Rayleigh-Lamb waves in magneto-thermoelastic homogeneous isotropic plate

The propagation of magnetic-thermoelastic plane wave in an initially unstressed, homogeneous isotropic, conducting plate under uniform static magnetic field has been investigated. The generalized theory of thermoelasticity is employed, by assuming electrical behaviour as quasi-static and the mechanical behaviour as dynamic, to study the problem. The secular equations for both symmetric and skew-symmetric waves have been obtained. The magneto-elastic shear horizontal (SH) mode of wave propagation gets decoupled from rest of the motion and it is not influenced by thermal variations and thermal relaxation times. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation, because a finite thickness plate in such a situation behaves like a semi-infinite medium. Thin plate results are also deduced at the end. Dispersion curves are represented graphically for various modes of wave propagation in different theories of thermoelasticity. The amplitudes of displacement, perturbed magnetic field and temperature change are also obtained analytically and computed numerically. The result in case of elastokinetics, magneto-elasticity and coupled magneto-elasticity has also been deduced as special cases at appropriate stages of this work.     

激光激发薄管中超声兰姆波的数值模拟

用有限元方法,对薄管中热弹机制产生的激光超声进行了研究。在考虑材料热物理参数随温度变化的前提下,得到了薄铝管中的温度场和表面的超声导波,描绘了薄铝管中的逆时针向不同接收点处表面导波的时域波形图。由波形图可知,薄圆管中的激光超声导波是典型的L(0,m)模态的超声Lamb波,同时数值结果验证了管道中L(0,2)模式是传播速度最快且频散较小的导波,为激光超声导波在管道无损检测中的应用打下了一定的基础。     

Effect of surface/interface on the dynamic stress of two interacting cylindrical nano-inhomogeneities under compressional waves

Based on the surface/interface elasticity theory, the effect of surface/interface on the dynamic stress of two interacting cylindrical nano-inhomogeneities under compressional waves is considered. The analytical solutions of displacement potentials are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions at the interfaces. The addition theorem for cylindrical wave function is used to accomplish the superposition of wave fields in different coordinate systems. Analyses show that the effect of the interface properties on the dynamic stress is significantly related to the wave frequency of incident waves, the shear modulus ratio of the nano-inhomogeneities to matrix, and the relative position and distance between the two nano-inhomogeneities.     

Surface waves in fibre-reinforced anisotropic elastic media

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.     

Crack front waves in dynamic fracture

A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an ideal two-dimensional material, where the crack tip is a singular point. When a material is translationally invariant in the direction normal to the crack's propagation direction, this idealization is justified. A real tensile crack, however, is a planar object whose leading edge forms a propagating one-dimensional singular front (a `crack front'). We consider the interaction of a crack front with localized material inhomogeneities (asperities), in otherwise ideal brittle amorphous materials. We review experiments in these materials which indicate that this interaction excites a new type of elastic wave, a front wave, which propagates along the crack front. We will show that front waves (FW) are highly localized nonlinear entities that propagate along the front at approximately the Rayleigh wave speed, relative to the material. We will first review some of their characteristics. We then show that by breaking the translational invariance of the material, FW effectively act as a mechanism by which initially `massless' cracks acquire inertia.     

Effect of voids on the propagation of waves in an elastic layer

The present paper investigates the propagation of waves in an elastic layer containing voids. Numerical calculations and discussions indicate that the velocity of the propagation of waves decreases due to the presence of voids in the material medium of the layer and the voids cause dispersion of the general waveform.     

On finite amplitude water waves

The modulation theory for finite amplitude water waves is developed using the variational technique. It is shown how Levi-Civita’s relation, Starr’s relation and the conservation equations all follow very simply and naturally from this approach. The present paper is limited to deep water waves, but the results can be extended to arbitrary depth. For deep water, the appropriate Lagrangian can be reduced to a single function, which can be taken from recent numerical calculations on periodic waves. This is used to discuss the stability of wavetrains to long modulations.     

Numerical simulation of one‐dimensional flows through porous media with shock waves

This work studies an unsaturated flow of a Newtonian fluid through a rigid porous matrix, using a mixture theory approach in its modelling. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid (Newtonian fluid) and an inert gas (to account for the mixture compressibility). A set of two nonlinear partial differential equations describes the problem, which is approximated by means of a Glimm's scheme, combined with an operator splitting technique. Copyright © 2001 John Wiley & Sons, Ltd.     

