有限长Timoshenko梁弹性碰撞接触瞬间的动态特性

给出了质点与有限长Timoshenko梁横向弹性碰撞接触问题的半解析解,分析了该碰撞问题在碰撞接触瞬间的动态响应特性：揭示了其中的波传播现象．     

流体饱和标准线性粘弹性多孔介质中的平面波

研究了流体饱和不可压标准线性粘弹性多孔介质中平面波的传播和反射问题．在固相骨架小变形的假定下,得到了粘弹性多孔介质中波动方程的一般解,讨论了弥散关系和波的衰减特性．结果表明：在流体饱和不可压粘弹性多孔介质中,仅存在一个耦合纵波和一个耦合横波,纵波和横波的波速、衰减率等取决于孔隙流体与固相骨架间的相互作用以及固相骨架本身的粘性．同时,研究了半空间自由边界上入射波(纵波、横波)的反射问题。得到了非均匀反射波的波速、反射系数、衰减率等的表达式及其相关的数值结果．     

Propagation of plane elastic waves at a plane interface between two electro-microelastic solid half-spaces

This work is concerned with the wave propagation and their reflection and transmission from a plane interface between two different electro-microelastic solid half-spaces in perfect contact. It is found that there exist five basic waves in an infinite electro-microelastic solid, namely an independent longitudinal micro-rotational wave, two sets of coupled longitudinal waves influenced by the electric effect, and two sets of coupled transverse waves. The existence of the two sets of coupled longitudinal waves is new. In the absence of microstretch and electric effects, these two coupled longitudinal waves reduce to a longitudinal displacement wave of micropolar elasticity. Amplitude and energy ratios of various reflected and transmitted waves are presented when (i) a set of coupled longitudinal wave is made incident and (ii) a set of coupled transverse wave is made incident. Numerical computations have been performed for a particular model and the variations of amplitude and energy ratios are obtained against the angle of incidence. The results obtained are depicted graphically. It has been verified that the sum of energy ratios is equal to unity at the interface and the amplitude ratios of reflected and transmitted waves depend upon the angle of incidence, frequency and elastic properties of the media. Results of some earlier workers have also been reduced from the present formulation.     

Phase and signal velocities of waves in dissipative media. Special relativistic theory

The signal and phase velocities (and their frequency dependence) for all possible plane waves in a relativistic gas (of molecules or photons) with dissipation have been determined from the linearized relativistic 13-moment theory. For each direction in 3-space, and for each frequency, one transverse and two longitudinal waves were found. (In addition, some waves are associated with the mass flow and have the mass flow speed.) Of the longitudinal waves, the fast one is a pressure (sound) wave. It is accompanied by a slow longitudinal thermal dissipation wave and a transverse viscous dissipation wave. The pressure wave has a velocity larger than the Laplace adiabatic speed of sound, while the two dissipation waves have a velocity less than the Laplace speed. All the speeds have been expressed explicitly in terms of quantities associated with the state of equilibrium which existed before passage of the wave. It has also been shown that in the ultrarelativistic limit (extremely high temperatures) all signal speeds remain less than the speed of light in vacuo.The major part of this article was presented at the Seminar on Natural Philosophy at The Johns Hopkins University, Baltimore, on November 24, 1971.     

Interesting effects in harmonic generation by plane elastic waves

The harmonics of plane longitudinal and trans-verse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic. This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a pri-mary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.     

Spall Characterization in Epoxy Via Laser Spallation

Background: The strength of materials under extreme dynamic loading conditions, such as in the case of shock wave loading, is assessed from their spallation characteristics. Under laboratory conditions, flyer plate impact, or sometimes laser-induced stress waves, is employed to instigate spall in a material. These methods are often combined with velocity interferometer system for any reflector (VISAR) technique for performing transient measurements. Although the VISAR can record the velocity of extremely fast-moving surfaces, it requires a complex optical setup and a specialized data reduction technique. Objective: In this study, a simpler approach is adopted by extending laser spallation method to determine the spall strength of epoxy, while performing in situ interferometric measurements, directly on top of thick epoxy films. Methods: The glass/epoxy test samples are prepared by transferring an aluminum coating on top of epoxy layers with different thicknesses. Laser-induced stress waves transmit across the substrate/film interface and induce subsurface failure in the epoxy at sufficiently high incident laser energy. The nature and magnitude of the waves are deciphered from the out-of-plane displacement histories of the top reflective sample surfaces, which are recorded by using a Michelson interferometer. Results: The interferometric data reveal the development of two (temporally) well-separated stress waves: an ablation-induced high-amplitude short-duration longitudinal pulse, which is referred to as the primary wave, and a secondary wave, which travels at a comparatively slower speed. The complex constructive interaction of the two waves develops a high-magnitude tensile stress region in the epoxy layer. The spall strength is quantified by superimposing the two stress wave histories associated with the critical energy fluence. Conclusions: The spall depths predicted from spatiotemporal wave travel analyses are in excellent agreement with the experimental observations. The newly adopted methodology estimates the spall strength of epoxy as 260?±?20 MPa.

