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1.
Alessandro Marzani 《International Journal of Solids and Structures》2008,45(25-26):6347-6368
Herein, an enhanced spectral finite element (SFE) formulation to calculate the time–transient response in cylindrical waveguides is proposed. The original aspect over SFE-based formulations consists in the possibility to account for the effect of material absorption, i.e. guided waves attenuation, on the calculation of the time–transient response.First, the damped steady-state response is constructed by a weighted superposition of the waveguide modal properties obtained from the spectral decomposition of the governing wave equation. To this purpose an enhanced spectrally formulated finite element is developed, in which material damping is included allowing for complex stress–strain viscoelastic constitutive relations in force of the correspondence principle. Dispersive modal properties for the damped waveguide (phase velocity, energy velocity, attenuation and wavestructures) follow straightforwardly by simple formulae. Next, the frequency response of the problem is calculated by weighting the modal data and the spectrum of the applied time-dependent force via Cauchy residue theorem. Finally, the inverse Fourier transform of the frequency response leads to the time–transient response for propagative damped guided waves.The approach is not restricted to any anisotropy degree, holds for any linear viscoelastic constitutive relation that can be characterized and formulated in the frequency domain and it can be applied to SFE formulations for arbitrary cross-section waveguides. A study on guided waves propagating in a scheduled 4.in-40 ANSI steel pipe is presented, where the steel is considered first as perfectly elastic and then as an hysteretic viscoelastic medium, in order to show the effect of material absorption on the time–transient response. 相似文献
2.
This article is concerned with Rayleigh waves propagating along the free surface of a macroscopically homogeneous, prestressed
half-space. In the meso-scale, the half-space in question is taken to be a textured polycrystalline aggregate of cubic crystallites,
which has the normal to its free surface being a 2-fold axis of monoclinic sample symmetry. Under the theoretical framework
of linear elasticity with initial stress, an angular dependence formula, which shows explicitly how the phase velocity of
Rayleigh waves depends on the propagation direction, the prestress, and the crystallographic texture, is derived from a constitutive
equation motivated by Hartig's law. This velocity formula includes terms which describe the effects of texture on acoustoelastic
coefficients, and it is correct to within terms linear in the initial stress and in the anisotropic part of the incremental
elasticity tensor. Since its derivation makes no presumption on the origin of the initial stress, this velocity formula is
meant to be applicable when the prestress is induced by plastic deformations such as those incurred during the surface enhancement
treatment of low plasticity burnishing. The angular dependence formula assumes a simpler form when the texture of the prestressed
half-space is orthorhombic.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
This paper completes an earlier study (Tanuma and Man, Journal of Elasticity, 85, 21–37, 2006) where we derive a first-order perturbation formula for the phase velocity of Rayleigh waves that propagate along the free
surface of a macroscopically homogeneous, anisotropic, prestressed half-space. We adopt the formulation of linear elasticity
with initial stress and assume that the deviation of the prestressed anisotropic medium from a suitably-chosen, comparative,
unstressed and isotropic state be small. No assumption, however, is made on the material anisotropy of the incremental elasticity
tensor. With the help of the Stroh formalism, here we derive first-order perturbation formulas for the changes in polarization
ratio and phase shift of Rayleigh waves from their respective comparative isotropic value. Examples are given, which show
that the perturbation formulas for phase velocity and polarization ratio can serve as a starting point for investigations
on the possible advantages of using Rayleigh-wave polarization, as compared with using wave speed, for acoustoelastic measurement
of stress.
相似文献
4.
Herein we consider Rayleigh waves propagating along the free surface of a macroscopically homogeneous, anisotropic, prestressed half-space. We adopt the formulation of linear elasticity with initial stress and assume that the deviation of the prestressed anisotropic medium from a comparative ‘unperturbed’, unstressed and isotropic state, as formally caused by the initial stress and by the anisotropic part of the incremental elasticity tensor, be small. No assumption, however, is made on the material anisotropy of the incremental elasticity tensor. With the help of the Stroh formalism, we derive a first-order perturbation formula for the shift of phase velocity of Rayleigh waves from its comparative isotropic value. Our perturbation formula does not agree totally with that which was derived some years ago by Delsanto and Clark, and we provide another argument as further support for our version of the formula. According to our first-order formula, the anisotropy-induced velocity shifts of Rayleigh waves, taken in totality of all propagation directions on the free surface, carry information only on 13 elastic constants of the anisotropic part of the incremental elasticity tensor. The remaining eight elastic constants are those which would become zero if were monoclinic with the two-fold symmetry axis normal to the free surface of the material half-space in question. 相似文献
5.
