitude at infinity. The two methods produce almost the same numerical results. The results are illustrated graphically, and a comparison is made with the deep-water result. It is observed that the deep-water result effectively holds good if the plate is partially immersed to the order of one-tenth of the bottom depth.This work was initiated when the first Author was visiting Mathematics Department, Indian Institute of Science, Bangalore. It was partially supported by DST, and by CSIR. The authors take this opportunity to thank the Managing Editor for his suggestions to improve the paper in the present form.     

Effect of a biasing electric field on the propagation of symmetric Lamb waves in piezoelectric plates

This paper is concerned with the effect of a biasing electric field on the propagation of Lamb waves in a piezoelectric plate. On the basis of three dimensional linear elastic equations and piezoelectric constitutive relations, the differential equations of motion under a biasing electric field are obtained and solved. Due to the symmetry of the plate, there are symmetric and antisymmetric modes with respect to the median plane of the piezoelectric plate. According to the characteristics of symmetric modes (odd potential state) and antisymmetric modes (even potential state), the phase velocity equations of symmetric and antisymmetric modes of Lamb wave propagation are obtained for both electrically open and shorted cases. The effect of a biasing electric field on the phase velocity, electromechanical coupling coefficient, stress field and mechanical displacement of symmetric and antisymmetric Lamb wave modes are discussed in this paper and an accompanying paper respectively. It is shown that the biasing electric field has significant effect on the phase velocity and electromechanical coupling coefficient, the time delay owning to the velocity change is useful for high voltage measurement and temperature compensation, the increase in the electromechanical coupling coefficient can be used to improve the efficiency of transduction.     

Wave propagation in a non-ideal dusty gas

In this paper we have studied the behavior of wave motion as propagating wavelets and their culmination into shock waves in a non-ideal gas with dust particles. In the absence of non-ideal effect the gas satisfies an equation of state of Mie–Gruneisen type. An expansion wave resulting from the action of receding piston is considered and the solutions to this problem showing effects of dust particles and non-idealness are obtained. The propagation of weak waves is considered and the flow variables in the region bounded by the piston and the characteristic wave front are found out. The expansive action of a receding piston undergoing an abrupt change in velocity is discussed. Cases of central expansion fan and shock fronts are studied and the solutions up to first order in the physical plane are obtained. The effects of non-idealness and dust particles are discussed in each case.     

The oblique-plate impact experiment

An experimental method is presented for the study of one-dimensional plane waves corresponding to combined pressure and shear. The experiment involves the impact of two skewed flat plates. A projectile plate is accelerated using a gas gun and made to impact a target plate in a vacuum chamber. The projectile and target plates are parallel, but inclined relative to the axis of the gun so that the particle velocity in the target has components both normal and parallel to the plane of impact. The particle velocity at the target rear (free) surface is recorded as a function of time. The normal velocity component is monitored using a laser velocity interferometer; the transverse motion is monitored using a shadow technique. The measured wave profiles can be compared to theoretical predictions based on one-dimensional-wave theory.     

Unsteady motion of a source in a fluid under a floating plate

This paper studies the three-dimensional unsteady problem of the hydroelastic behavior of a floating infinite plate under the impact of waves generated by horizontal straight motion of a point source of mass in a fluid of infinite depth. The solution is carried out using known integral and asymptotic methods. The formulas obtained are used to numerically analyze the effect of plate thickness, depth of submergence of the source, and its acceleration, deceleration, and velocity of uniform motion on the deflection of the floating plate.     

