On wave propagation in anisotropic elastic cylinders at nanoscale: surface elasticity and its effect

Material heterogeneity induced by a surface or interface may be neglected at macroscale since the surface-to-volume ratio is usually small. However, its effect can become significant for structures at nanoscale with a large surface-to-volume ratio. In this paper, we incorporate such surface material heterogeneity into wave propagation analysis of a nanosized transversely isotropic cylinder. This is achieved by using the concept of surface elasticity. Instead of directly using the well-known Gurtin–Murdoch (GM) surface elasticity, we develop here another general framework based on a thin layer model. A novel approach based on state-space formalism is used to derive the approximate governing equations. Three different sources of surface effect can be identified in the first-order surface elasticity, i.e., the elasticity effect, the inertia effect and the thickness effect. It is found that the derived theory becomes identical to the GM surface elasticity if the thickness effect is dropped and when the material is isotropic. The axisymmetric wave propagation in a transversely isotropic cylinder with surface effect is then studied, and an exact solution is presented. Numerical results are finally given to show that the surface effect will play a very pronounced role in wave propagation in cylinders at nanoscale.     

Effect of surface stresses on surface waves in elastic solids

This paper deals with the propagation of surface waves in homogeneous, elastic solid media whose free surfaces or interfaces of separation are capable of supporting their own stress fields. The general theory for the propagation of surface waves in a medium which supports surface stresses is first deduced, and then this theory is employed to investigate the particular cases of surface waves, viz. (a) Rayleigh waves, (b) Love waves and (c) Stoneley waves. It is seen that the Rayleigh waves become dispersive in nature; and, in case of low frequency with residual surface tension, a critical wavelength exists, below which the propagation of Rayleigh waves is not possible. This critical wave length is directly proportional to the surface tension. Some numerical calculations have been made in the case of Love waves and conclusions have been drawn.     

Surface waves in fiber-reinforced anisotropic general viscoelastic media of higher orders with voids,rotation, and electromagnetic field

In this article, we investigated an effect of external magnetic field on the propagation of surface waves in a perfect electrically conducting fiber-reinforced anisotropic general viscoelastic media of rational and higher orders with voids in a rotating medium. The general surface wave speed is derived to investigate effect of electromagnetic field and rotation on surface waves in the presence of voids and viscosity. Boundary conditions are applied to obtain the secular equation for generalized types of waves. Particular cases of Stoneley, Love and Rayleigh waves are derived. The results obtained are more general in the sense that some earlier published results are obtained from our result as special cases. In the absence of voids, the results for viscoelasticity of order zero are in good agreement with the fiber-reinforced materials. Also by neglecting the reinforced elastic parameters, the results reduce to a well-known isotropic medium. It is observed that surface waves cannot propagate in a strong initially applied electromagnetic field and rotation. Numerical results for particular cases have been obtained and displayed graphically. The results indicate that the effects of voids, anisotropic, fiber-reinforcement, rotation and electromagnetic field are very pronounced and applicable for the phenomena.     

Surface plasmon polariton analogue to Young's double-slit experiment

When a light wave strikes a metal film it can, under appropriate conditions, excite a surface plasmon polariton (SPP)--a surface electromagnetic wave that is coupled to the free electrons in the metal. Such SPPs are involved in a wide range of phenomena, including nanoscale optical waveguiding, perfect lensing, extraordinary optical transmission, subwavelength lithography and ultrahigh-sensitivity biosensing. However, before the full potential of technology based on SPPs (termed 'plasmonics') can be realized, many fundamental questions regarding the interaction between light and matter at the nanoscale need to be answered. For over 200 years, Young's double-slit experiment has been a valuable pedagogical tool for demonstrating the wave nature of light. Here, we perform a double-slit experiment with SPPs to reveal the strong analogy between SPP propagation along the surface of metallic structures and light propagation in conventional dielectric components (such as glass waveguides). This allows us to construct a general framework to describe the propagation, diffraction and interference of SPPs. It also suggests that there is an effective diffraction limit for the lateral confinement of SPPs on metal stripe waveguides, and justifies the use of well-developed concepts from conventional optics and photonics in the design of new plasmonic devices.     