《European Journal of Mechanics - B/Fluids》1999,18(1):13-34
The initial growth of a large scale perturbation on a fine-grained turbulent jet is studied via linear stability analysis. The turbulent jet is assumed to be homogeneous and isotropic with zero mean shear, and the inviscid stream outside the jet has a uniform velocity profile. The incremental Reynolds stress caused by the large scale perturbation is modeled by a viscoelastic constitutive equation, following the analysis of Crow (1968). It is found that the jet is always unstable to both sinuous and varicose types of perturbation, with the sinuous mode having a larger growth rate. In particular, short waves are always amplified, in contrast to the short wave stabilization at low speed found by Townsend (1966) for a purely elastic jet. The growth rates of these short waves are finite, and are smaller than those for the classical Kelvin-Helmholtz instability of an inviscid jet, but larger than those for the Hooper-Boyd (1983) instability of a viscous jet with continuous velocity profile. 相似文献
6.
This paper investigates the propagation of torsional wave in an initially stressed poroelastic layer with corrugated as well as loosely bonded boundary surfaces, sandwiched between a corrugated fiber-reinforced layer and a viscoelastic half-space under initial stress. The velocity equation has been obtained in closed form analytically and the substantial effect of affecting parameters on the phase velocity of torsional surface wave has been demonstrated numerically and graphically. Comparative study has been made to observe the effect of flatness parameter, reinforcement, viscoelasticity and porosity on the phase velocity, meticulously. Some particular cases have also been discussed and it is found that velocity equation is in well-agreement to the classical Love wave equation. Moreover, some remarkable observation has been made through numerical computation and graphical demonstration for fiber-reinforced layer of carbon fiber-epoxy resin, poroelastic layer of sandstone and a viscoelastic half-space. 相似文献
7.
A. Chattopadhyay S. Gupta S. A. Sahu S. Dhua 《Archive of Applied Mechanics (Ingenieur Archiv)》2013,83(3):357-366
The present paper is concerned with the propagation of torsional surface waves in a heterogeneous anisotropic half-space under the initial compressive stress. The heterogeneity in the half-space is caused by the linear variation in rigidity, initial compressive stress and density. The solution part of the problem involves the use of Whittaker function. The dispersion equation has been obtained in a closed form, which shows the variation of phase velocity with corresponding wave number. Effects of anisotropy and initial stress have been shown by the means of graphs for different anisotropic materials. It has found that the phase velocity of torsional waves decreases with increment in initial stress and inhomogeneity. Obtained phase velocity of torsional surface wave is found to be less than the shear wave velocity, which agrees with the standard result. 相似文献
8.
9.
Rodney J. Clifton 《International Journal of Plasticity》1985,1(4):289-302
Plastic wave experiments are reviewed, beginning with the earliest experiments of Bell on the propagation of incremental waves in prestressed bars. Attention is directed to experiments in which the plastic wave profile at different distances of propagation is used to infer information on the dynamic plastic response of the material in which the wave is propagating. Plastic waves in bars, tubes, and plates are considered. Principal results are reviewed on such primary physical features as the velocity of propagation of incremental waves, the dynamic elastic limit, the wave profiles of finite amplitude waves, and the effects of nonproportional loading. Objectives for future research are suggested. 相似文献
10.
The present paper studies the propagation of shear waves (SH-type waves) in an homogeneous isotropic medium sandwiched between two semi infinite media. The upper half-space is considered as orthotropic medium under initial stress and lower half-space considered as heterogeneous medium. We have obtained the dispersion equation of phase velocity for SH-type waves. The propagation of SH-type waves are influenced by inhomogeneity parameters and initial stress parameter. The velocity of SH-type wave has been computed for different cases. We have also obtained the dispersion equation of phase velocity in homogeneous media in the absence of initial stress. The velocities of SH-type waves are calculated numerically as a function of kH (non-dimensional wave number) and presented in a number of graphs. To study the effect of inhomogeneity parameters and initial stress parameter we have plotted the velocity of SH-type wave in several figure. We have observed that the velocity of wave increases with the increase inhomogeneity parameters. We found that in both homogeneous and inhomogeneous media the velocity of SH-type wave increases with the increase of initial stress parameter. The results may be useful for the study of seismic waves propagation during any earthquake and artificial explosions. 相似文献
11.