Decompaction waves in falling granular flows

We study the falling of a 2D column of granular material placed initially into a container formed by two lateral vertical walls with a positive friction coefficient by using molecular dynamics simulations. The time evolution of the mean velocity shows an intermediary region where the grains velocity is relatively constant. Follows a decompaction of the granular flow propagating from the bottom to the top of the column with a velocity of approximately 450 cm/s. Just before the flow decompaction an analysis of the forces exhibits a peculiar behavior which can be assimilated to stick-slip. Finally, after the passage of the decompaction wave low and high density regions coexist both descending with relatively the same velocity and the density exhibits a power law spectrum in 1/f ^a , with a≈ 1.51. Received: 9 May 1999     

Effects of inhomogeneity on surface waves in anisotropic media

This paper investigates the effects of anisotropy and inhomogeneity on surface waves in elastic media. Exponential variation in properties are assumed for the elastic parameters and material density. The classical equations of motion for propagation of waves in an inhomogeneous transversely isotropic elastic solid are deduced. The equations of motion for surface waves are derived and general surface waves are investigated. This general theory is then utilized to investigate Rayleigh, Love and Stoneley waves. Results obtained in the above cases reduce to the corresponding well-known classical results when inhomogeneity and anisotropy are not present. It is seen that inhomogeneity has significant effects on dispersion characteristics. Numerical calculations are included for Love waves and some conclusions have been drawn from the above calculations.     

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.     

Elementary water waves

New elementary farfield and nearfield time-harmonic water waves, observed from a Galilean reference frame, are given. These two related classes of waves are modifications of classical elementary plane waves that are obtained in a simple way, using only elementary fundamental considerations, by analyzing waves that slowly grow from rest at time T = −∞ and are bounded in the farfield. This approach circumvents the need for a radiation condition, which may indeed be regarded as (indirectly) satisfied ab initio by the elementary farfield and nearfield waves given here. The farfield waves are the product of classical elementary waves by a function, called radiation function, that is defined explicitly in terms of the dispersion function. Thus, this radiation function is valid not only for water waves, but more generally for a broad class of linear dispersive waves. For illustration and verification purposes, elementary stationary-phase considerations are used to determine the main properties (phase and group velocities, wave patterns, asymptote and cusp lines) of farfield waves, and two particular classes of water waves—steady ship waves and time-harmonic waves generated by an offshore structure—in uniform finite water depth are considered. The elementary nearfield waves can readily be used to construct free-surface Green functions or in a spectral representation of nearfield flows.     

On a model for thermo-poroacoustic waves

We present a model for acoustic wave propagation in a porous material which also allows for propagation of a thermal wave. We provide a thermodynamic development of a Darcy law theory which is consistent with a relaxation time for the heat flux. Nonlinear acceleration wave evolution is considered in detail.     

Numerical modelling of the scattering of elastic waves in plates

This paper describes the application of finite difference methods to the calculation of the scattering of elastic waves. The emphasis is on cracklike defects in plates, and it is shown that a common numerical technique can span a range of wavelengths from Lamb waves to ultrasonic waves with many reflections from the surfaces of the plate. Quantitative results are given for the scattering of Lamb waves and ultrasonic shear waves from surface-breaking cracks.     

Numerical simulation of transient waves in a heterogeneous soil layer

The passage of elastic waves through the upper soil strata is modeled by a rather simple solution based on freely propagating waves in a continuously heterogeneous material with amplitude dependence on a single coordinate corresponding to the direction of propagation. Specifically, pseudo-dilational and pseudo-rotational waves are developed for an elastic medium with position-dependent density and thus position-dependent pressure (P) and shear (S) wavespeeds, although in a strict sense these no longer exist as such due to coupling through the material heterogeneity. Time harmonic conditions are assumed to hold at the fundamental solution level and transient signal generation is achieved through Fourier synthesis. Numerical examples for the square root of linear in the depth coordinate wavespeed profiles are used in modeling the passage of impulsively-generated signals in a soft soil deposit under two-dimensional conditions.     

On Axisymmetric Longitudinal Wave Propagation in Double-Walled Carbon Nanotubes

An attempt is made into the investigation of longitudinal axisymmetric wave propagation in the DWCNT with the use of the exact equations of motion of the linear theory of elastodynamics. The DWCNT is modeled as concentricallynested two circular hollow cylinders between which there is free space. The difference in the radial displacements of these cylinders is coupled with the van der Waals forces and it is assumed that full slipping conditions occur on the inner surface of the outer tube and on the outer surface of the inner tube. Numerical results on the influence of the problem parameters such as the thickness/radius ratio, the distance between the tubes of the DWCNT and the van der Waals forces on the dispersion curves are presented and discussed. In particular, it is established that new types of modes arise under propagation of axisymmetric longitudinal waves as a result of the van der Waals interaction between the tubes of the DWCNT. The limit values of the wave propagation velocity are also analyzed.     

Internal waves in an elliptical channel

Abstract

Internal waves in open channels of various depths are studied, in this paper, and a wetted cross section with an elliptical bottom is considered. The frequencies of the first three sloshing modes of internal waves in two superposed fluids contained in an elliptical channel are calculated for various ratios of the depths of the two layers. Numerical solutions converge to analytical solutions based on the shallow water theory as the depth of the thin lower layer approaches zero. Also, solutions for the frequencies of the longitudinal modes of progressive internal waves in two superposed fluid layers contained in an elliptical channel are calculated for various ratios of the depths of the two layers and for two different wave numbers k.