On the surface waves in an elastic micropolar and microstretch medium with nonlocal cohesion

Summary A brief review of the main points of Eringen's theory of micromorphic bodies is first given, and balance equations for the linear isotropic micropolar and microstretch body are established. By appeal to the Fourier exponential transformation, nonlocal constitutive equations are derived, and assumptions with regard to the nonlocal moduli are made. The general field equations governing the propagation of a nonlocal surface wave are particularized so as to coincide with the results obtained directly in references [12], [17], [22], and [23], respectively. As an illustrative example, propagation of a microrotation and microstretch wave in a nonlocal medium in the entire Brillouin zone is examined.     

On the existence of surface acoustic waves on piezoelectric substrates

The existence of surface waves on anisotropic materials was proven under fairly general conditions by Lothe and Barnett in 1976. But, until now, the status of surface waves on piezoelectric materials has remained unresolved. This paper presents general existence theorems for surface waves on piezoelectric substrates. It is demonstrated that for short circuit boundary conditions a surface wave solution must exist under virtually any circumstances. However, for a free surface, comparatively stringent existence conditions are required. Numerical examples are given for both free and shorted surfaces, and it is demonstrated that, in some situations, a surface wave solution may not exist for free surface propagation. The existence proofs were developed as a result of theoretical work on Green function modeling, which is now the preferred technique for rigorous SAW and pseudo-SAW device analysis. The mechanisms of the existence proofs and the associated mathematical results give great insight into the structure and properties of the Green functions and include many results that are directly relevant to device analysis     

Surface wave propagation in a fluid-saturated incompressible porous medium

A study of surface wave propagation in a fluid-saturated incompressible porous half-space lying under a uniform layer of liquid is presented. The dispersion relation connecting the phase velocity with wave number is derived. The variation of phase velocity and attenuation coefficients with wave number is presented graphically and discussed. As a particular case, the propagation of Rayleigh type surface waves at the free surface of an incompressible porous half-space is also deduced and discussed.     

Propagation properties of longitudinal leaky surface waves on lithium tetraborate

Theoretical and experimental results of longitudinal leaky surface waves with a higher phase velocity than that of ordinary leaky surface waves and a low propagation loss on lithium tetraborate (LBO) are investigated in detail. They propagate along the surface with a phase velocity close to that of longitudinal bulk wave, slightly radiating two kinds of shear bulk waves (or one shear bulk wave in the case that one of two shear wave terms is uncoupled) into the solid. Most surface components of the mode consist of a longitudinal wave term and an electromagnetic wave term. The detailed propagation properties of the longitudinal leaky surface waves on LBO with the Euler angles (phi, theta, 90 degrees ) are investigated theoretically and experimentally. The (011) cut of LBO was found to be desirable for higher frequency SAW devices. One of the reasons why that mode on LBO has a low propagation loss is also discussed.     

Nonlocal piezoelasticity based wave propagation of bonded double-piezoelectric nanobeam-systems

Piezoelectric nanobeam (PNB) offer the possibility of being used in micro-electromechanical systems and nano-electromechanical systems and the dynamic testing of such structures often produces stress wave propagation in them. This work concerns with the size-dependent wave propagation of double-piezoelectric nanobeam-systems (DPNBSs) based on Euler–Bernoulli beam model. The two piezoelectric nanobeams are coupled by an enclosing elastic medium which is simulated by Pasternak foundation. Nonlocal piezoelasticity theory is used to derive the general differential equation based on Hamilton’s principal to include those scale effects. Particular attention is paid to the wave propagation piezoelectric control of the coupled system in three cases namely in-phase wave propagation, out-of-phase wave propagation and wave propagation when one PNB is stationary. In three mentioned cases, an analytical method is proposed to obtain phase velocity; cut-off and escape frequencies of the DPNBSs. Results indicate that the imposed external voltage is an effective controlling parameter for wave propagation of the coupled system. Furthermore, the phase velocity of in-phase wave propagation is independent of elastic medium stiffness.     