Farouk Benmeddour Fabien Treyssède Laurent Laguerre 《International Journal of Solids and Structures》2011,48(5):764-774
A three dimensional (3D) hybrid method combining the classical finite element (FE) method with the semi-analytical finite element (SAFE) technique is developed. This hybrid method is employed to study the interaction of guided waves with non-axisymmetric damages in cylinders. The near field surrounding the damage is analysed with the 3D FE method. The solution is expanded into sums of guided modes on both inlet and outlet cross-sections. Such eigenmode expansions enable separation into ingoing and outgoing waves, i.e., incident, reflected and transmitted waves. Using the SAFE method, elastic guided modes are then computed at the aforementioned cross-sections thus reducing the analysis to two dimensions (2D). The amplitudes of the incident modes are imposed, whereas those of the scattered modes are determined by solving the global system of the 3D hybrid FE-SAFE model. In this paper, a formula is proposed for the calculation of eigenforces and modal power flows from eigendisplacements and SAFE matrices. This has the advantage of simplifying the post-process of load eigenvectors in hybrid FE-SAFE methods. Results obtained for a vertical free-end cylinder are in good agreement with those published in the literature. Moreover, first results of the interaction of the fundamental compressional, flexural and torsional Pochhammer–Chree modes with non-axisymmetric vertical cracks are obtained and discussed. Then, the interactions of the fundamental compressional mode with oblique free-ends and cracks are briefly addressed. The power balance is shown to be satisfied with a good accuracy. 相似文献
12.
IntroductionThatthebloodhasviscoelasticpropertiesisawell_knownfact.TheresearchesforthebloodviscoelasticitybyG .B .Thurston[1~4]andS .Chien[5 ]showthatthebloodnotonlyappearstheviscoelasticityinvariousoscillatorybloodflows,butalsohasquitestrongelasticityinsome… 相似文献
13.
The frequency equation giving the phase velocity of a wave at the edge of a thick plate under initial stress is obtained.
Some particular cases are discussed to derive (a) the velocity of edge waves in a thin plate and (b) the velocity of Rayleigh
waves in a plate of infinite thickness under initial stress.
The results are compared with those for zero initial stress. 相似文献
14.
15.
EIGEN THEORY OF VISCOELASTIC MECHANICS FOR ANISOTROPIC SOLIDS 总被引:4,自引:0,他引:4
Guo Shaohua 《Acta Mechanica Solida Sinica》2001,14(1):74-80
Anisotropic viscoelastic mechanics is studied under anisotropic subspace. It is proved that there also exist the eigen properties
for viscoelastic medium. The modal Maxwell's equation, modal dynamical equation (or modal equilibrium equation) and modal
compatibility equation are obtained. Based on them, a new theory of anisotropic viscoelastic mechanics is presented. The advantages
of the theory are as follows: 1) the equations are all scalar, and independent of each other. The number of equations is equal
to that of anisotropic subspaces, 2) no matter how complicated the anisotropy of solids may be, the form of the definite equation
and the boundary condition are in common and explicit, 3) there is no distinction between the force method and the displacement
method for statics, that is, the equilibrium equation and the compatibility equation are indistinguishable under the mechanical
space, 4) each model equation has a definite physical meaning, for example, the modal equations of order one and order two
express the volume change and shear deformation respectively for isotropic solids, 5) there also exist the potential functions
which are similar to the stress functions of elastic mechanics for viscoelastic mechanics, but they are not man-made, 6) the
final solution of stress or strain is given in the form of modal superimposition, which is suitable to the proximate calculation
in engineering. 相似文献
16.