Flexural gravity wave motion over poroelastic bed

Using Biot’s consolidation theory, effect of poroelastic bed on flexural gravity wave motion is analyzed in both the cases of single-layer and two-layer fluids. The model for the flexural gravity waves is developed using linear water wave theory and small amplitude structural response in finite water depth. The effects of permeability and shear modulus of poroelastic bed and time period on flexural gravity wave motion are studied by analyzing the dispersion relation, phase speed, plate deflection, interface elevation and pressure distribution along water depth. Various results for surface gravity waves are analyzed as special cases. The study reveals that bed permeability retards the hydrodynamic pressure distribution along the water depth significantly compared to shear modulus whilst, floating plate deflection decreases significantly with change in shear modulus compared to permeability of the poroelastic bed. The present study can be generalized to analyze various wave–structure interaction problems over poroelastic bed.     

Fine structure of a stratified flow near a flat-plate surface

The pattern of disturbances arising during the motion of a strip along a horizontal surface in a continuously stratified fluid with identified upstream and attached internal waves, boundary layers, and edge singularities is calculated in the liner approximation. The flow pattern behind a flat plate moving with a constant velocity in a continuously stratified fluid is studied with the use of the optical schlieren technique; transformation of waves and finely structured elements of the flow with increasing plate velocity is analyzed. The calculated and experimentally observed patterns of internal waves at low velocities are demonstrated to be in good agreement. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 77–91, November–December, 2007.     

Motion of a slender body in a fluid under a floating plate

This paper studies the three-dimensional unsteady problem of the hydroelastic behavior of a floating infinite plate under the impact of waves generated by horizontal rectilinear motion of a slender solid in a fluid of infinite depth. An analytic solution of the problem is found based on the known solutions for the unsteady motion of a point source of mass in a fluid of infinite depth under a floating plate. Asymptotic formulas are obtained which model the motion of a solid slender body in a fluid by replacing the body with a source-sink system. These formulas are used to numerically analyze the effect of plate thickness, depth of the body, its dimensions and the velocity of rectilinear motion on the amplitude of deflection of the floating plate. The motion of a submarine under a nonbreakable plate was modeled experimentally. Theoretical and experimental data are in good agreement.     

Scattering of water waves by a submerged thin vertical elastic plate

The problem of water wave scattering by a thin vertical elastic plate submerged in infinitely deep water is investigated here assuming linear theory. The boundary condition on the elastic plate is derived from the Bernoulli–Euler equation of motion satisfied by the plate. This is converted into the condition that the normal velocity of the plate is prescribed in terms of an integral involving the difference in velocity potentials (unknown) across the plate multiplied by an appropriate Green’s function. The reflection and transmission coefficients are obtained in terms of integrals involving combinations of the unknown velocity potential on the two sides of the plate and its normal derivative on the plate, which satisfy three simultaneous integral equations, solved numerically. These coefficients are computed numerically for various values of different parameters and are depicted graphically against the wave number for different situations. The energy identity relating these coefficients is also derived analytically by employing Green’s integral theorem. Results for a rigid plate are recovered when the parameters characterizing the elastic plate are chosen negligibly small.     

Oscillatory Motion of a Viscous Fluid in Contact with a Flat Layer of a Porous Medium

Analytical solutions are obtained for two problems of transverse internal waves in a viscous fluid contacting with a flat layer of a fixed porous medium. In the first problem, the waves are considered which are caused by the motion of an infinite flat plate located on the fluid surface and performing harmonic oscillations in its plane. In the second problem, the waves are caused by periodic shear stresses applied to the free surface of the fluid. To describe the fluid motion in the porous medium, the unsteady Brinkman equation is used, and the motion of the fluid outside the porous medium is described by the Navier–Stokes equation. Examples of numerical calculations of the fluid velocity and filtration velocity profiles are presented. The existence of fluid layers with counter-directed velocities is revealed.     