On the transport of energy in water waves

Theory is developed and utilized for the calculation of the separate transport of kinetic, gravity potential, and surface-tension energies within sinusoidal surface waves in water of arbitrary depth. In Sect. 2 it is shown that each of these three types of energy constituting the wave travel at different speeds, and that the group velocity, c _g , is the energy-weighted average of these speeds, depth- and time-averaged in the case of the kinetic energy. It is shown that the time-averaged kinetic energy travels at every depth horizontally either with (deep water), or faster than the wave itself, and that the propagation of a sinusoidal wave is made possible by the vertical transport of kinetic energy to the free surface, where it provides the oscillating balance in surface energy just necessary to allow the propagation of the wave.The propagation speed along the surface of the gravity potential energy is null, while the surface-tension energy travels forward along the wave surface everywhere at twice the wave velocity, c. The flux of kinetic energy, when viewed traveling with a wave, provides a pattern of steady flux lines which originate and end on the free surface after making vertical excursions into the wave, even to the bottom, and these are calculated. The pictures produced in this way provide immediate insight into the basic mechanisms of wave motion. In Sect. 3 the modulated gravity wave is considered in deep water and the balance of terms involved in the propagation of the energy in the wave group is determined; it is shown again that vertical transport of kinetic energy to the surface is fundamental in allowing the propagation of the modulation, and in determining the well-known speed of the modulation envelope, c _g . Dedicated to Professor J.N. Newman in recollection of his many significant contributions to the theory and computation of waves and floating bodies and to the founding of the IWWWFB.     

A state-space dynamical representation for multibody mechanical systems part I: Systems with tree configuration

Summary This paper deals with the problem of transient wave propagation in isotropic inhomogeneous elastic Cosserat plates of uniform thickness by the method of singular wave curves. The transport equations governing the growth-decay behaviour of all extensional and bending wave modes are explicitly integrated to provide a common general formula involving the material parameters and wave geometry. An example of wave propagation, due to an initially straight wave in a plate with prescribed variable density is worked out in detail.     

Study of wave propagation in nanowires with surface effects by using a high-order continuum theory

A high-order continuum model is developed to study wave propagation in nanowires. By using the model, heterogeneous nanostructure effects can be captured especially for high wave frequency cases. Surface stress effects are also included by using the incremental deformation approach. The governing equations of motion in the nanowire are derived including both the strain-independent and strain-dependent surface stresses. For simplicity and clarity, specific attention will be paid to the effects of strain-independent surface stress in this study. The accuracy of the proposed model is validated by comparing dispersion curves of longitudinal wave propagation from the current model with those from the exact solution. By conducting a reduced formulation, the results predicted by the current model will be compared with those based on existed high-order models to show capability of the current model. Numerical simulations are then conducted to study both longitudinal and flexural wave propagation in nanowires. The surface stress effects upon both longitudinal and flexural wave propagation in nanowires are demonstrated, from which the size dependent wave information in nanowires can be observed. Some new physical wave phenomena related to the surface stress effects are discussed.     

Photoelastic investigation of dynamic load transfer in granular media

Summary Dynamic photoelasticity in conjunction with high-speed photography is utilized to study impact wave propagation and dynamic load transfer in granular soil. Series of sequentially recorded isochromatic fringe patterns provide full field information of the dynamic event. Experimental results show that the wave propagation process is governed by a contact wave which increases the density of contacts in propagation direction. The study of dynamic load transfer along specific representative load chains provides basic information about wave velocities, contact duration, and directional stability necessary for a rigorous analysis of the general complex dynamic wave-soil interaction problem.With 7 Figures     

Wave propagation of coupled double-DWBNNTs conveying fluid-systems using different nonlocal surface piezoelasticity theories

This work is concerned with the size-dependent wave propagation of coupled double-walled boron nitride nanotubes (DWBNNTs) conveying nanoflow-systems based on Timoshenko beam theory. The two DWBNNTs are coupled by an enclosing visco-Pasternak medium. The small-scale effects are captured applying different surface piezoelasticity theories, including stress gradient, strain gradient, and strain inertia gradient. An analytical method is proposed to obtain phase velocity, cut-off, and escape frequencies of the system. Three cases of in-phase wave propagation, out-of-phase wave propagation, and wave propagation with one DWBNNT fixed are considered. Results indicate that ignoring surface and small-scale effects lead to inaccurate results.     