     

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids.The propagation of three longitudinal waves is represented through three scalar potential functions.The lone transverse wave is presented by a vector potential function.The displacements of particles in different phases of the aggregate are defined in terms of these potential functions.It is shown that there exist three longitudinal waves and one transverse wave.The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated.For the presence of viscosity in pore-fluids,the waves refracted to the porous medium attenuate in the direction normal to the interface.The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations.These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave.The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model.The conservation of the energy across the interface is verified.The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.     

Propagation of acceleration waves in incompressible saturated porous solids

Within the framework of the incompressible porous media model, the propagation properties of acceleration waves in liquid-filled porous solids is discussed. The incompressibility of the two constituents in the model forces the amplitudes of the longitudinal waves in the skeleton and in the liquid to satisfy a certain relation. The two propagation speeds are presented by examination for the existence of acceleration waves and only longitudinal and transverse waves are realizable in the incompressible two-phase porous materials.     

Wave Processes in the Hypersonic Shock Layer on a Flat Plate

An electron-beam fluorescence technique is used to investigate the properties of density waves in the shock layer on a flat plate placed in a hypersonic stream (M_x=21) at zero incidence; the Reynolds number based on the longitudinal coordinate and the freestream parameters is Re_x=(2.7–3)·10⁵. Transverse profiles of the mean density and the overall and spectral levels of the density fluctuations are obtained, the longitudinal and lateral phase velocities of the waves and the correlation scales are determined, and the longitudinal increments of the waves are derived. The data are compared with the experimental results obtained at Re_x=(2.6–7)10·⁴.     

Waves in Nonlocal Elastic Solid with Voids

In this paper, the governing relations and equations are derived for nonlocal elastic solid with voids. The propagation of time harmonic plane waves is investigated in an infinite nonlocal elastic solid material with voids. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent transverse wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the presence of voids and nonlocality parameters in the medium. The transverse wave is dispersive but non-attenuating, influenced by the nonlocality and independent of void parameters. Furthermore, the transverse wave is found to face critical frequency, while the coupled waves may face critical frequencies conditionally. Beyond each critical frequency, the respective wave is no more a propagating wave. Reflection phenomenon of an incident coupled longitudinal waves from stress-free boundary surface of a nonlocal elastic solid half-space with voids has also been studied. Using appropriate boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, the effects of non-locality and dissipation parameter (\(\tau \)) have been depicted on phase speeds and attenuation coefficients of propagating waves. The effect of nonlocality on reflection coefficients has also been observed and shown graphically.     

Propagation and Evolution of Wave Fronts in Two-Phase Porous Media

An investigation is made into the propagation and evolution of wave fronts in a porous medium which is intended to contain two phases: the porous solid, referred to as the skeleton, and the fluid within the interconnected pores formed by the skeleton. In particular, the microscopic density of each real material is assumed to be unchangeable, while the macroscopic density of each phase may change, associated with the volume fractions. A two-phase porous medium model is concisely introduced based on the work by de Boer. Propagation conditions and amplitude evolution of the discontinuity waves are presented by use of the idea of surfaces of discontinuity, where the wave front is treated as a surface of discontinuity. It is demonstrated that the saturation condition entails certain restrictions between the amplitudes of the longitudinal waves in the solid and fluid phases. Two propagation velocities are attained upon examining the existence of the discontinuity waves. It is found that a completely coupled longitudinal wave and a pure transverse wave are realizable in the two-phase porous medium. The discontinuity strength of the pore-pressure may be determined by the amplitude of the coupled longitudinal wave. In the case of homogeneous weak discontinuities, explicit evolution equations of the amplitudes for two types of discontinuity waves are derived.     

Asymmetric Surging of Ships in Following Seas and its Repercussions for Safety

A comprehensive investigation of an asymmetric longitudinal motion of ships displayed in long and steep following waves is presented. The focus is on the strongly nonlinear response, on the verge of the so called surf-riding condition, where a ship could be performing large-amplitude longitudinal oscillations around a mean forward speed. Expressions, in closed form, describing transient surge motion on the phase-plane are derived. For steady-state in particular, is shown that it is possible to determine an explicit analytical solution in the time-domain. Simple prediction formulae for the higher limit of asymmetric surging (threshold of global surf-riding) are derived on the basis of two alternative methods. Also, we investigate the effect of asymmetric surging on a ship's tendency for capsize in the neighborhood of wave crests where restoring capability is often reduced. The paper includes, as an Appendix, a review of types of ship instability and a summary of the historical roots of the field. For a better introduction to the subject we include, as Appendix A, a historical note on the evolution of the theory ship stability together with a summary of known types of ship instability distinguished on the basis of the angle of encounter between ship and waves.     