一维颗粒链的一端受到一个有初速度颗粒的撞击,导致颗粒连中产生稳定传播的应力波——高度非线性孤立波,该应力波的波长、波速以及幅值都能保持很好的稳定性,且遇到边界才会反射. 孤立波是一种良好的信息载体,广泛应用于无损检测技术中. 基于孤立波的特性,研究高度非线性孤立波与弹性大板耦合作用,基于赫兹定律和板的内在非弹性理论,推导出晶体链与大板的耦合微分方程组. 用龙格库塔法求解该微分方程组,得到颗粒链中各颗粒的位移、速度曲线. 通过分析回弹波出现的时间、回弹波所携带的能量以及模量、厚度、重力等对孤立波的影响,发现反射孤立波对大板的弹性模量和厚度尤为敏感,此外,颗粒链的摆放对整个耦合过程也有影响. 研究的结果为孤立波对结构体的无损探伤提供了理论依据,该技术可实现对结构体的快速检查和可控性研究. 相似文献
17.
地下爆炸与介质的能量耦合和介质中的波传播机制是理解地下爆炸源物理的重要基础。为研究地下爆炸辐射地震波能量的传播衰减规律,分析了黏弹性介质中地下爆炸地震波能量的组成。基于无限介质中黏弹性球面波理论,给出了速度、位移、应力、应变等物理量Laplace域的理论解。利用Laplace数值逆求解方法,建立了黏弹性介质中地下爆炸辐射地震波场的计算方法。以干黄土作为典型黏弹性材料,计算给出了地震波能量的传播特征,分析了地下爆炸辐射能量的传播衰减规律。结果表明:(1)在黏弹性介质中,某球面处流入的能量随半径增加而逐渐降低。在理想弹性介质中,某球面处流入的能量在几倍弹性半径外即可稳定到某一定值;(2)在某一固定的有限观测区域内,当观测时间足够长时,势能和耗散能均趋于某一定值,辐射动能趋于零;(3)当有限的观测区域能容纳一个完整波长的地震波时,地震波辐射动能的稳态值随波传播距离的增大而减小,总体上可以用指数函数和幂函数进行分段拟合。 相似文献
18.
The present investigation is concerned with the wave propagation at the boundary surface of elastic half-space and initially stressed viscothermoelastic diffusion with voids half-space. The longitudinal and transverse waves are incident obliquely at the plane interface between uniform elastic half-space and initially stressed viscothermoelastic diffusion with voids half-space. It is found that the amplitude ratios of various reflected and transmitted waves are functions of angle of incidence, frequency of incident wave and are influenced by the initial stress, diffusion, voids, elastic and viscoelastic properties of media. The expressions of amplitude ratios and energy ratios are obtained in closed form and computed numerically for a specific model. The variations of energy ratios with angle of incidence are shown graphically. The conservation of energy at the interface is verified. 相似文献
19.
The paper studies the relationship between the physical characteristics of a cylinder and the properties of normal axisymmetric waves in elastic–liquid waveguides. The cylinder is made of a compliant material in which the velocity of shear waves is less than the sonic velocity in a perfect compressible liquid. The complete system of dynamic elasticity equations and the wave equation are used to describe the wave fields in the elastic cylinder and fluid, respectively. This approach allows obtaining the dispersion characteristics of coupled normal waves in compound waveguides over wide ranges of frequencies and wavelengths. The curves of real, imaginary, and complex wave numbers versus frequency are plotted for specific pairs of waveguide materials. Computations are carried out for a thick-walled cylinder filled with a fluid and immersed in either vacuum or a fluid. It is found out that compliant and rigid materials of the cylinder affect differently the wave interaction process in elastic–liquid waveguides 相似文献
20.
In this paper we consider the propagation of Rayleigh surface waves in an exponentially graded half-space made of an isotropic Kelvin-Voigt viscoelastic material. Here we take into account the effect of the viscoelastic dissipation energy upon the corresponding wave solutions. As a consequence we introduce the damped in time wave solutions and then we treat the Rayleigh surface wave problem in terms of such solutions. The explicit form of the secular equation is obtained in terms of the wave speed and the viscoelastic inhomogeneous profile. Furthermore, we use numerical methods and computations to solve the secular equation for some special homogeneous materials. The results sustain the idea, existent in literature on the argument, that there is possible to have more than one surface wave for the Rayleigh wave problem. 相似文献