Fracture mechanical analysis of self-fatigue in surface compression strengthened glass plates

This paper presents a fracture mechanical analysis of the static fatigue and spontaneous fragmentation of surface compression-strengthened glass plates in the absence of applied load. It is suggested that if an initial surface crack which is sufficiently deep to penetrate into the tensile zone within the plate interior is introduced into the plate, then static fatigue, and eventually spontaneous fracture may follow. The crack problem for glass plates under various internal stress fields is solved and the stress intensity factor is obtained as a function of the crack depth. Using the fracture toughness and the slow crack growth characterization of the material, the conditions for no crack propagation, crack propagation leading to crack arrest, and that leading to catastrophic failure are established and discussed. The general results obtained are illustrated by means of a numerical example based on a 2 mm thick surface compression-strengthened glass plate exposed to water at 25° C.Such a problem was encountered in relation to an eye-lens during a consulting case by one of the authors (DPHH).     

具有非均匀损伤带状区域中波的传播

对弹性波在二次曲线变化的非均匀损伤介质中的传播理论进行了研究。通过非均匀损伤区两端界面处力的平衡条件和位移连续性条件对方程式进行求解，利用勒让德多项式，求出了二次曲线变化的非均匀损伤介质中波动方程的解析形式解。对带状渐增和渐减的非均匀损伤介质中波的传播进行了实例计算分析，讨论了弹性波在二次曲线变化的非均匀损伤介质中传播的一般性质。     

用改进的Boussinesq方程模拟潜堤上的波浪变形

研究了一种改进的Boussinesq方程,采用预报校正格式对该方程进行了数值离散,并对淹没潜堤上的波浪变形进行了数值模拟,从数值模拟结果和实测值的比较结果来看,该方程能较好地模拟波浪在潜堤上传播时波面的变形过程,可以用于实际中的波浪问题计算。这种改进的Boussinesq方程本身及其求解方法需做进一步的完善。研究结果为实际应用Boussinesq方程来研究复杂地形上的波浪传播提供一定的理论指导。     

Acoustic waves in bounded anisotropic media: theorems, estimations, and computations

This paper discusses some basic achievements in theoretical studies on acoustic wave propagation along boundaries in anisotropic solids. In particular, the following issues are reviewed: existence theorems for subsonic surface and interface waves, leaky surface acoustic waves (SAW) and their relation to "supersonic" SAWs and fast exceptional bulk waves, the resonance reflection of bulk waves in the vicinity of leaky wave branches. General conclusions are illustrated by numerical examples.     

Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media

A mathematical model for the propagation of harmonic plane waves in an anisotropic piezo-thermoelastic medium is explained through three relations. Two of them relate the stress-induced harmonic variations in temperature and electric potential to mechanical displacement of material particles. The third is a system that defines modified Christoffel equations for wave propagation in the medium. The solution of this system is ensured by a quartic equation whose complex roots explain the existence and propagation of four attenuating waves in the medium. The effects of piezoelectricity and thermoelasticity on the wave propagation are analyzed in the discussion of special cases. An angle between propagation direction and direction of maximum attenuation defines the attenuated wave as inhomogeneous wave. The complex slowness vector for each of the four attenuated waves in the medium is resolved to calculate the phase velocity and the attenuation factor for its propagation as an inhomogeneous wave along a general direction in three-dimensional space. The variations in phase velocities and attenuation factors with propagation direction are computed, for a realistic numerical model.