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1.
Constitutive relations and field equations are developed for an elastic solid with voids subjected to electro-magnetic field. The linearized form of the relations and equations are presented separately when medium is subjected to a large magnetic field and when it is subjected to a large electric field. The possibility of propagation of time harmonic plane waves in an infinite elastic solid with voids has been explored. It is found that when the medium is subjected to large magnetic field, there exist two coupled longitudinal waves propagating with distinct speeds and a transverse wave mode. However, when the medium is subjected to a large electric field, there may propagate five basic waves comprising of four coupled longitudinal waves propagating with distinct speeds and a lone transverse wave. The effects of magnetic and electric fields are observed on the propagation characteristics of the existing waves. Under the limiting cases of frequency and for different electric conductive materials, the speeds of various waves are investigated. The phase speeds of different waves and their corresponding attenuations have been computed against the frequency parameter and depicted graphically for a specific material. 相似文献
2.
The generalized thermoelasticity theory based upon the Green and Naghdi model II of thermoelasticity as well as the Eringen’s nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves which are dispersive in nature and associated with attenuation. In addition to the coupled waves, there also exists one independent vertically shear type wave which is dispersive but without any attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear type wave is found to to be associated with a critical frequency, while the coupled longitudinal waves may have critical frequencies under constraints. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on the phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients as well as the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted. 相似文献
3.
Narayan Das Soumen De Nantu Sarkar 《Mathematical Methods in the Applied Sciences》2020,43(3):1313-1336
The generalized thermoelasticity theory based upon the Green and Naghdi model III of thermoelasticity as well as the Eringen's nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves, which are dispersive in nature and experience attenuation. In addition to the coupled waves, there also exists one independent vertically shear-type wave, which is dispersive but experiences no attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear-type wave is found to face a critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients and the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted. 相似文献
4.
The propagation of plane harmonic waves are studied in a microstretch fluid medium. It is found that five basic waves can propagate at distinct speeds in an infinite linear homogeneous isotropic microstretch fluid. Out of these five waves, one is a longitudinal micro-rotational wave, two are coupled longitudinal waves and remaining two are coupled transverse waves. The longitudinal micro-rotational wave travels independently and is not influenced by the microstretching of the medium, while the coupled longitudinal waves arise due to the presence of microstretching and coupled transverse waves arise due to the presence of micro-rotation in the medium. Speed of propagation of all the waves are found to be complex valued and dispersive at low frequency, but almost non-dispersive at high frequency. Due to complex valued speeds of propagation, all the waves are attenuating but differently. Coupled sets of longitudinal waves reduce to a longitudinal wave of micropolar fluid in the absence of microstretching. Reflection phenomena of a set of coupled longitudinal waves incident obliquely at the free surface of a microstretch fluid half-space has been investigated. Closed formulae for the reflection coefficients are presented and computed numerically for a particular medium. The real and imaginary parts of the complex speeds of all the waves and their corresponding attenuation coefficients have also been studied numerically and depicted graphically against frequency parameter. 相似文献
5.
The present investigation is concerned with the reflection of plane waves from the free surface of a homogeneous, anisotropic, fiber-reinforced thermoelastic rotating medium under two-temperature and dual-phase-lag model. It has been observed that three coupled plane waves travel in the medium with distinct speeds. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. The numerical values of the modulus of reflection coefficients are presented graphically to exhibit the two-temperature, phase lag and rotation parameter effects. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence. 相似文献
6.
A.M. Abd-Alla S.R. Mahmoud S.M. Abo-Dahab M.I. Helmy 《Applied mathematics and computation》2011,217(9):4321-4332
In this paper, propagation of shear waves in a non-homogeneous anisotropic incompressible, gravity field and initially stressed medium is studied. Analytical analysis reveals that the velocity of propagation of the shear waves depends upon the direction of propagation, the anisotropy, gravity field, non-homogeneity of the medium, and the initial stress. The frequency equation that determines the velocity of the shear wave has been obtained. The dispersion equations have been obtained and investigated for different cases. A comparison is made with the results predicted by Abd-Alla et al. [22] in the absence of initial stress and gravity field. The results obtained are discussed and presented graphically. 相似文献
7.