非线性弹性介质中冲击波斜反射的研究

本文讨论了各向同性非线性超弹性介质在平面小应变下的冲击波斜反射问题。给出了本构关系、简单波解和冲击波解,并作为例子求解了入射冲击波在自由面的斜反射问题。     

Numerical Simulation of the Wave Pattern within a Harbor due to Ship Waves

A numerical simulation methodology to predict the wave pattern within a harbor due to ship waves is presented. It is based on the spectral decomposition of the solitary incident wave, assuming that non-linear effects are negligible, which is the usual case. Each component is transformed using Berkhoff's mild slope model. Superposition of the different solutions allows reconstruction of the wave temporal history, from which the maximum wave height at any point within the harbor can be obtained. An application of the proposed methodology to study the protection structure for the Argentine Yatch Club, located within Buenos Aires harbor, is presented. Details about the schematization and the necessary data are explained. The maximum wave height distribution for the projected structure and the original situation are compared. A variant of the project is proposed and analyzed, showing a significant extra attenuation of the maximum wave heights. This illustrates the utility of the methodology for design purposes.     

Observations on waveforms of capillary and gravity-capillary waves

Due to extreme conditions in the field, there has not been any observational report on three-dimensional waveforms of short ocean surface waves. Three-dimensional waveforms of short wind waves can be found from integrating surface gradient image data (Zhang 1996a). Ocean surface gradient images are captured by an optical surface gradient detector mounted on a raft operating in the water offshore California (Cox and Zhang 1997). Waveforms and spatial structures of short wind waves are compared with early laboratory wind wave data (Zhang 1994, 1995). Although the large-scale wind and wave conditions are quite different, the waveforms are resoundingly similar at the small scale. It is very common, among steep short wind waves, that waves in the capillary range feature sharp troughs and flat crests. The observations show that most short waves are far less steep than the limiting waveform under weak wind conditions. Waveforms that resemble capillary-gravity solitons are observed with a close match to the form theoretically predicted for potential flows (Longuet-Higgins 1989, Vanden-Broeck and Dias 1992). Capillaries are mainly found as parasitic capillaries on the forward face of short gravity waves. The maximum wavelength in a parasitic wave train is less than a centimeter. The profiles of parasitic wave trains and longitudinal variations are shown. The phenomenon of capillary blockage (Phillips 1981) on dispersive freely traveling short waves is observed in the tank but not at sea. The short waves seen at sea propagate in all directions while waves in the tank are much more unidirectional.     

管道中具有累积效应的二阶谐纵向导波生成点的数值验证

利用非线性导波检测早期损伤的潜在优势,在于其对微裂纹或以微结构变化的形式表现出来的材料性能退化的敏感性。而长距离传播能力使得振幅具有累积效应的非线性二阶谐纵向导波成为检测管道的理想方法。本文提出了在均匀各向同性的应力自由弹性固体管道中,产生轴对称二阶谐纵向导波的方案,该方案使用同频零阶纵向导波作为激励波。根据相速度匹配条件得到与此方案相对应的可能的谐导波生成点后,利用另一条件即非零功率流对生成点进行了数值验证,最终确定了在管道中产生二阶谐纵向导波的生成点。     

An inversion integral for crack-scattering data

The inverse problem of determining the size, shape and orientation of a flat crack from high-frequency far-field elastic waves scattered by the crack is investigated. The results show that desired information on a crack can be obtained from the first arriving scattered longitudinal waves only. It is shown that an approximate high-frequency solution to the direct problem, based on physical elastodynamics, yields an expression for the scattered far-field of longitudinal motion which suggests a solution to the inverse problem by application of Fourier-type inversion integrals to scattering data. Two kinds of inversion integrals are examined. The inversion problem becomes relatively simple if some a-priori information is available, either on the orientation of the plane of the crack or on a plane of symmetry. The method of inversion is verified for a flat crack of elliptical shape. Some computational technicalities are discussed, and the method is also applied to experimental scattering data.     

On the propagation waves in the theory of thermoelasticity with microtemperatures

The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasi-thermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.     

Intense bending waves in a bar

Summary In this paper, the work presented in [1] is extended to study higher-order approximations of nonlinear effects in a bar. It has been found that long bending waves, being the low-frequency modes involved in resonant triads, are stable against small perturbations. Consequently, a bending wave with group velocity which is less than that of longitudinal waves should behave as a linear quasi-harmonic wavetrain. On the other hand, one may expect self-modulation instability of intense bending wavetrains during the long-time evolution. This paper overcomes such a contradiction. To describe the nonlinear dynamics in detail, one should allow for higher-order approximation effects in the model. Such effects are associated with the diffusion of linear wave packets due to different group velocities, and amplitude dispersion caused by nonlinearity. Within the second-order approximation analysis, an amplitude modulation is indeed experienced for intense bending waves. As a result, envelope solitons can be formed from unstable bending wavetrains. The group matching of long longitudinal and short bending waves, being a particular case of the self-modulation, is of special interest as a limit case of the triple-wave resonant interactions. It demonstrates the relation between the first- and the second-order approximation effects. Accepted for publication 20 July 1996