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1.
In this paper, we constructed the equations of generalized thermoelastic isotropic and homogeneous half-space under hydrostatic initial stress in the context of the Green and Naghdi (GN) theory of types II and III. Normal mode analysis is used to obtain the exact expressions of temperature, displacement and stress. Comparisons are made with the results predicted by GN theory of types II and III in the presence and absence of the hydrostatic initial stress. The temperature, displacement and stress distributions are represented graphically. 相似文献
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V. V. Skripachev 《Journal of Applied Mechanics and Technical Physics》1968,9(2):208-209
An effective method for the approximate solution of the Eq. [1] for the intensity of a reflected shock wave in the case of oblique incidence of a detonation wave on an elastic half-space is described; the elastic half-space is described by a certain specific form of the equation of state. Formulas relating the front and particle velocities behind the transmitted wave front to physical parameters are derived. Values of the wave intensity and other quantities determined with the aid of a Ural-2 computer are cited.The author of [1, 2] investigated the regular reflection of shock waves from the boundary between two bodies. In the present paper we solve the analogous problem in the case of oblique incidence of a detonation wave on an elastic half-space. The detonation wave deforms the elastic half-space, which assumes the position OK1 (Fig. 1) forming the angle to the initial direction KO of the halfspace boundary. We assume that the acoustic stiffness of the halfspace is larger than the acoustic stiffness of the explosive. In this case, both reflected wave 2 and transmitted wave 3 are shock waves [3]. Let us denote the velocities of propagation of the detonation, reflected, and transmitted waves by Ui(i=1, 2, 3), respectively; let the pressure be pi and let the density bep
i(i=0, 1, 2, 3, 4). The quantities U1, 1, 0, and 4 are given. We determine the intensities of waves 2 and 3, their velocities of propagation, and the angles 2, 3 and . The parameters are constant within each of the domains a, b, c, d, and e. In domains a and e the medium is stationary, i.e., u0=u4 =0. The basic equations of the problem express the conditions at the wave fronts and the dynamic and kinematic relationships. 相似文献
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The generalized thermo-elasticity theory, i.e., Green and Naghdi (G-N) Ⅲ theory, with energy dissipation (TEWED) is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with com- plex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre's method. It reveals that the coupled magneto-thermoelastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented. 相似文献
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The problem of reflection and transmission due to longitudinal and transverse waves incident obliquely at a plane interface between uniform elastic solid half-space and fractional order thermoelastic solid half-space has been studied. It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence and frequency of incident wave and are influenced by the fractional order thermoelastic properties of media. The expressions of amplitude ratios and energy ratios have been computed numerically for a particular model. The variation of amplitude and energy ratios with angle of incidence is shown graphically. The conservation of energy at the interface is verified. 相似文献
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The paper deals with the phenomena of reflection and refraction of plane elastic waves at a plane interface between two semi-infinite elastic solid media in contact, when both the media are initially stressed. It has been shown analytically that both reflected and refracted P and SV waves depend on initial stresses present in the media. The numerical values of reflection and refraction coefficients for different initial stresses and the angle of incidence have been calculated by computer and the results are given in the form of graphs. Many results are found in the paper which are not seen in initially stress-free media. 相似文献
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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
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Baljeet Singh 《European Journal of Mechanics - A/Solids》2010,29(5):911-916
Lord–Shulman and Green–Lindsay theories of generalized thermoelasticity are applied to study the reflection from a thermally insulated stress-free thermoelastic solid half-space of monoclinic type. A particular model is chosen for the numerical computations of reflection coefficients. Effects of anisotropy and relaxation times are observed on reflection coefficients. 相似文献
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The paper deals with the phenomenon of reflection of plane elastic waves in a free surface when the medium is initially stressed. It has been shown analytically that the reflected P and SV waves depend on initial stresses present in the medium. The numerical values of reflection coefficients for different initial stresses and the angle of incidence have been calculated by the Computer I.C.L. 1901-A and the results are given in the form of graphs. Many interesting results are found in the paper which are not seen in an initially stress-free medium. 相似文献
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The problem of reflection and refraction of waves at the interface of an elastic solid and microstretch thermoelastic solid with microtemperatures has been investigated. It is shown that due to incidence of P-wave or SV-wave at the interface, the waves are reflected and refracted. The amplitude ratios of these various reflected and refracted waves have been computed numerically, and graphical representation of their variations is made with the angle of incidence. Effect of microrotation on these amplitude ratios has been shown graphically. Some particular cases of interest have also been discussed. 相似文献
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The reflection and transmission of plane waves from a fluid-piezothermoelastic solid interface are studied. The expressions for amplitude ratios and energy ratios corresponding to reflected waves and transmitted waves are derived analytically. The piezo-thermoelastic solid half-space is assumed to have 6mm type symmetry and assumed to be loaded with water. The effects of angle of the incidence, the frequency, the specific heat, the relaxation time, and the thermal conductivity on the reflected and transmitted energy ratios are studied numerically for a particular model of cadmium selenide (CdSe) and water. Some special cases are also studied. 相似文献
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Abo-el-nour N. Abd-alla Fatimah A. Alsheikh 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(9):843-857
This paper is devoted to study a problem of reflection and refraction of quasi-longitudinal waves under initial stresses at
an interface of two anisotropic piezoelectric media with different properties. One of the two media is aluminum nitride, which
is considered the down piezoelectric medium and the above medium is chosen as PZT-5H ceramics. The two piezoelectric media
welded are assumed to be anisotropic of a type of a transversely isotropic crystals (hexagonal crystal structure, class 6 mm).
The equations of motion and constitutive relations for the piezoelectric media have been written. Suitable boundary conditions
are used to obtain the reflection and refraction coefficients. For an incidence of quasi-longitudinal plane waves, four independent-type
amplitude ratios of elastic displacement components for plane waves, called quasi-longitudinal (qP) and quasi-shear vertical
(qSV) waves, are shown to exist. Also, it is observed that there exist four dependent amplitude ratios of electric potential,
which are proportional to the previous four types. Finally, it is found that the coefficients of reflection and refraction
are functions of angle of incidence, elastic constants, piezoelectric potential parameters and the initial stresses. Numerical
computations and the results obtained are depicted graphically. In the end, a particular case has been reduced from the present
study. This investigation is considered important because the initial stresses in such practical problems are inevitable and
may result in frequency shift, a change in the velocity of surface waves and controlling the selectivity of a filter compensation
of the devices. 相似文献
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We solve the problem on the interaction of plane elastic nonstationary waves with a thin elastic strip-shaped inclusion. The
inclusion is contained in an unbounded body (matrix) which in under conditions of plane strain. It is assumed that the condition
of perfect adhesion between the inclusion and the matrix is satisfied. Because of the small thickness of the inclusion we
assume that the bending and shear displacements at any inclusion point coincide with the displacements of the corresponding
points of its midplane. The displacements on the midplane itself are found from the corresponding equations of the theory
of plates. The statement of the boundary conditions for these equations takes into account the forces and moments acting on
the inclusion edges from the matrix. The solution method is based on representing the displacements in the space of Laplace
transforms as a discontinuous solution of the Lame’ equations for the plane strain with subsequent determining the transforms
of the unknown jumps from integral equations. The passage to the original functions is performed numerically by methods based
on replacement of the Mellin integral by the Fourier series. As a result, we obtain approximate formulas for calculating the
stress intensity factors for the inclusion. These formulas are used to study the time dependence of the stress intensity factors
and the influence of the inclusion rigidity on their values. We also study the possibility of treating inclusions of high
rigidity as absolutely rigid inclusions. 相似文献
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International Applied Mechanics - 相似文献
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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