Effect of micro-inertia in the propagation of waves in micropolar thermoelastic materials with voids
The effect of micro-inertia in the propagation of waves in micropolar thermoelastic materials with voids has been investigated. Elastic waves are reflected due to incident coupled longitudinal and coupled shear waves from a plane free boundary of micropolar thermoelastic materials with voids. The amplitude ratios corresponding to the reflected coupled longitudinal and coupled shear waves are derived by using appropriate boundary conditions. Energy partition in the free surface has been presented. The amplitude and energy ratios of the reflected waves are also computed numerically for a particular model. 相似文献
8.
L. A. Alexeyeva G. K. Kaishybaeva 《Computational Mathematics and Mathematical Physics》2016,56(7):1343-1354
The Lamé system describing the dynamics of an isotropic elastic medium affected by a steady transport load moving at subsonic, transonic, or supersonic speed is considered. Its fundamental and generalized solutions in a moving frame of reference tied to the transport load are analyzed. Shock waves arising in the medium at supersonic speeds are studied. Conditions on the jump in the stress, displacement rate, and energy across the shock front are obtained using distribution theory. Numerical results concerning the dynamics of an elastic medium influenced by concentrated transport loads moving at sub-, tran- and supersonic speeds are presented. 相似文献
9.
The model of the equations of generalized magneto-thermoelasticity with two relaxation times in an isotropic elastic medium under the effect of reference temperature on the modulus of elasticity is established. The modulus of elasticity is taken as a linear function of reference temperature. Reflection of magneto-thermoelastic waves under generalized thermoelasticity theory is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid in a vacuum. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained. Similarly, the reflection coefficients ratios variations with the angle of incident under different conditions are shown graphically. A comparison is made with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature. 相似文献
10.
This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field, where deformations are relatively small, a linear elastic constitutive behavior is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model using a subdomain formulation. The results show that, in the near field, the response of the soil is dominated by a vertically polarized shear wave, whereas in the far field, Rayleigh waves dominate the ground vibration and body waves are importantly attenuated. Finally, the computed ground vibrations are compared with the results of field measurements reported in the literature. 相似文献
11.
A. P. Sarvazyan 《Mechanics of Composite Materials》1975,11(4):594-597
The laws of propagation of elastic waves of different types in biological tissues in the acoustic frequency range have been theoretically and experimentally investigated. The contributions of the imaginary and real components of the complex modulus of elasticity to the elastic wave velocity are analyzed. It is shown that in soft tissues, low-frequency elastic disturbances are propagated chiefly by shear (transverse) waves. The geometric dispersion of the elastic wave velocity has been investigated in experiments on gel model systems; the results of the measurements are in agreement with the theoretical dispersion curve. 相似文献
12.
Prashant Saxena Ray W. Ogden 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,63(6):1177-1200
In this paper, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space of an incompressible non-conducting magnetoelastic material in the presence of an initial uniform magnetic field is analyzed. The equations and boundary conditions governing linearized incremental motions superimposed on an underlying deformation and magnetic field for a magnetoelastic material are summarized and then specialized to a form appropriate for the study of Love-type waves in a layered half-space. The wave propagation problem is then analyzed for different directions of the initial magnetic field for two different magnetoelastic energy functions, which are generalizations of the standard neo-Hookean and Mooney?CRivlin elasticity models. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein?CGulyaev waves in piezoelectric materials. Such waves are discussed briefly at the end of the paper. 相似文献
13.
T. W. Wright 《Studies in Applied Mathematics》1985,72(2):149-160
A nonlinear intrinsic theory is used to describe the motions of a straight round elastic rod including the influence of radial shear and inertia. Consideration of steady wave motions reduces the two coupled partial differential equations to ordinary differential equations for which two integrals of the motion may be found. For incompressible elastic materials with the restriction of small strain gradients, but arbitrary finite strains, a large variety of exact solutions may be found by quadrature. These include large amplitude periodic waves (which may contain shocks), solitary waves, and in some cases waves that are transitional from one stress level to another. Such solutions may be found for uniform stress strain curves that are concave up or down or that contain inflections, and even for nonmontonic curves, which have been used to represent phase transitions. 相似文献
14.
Zheng Li Ya-Guang Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,61(6):1033-1051
This paper is devoted to the study of asymptotic behavior in the propagation and reflection of discontinuous solutions to linear and semilinear thermoelastic equations with second sound in one space variable. When the relaxation parameter goes to zero, we obtain that the jump of temperature vanishes while jumps of elastic waves and heat flux are propagated and reflected with the elastic speeds. Furthermore, it is observed that these jumps decay exponentially when the time goes to infinity, and the decay rates not only depend on the growth rate of the nonlinear source terms and heat conduction coefficient, but also depend on the change rates of speeds of elastic waves. 相似文献
15.