Investigation of the properties of a shock wave arising in a supersonic flow of plasma,passing through a transverse magnetic field

In a flow of plasma, set up by an ionizing shock wave and moving through a transverse magnetic field, under definite conditions there arises a gasdynamic shock wave. The appearance of such shock waves has been observed in experimental [1–4] and theoretical [5–7] work, where an investigation was made of the interaction between a plasma and electrical and magnetic fields. The aim of the present work was a determination of the effect of the intensity of the interaction between the plasma and the magnetic field on the velocity of the motion of this shock wave. The investigation was carried out in a magnetohydrogasdynamic unit, described in [8]. The process was recorded by the Töpler method (IAB-451 instrument) through a slit along the axis of the channel, on a film moving in a direction perpendicular to the slit. The calculation of the flow is based on the one-dimensional unsteady-state equations of magnetic gasdynamics. Using a model of the process described in [9], calculations were made for conditions close to those realized experimentally. In addition, a simplified calculation is made of the velocity of the motion of the above shock wave, under the assumption that its front moves at a constant velocity ahead of the region of interaction, while in the region of interaction itself the flow is steady-state.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 86–91, January–February, 1975.     

Nonlinear analysis of governing laws of realization of the wave motion on the surface of a charged jet moving with respect to a material medium

On the base of analytic asymptotic calculations which are quadratic with respect to the ratio of the wave amplitude and the jet radius it is shown that the presence of a tangential jump in the velocity field on the jet surface leads to generation of a periodic wave motion on the interface between the media and has the destabilizing effect for both axisymmetric and bending and bending-deformation waves. It is found that there is a degenerate internal nonlinear resonance interaction between waves on the jet surface. This interaction may be of six different types in which the energy can be transferred between the interacting waves including waves of different symmetry. In the last case the energy is transferred from waves determining the initial deformation to axisymmetric waves.     

钛/钢复合板爆炸焊接实验

以3mm 厚的TA2钛板和26mm 厚的正火态Q345R为材料,通过爆炸焊接实验,对钛/钢复合板 爆炸焊接的动态参数进行了研究。结合复合板结合界面特征、复合板结合强度(剪切强度)以及界面波的金相 组织,讨论了钛/钢爆炸焊接时获得高强度结合和规则的界面结合波状形态的条件。对于3mm 厚TA2与 26mm厚正火态Q345R,该条件是动态碰撞角17,动态碰撞速度vp760m/s。根据界面波及基板轧制 金相组织形态,分析了形成界面波的机理,认为射流阻碍复板连续碰撞基板是形成界面波的一个主要原因。     

Transient bending waves in plates studied by hologram interferometry

Propagating bending waves are studied in plates made of aluminum and wood. The waves are generated by the impact of a ballistic pendulum. Hologram interferometry, with a double pulsed ruby laser as the light source, is used to record the out of plane motion of the waves. Elliptic-like fringes visualize differences in wave speed for different directions in the anisotropic plate and circular ones are obtained for the isotropic plate. The experimental data for the isotropic plate compare favorably with analytical results derived from the Kirchhoff-plate equation with a point impact of finite duration. A similarity variable is found when starting conditions are modeled as a Dirac pulse in space and time, that brings new understanding to the importance of specific parameters for wave propagation in plates. A formal solution is obtained for a point force with an arbitrary time dependence. For times much larger than the contact time, the plate deflection is shown to be identical to that from a Dirac pulse applied at the mean contact time. A method for determining material parameters, and the mean contact time, from the interferograms is hence developed.     

Features of how surface waves form in a cylinder made of a hard material and filled with a fluid

The properties of harmonic surface waves in an elastic cylinder made of a rigid material and filled with a fluid are studied. The problem is solved using the dynamic equations of elasticity and the equations of motion of a perfect compressible fluid. It is shown that two surface (Stoneley and Rayleigh) waves exist in this waveguide system. The first normal wave generates a Stoneley wave on the inner surface of the cylinder. If the material is rigid, no normal wave exists to transform into a Rayleigh wave. The Rayleigh wave on the outer surface forms on certain sections of different dispersion curves. The kinematic and energy characteristics of surface waves are analyzed. As the wave number increases, the phase velocities of all normal waves, except the first one, tend to the sonic velocity in the fluid from above __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 48–62, September 2007.