This paper is devoted to the study of asymptotic behavior in the propagation and reflection of discontinuous solutions to
linear and semilinear thermoelastic equations with second sound in one space variable. When the relaxation parameter goes
to zero, we obtain that the jump of temperature vanishes while jumps of elastic waves and heat flux are propagated and reflected
with the elastic speeds. Furthermore, it is observed that these jumps decay exponentially when the time goes to infinity,
and the decay rates not only depend on the growth rate of the nonlinear source terms and heat conduction coefficient, but
also depend on the change rates of speeds of elastic waves. 相似文献
16.
《Chaos, solitons, and fractals》2001,12(2):381-389
The object of the present study is to investigate the propagation of two-dimensional waves in a weakly nonlinear and weakly dispersive elastic solid. The reductive perturbation method is directly applied to a Lagrangian whose Euler–Lagrange equations give the field equations for a quadratically nonlinear elastic medium with higher order gradients. In the long-wave approximation, it is shown that the long-time behavior of the two transverse waves is governed by the two coupled modified Kadomtsev–Petviashvili (CMKP) equations. Depending on the choice of the direction of perpendicular dynamics, various forms of the CMKP equations are obtained. Some special solutions are also presented for a simplified form of the CMKP equations. 相似文献
17.
A.D. Chernyshov 《Journal of Applied Mathematics and Mechanics》2008,72(1):54-58
Two exact solutions of the plane strain problem of the harmonic oscillations of a viscoelastic rod, the cross-section of which is a right triangle, are proposed. Either the normal displacement and the shear stress or the shear displacement and the normal stress of the side surface of the rod are given. Six dimensionless parameters which affect the dynamic deformation process are derived. Two parameters characterize the contribution of the viscous properties with respect to the elastic properties, two others define the logarithmic decrement of the longitudinal and shear harmonic waves, and two other parameters affect the wavelength of the corresponding wave and the velocity of motion of the wave front of these waves. The velocities of both types of waves and their wavelengths turn out to be greater than the velocities and wavelengths of the corresponding elastic waves. It is shown that, for certain values of the viscosity and the oscillation frequency, pseudo-resonance frequencies are possible which are higher than the resonance frequencies for an elastic medium. 相似文献
18.
M. Ciarletta 《Journal of Mathematical Analysis and Applications》2007,333(1):142-150
A model for coupled elasto-acoustic waves, thermal waves, and waves associated with the voids, in a porous medium is investigated. Due to the use of lighter materials in modern buildings and noise concerns in the environment such models for thermo-poroacoustic waves are of much interest to the building industry. Analysis of such waves is also of interest in acoustic microscopy where the identification of material defects is of paramount importance to industry and medicine. We present a model for acoustic wave propagation in a porous material which also allows for propagation of a thermal wave. The thermodynamics is based on an entropy inequality of A.E. Green, F.R.S. and N. Laws and is presented for a modification of the theory of elastic materials with voids due to J.W. Nunziato and S.C. Cowin. A fully nonlinear acceleration wave analysis is initiated. 相似文献
19.
The response of a weak interface inside an isotropic elastic medium to an approaching source is considered. It is shown that
a strong shear wave arises in the wave field reflected at an angle greater than a critical one. Properties of this wave are
studied, and theoretical seismograms describing the contribution of all reflected waves to the total field are presented.
Bibliography: 19 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 89–100. 相似文献
20.
Semra Ahmetolan Mevlut Teymur 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(3):457-474
Propagation of nonlinear shear horizontal (SH) waves in a homogeneous, isotropic and incompressible elastic plate of uniform
thickness is considered. The constituent material of the plate is assumed to be generalized neo-Hookean. By employing a perturbation
method and balancing the weak nonlinearity and dispersion in the analysis, it is shown that the nonlinear modulation of waves
is governed asymptotically by a nonlinear Schr?dinger (NLS) equation. Then the effect of nonlinearity on the propagation characteristics
of asymptotic waves is discussed on the basis of this equation. It is found that, irrespective of the plate thickness, the
wave number and the mode number, when the plate material is softening in shear then the nonlinear plane periodic waves are
unstable under infinitesimal perturbations and therefore the bright (envelope) solitary SH waves will exist and propagate
in such a plate. But if the plate material is hardening in shear in this case nonlinear plane periodic waves are stable and
only the dark solitary SH waves may exist. 相似文献