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1
Content available Study of axi-symmetric vibrations in a micropolar transversely isotropic layer
Gupta R. R., Gupta R. R.
International Journal of Applied Mechanics and Engineering
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2019
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Vol. 24, no. 2
259--268
EN
The present investigation deals with the propagation of circular crested Lamb waves in a homogeneous micropolar transversely isotropic medium. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation are computed numerically for magnesium as a material and the dispersion curves, amplitudes of displacements and microrotation for symmetric and skew-symmetric wave modes are presented graphically to evince the effect of anisotropy. Some special cases of interest are also deduced.
2
Content available Investigation of waves generated in transversely isotropic micropolar generalized thermoelastic half space under temperature dependent properties
Gupta R. R., Gupta R. R.
International Journal of Applied Mechanics and Engineering
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2019
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Vol. 24, no. 4
53--65
EN
The present study deals with the propagation of waves in a transversely isotropic micropolar generalized thermoelastic material possessing temperature dependent elastic properties. After developing the solution for LS, GL and CT theory, the phase velocities and attenuation quality factor have been obtained. The expressions for amplitudes of stresses, displacements, microratation and temperature distribution have been derived and computed numerically. The numerically evaluated results have been plotted graphically. Some particular cases of interest have also been obtained.
3
Content available remote Magnetoelastic shear wave propagation in pre-stressed anisotropic media under gravity
Kumari N., Chattopadhyay A., Singh A. K., Sahu S. A.
Acta Geophysica
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2017
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Vol. 65, no. 1
189--205
EN
The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker’s asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot’s gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.
4
Content available The fundamental solutions for the stress intensity factors of modes I, II and III. The axially symmetric problem
Rogowski B.
International Journal of Applied Mechanics and Engineering
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2015
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Vol. 20, no. 2
345--372
EN
The subject of the paper are Green’s functions for the stress intensity factors of modes I, II and III. Green’s functions are defined as a solution to the problem of an elastic, transversely isotropic solid with a penny-shaped or an external crack under general axisymmetric loadings acting along a circumference on the plane parallel to the crack plane. Exact solutions are presented in a closed form for the stress intensity factors under each type of axisymmetric ring forces as fundamental solutions. Numerical examples are employed and conclusions which can be utilized in engineering practice are formulated.
5
Content available Wave propagation in a micropolar transversely isotropic generalized thermoelastic half-space
Gupta R. R.
International Journal of Applied Mechanics and Engineering
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2014
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Vol. 19, no. 2
247--257
EN
Rayleigh waves in a half-space exhibiting microplar transversely isotropic generalized thermoelastic properties based on the Lord-Shulman (L-S), Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories are discussed. The phase velocity and attenuation coefficient in the previous three different theories have been obtained. A comparison is carried out of the phase velocity, attenuation coefficient and specific loss as calculated from the different theories of generalized thermoelasticity along with the comparison of anisotropy. The amplitudes of displacements, microrotation, stresses and temperature distribution were also obtained. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.
6
Content available Surface wave characteristics in a micropolar transversely isotropic halfspace underlying an inviscid liquid layer
Gupta R. R., Gupta R. R.
International Journal of Applied Mechanics and Engineering
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2014
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Vol. 19, no. 1
49--60
EN
The present investigation deals with the propagation of waves in a micropolar transversely isotropic half space with an overlying inviscid fluid layer. Effects of fluid loading and anisotropy on the phase velocity, attenuation coefficient, specific loss and relative frequency shift. Finally, a numerical solution was carried out for aluminium epoxy material and the computer simulated results for the phase velocity, attenuation coefficient, specific loss and relative frequency shift are presented graphically. A particular case for the propagation of Rayleigh waves in a micropolar transversely isotropic half-space is deduced and dispersion curves are plotted for the same as functions of the wave number. An amplitude of displacements and microrotation together with the path of surface particles are also calculated for the propagation of Rayleigh waves in the latter case.
7
Content available Reflection of waves in initially stressed transversely isotropic fibre-reinforced thermoelastic medium
Gupta R. R., Gupta R. R.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 3
671--685
EN
The present investigation deals with the reflection of plane periodic waves incident at the surface of a homogeneous initially stressed transversely isotropic fibrereinforced thermoelastic medium. The wave equations are solved by imposing proper conditions on displacements, stresses and temperature distribution. Numerically simulated results have been depicted graphically for different angles of incidence with respect to frequency. Some special cases of interest have also been deduced from the present investigation.
8
Content available Thermoelastic disturbances in a transversely isotropic half-space due to thermal point load
Verma K. L.
Journal of Theoretical and Applied Mechanics
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2012
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Vol. 50 nr 2
399-422
EN
The objective of this paper is to study disturbances due to thermal point load in a homogeneous transversely isotropic half-space in generalized thermoelasticity. A combination of the Fourier and Hankel transform technique is applied to obtain the solutions to governing equations. Cagniared’s technique is used to invert the transformed solutions for small times. Theoretically obtained results, for temperature, stresses are computed numerically for a zinc material. It is found that variations in stresses and temperature are more prominent at small times and decrease with passage of time. Theg results obtained theoretically are represented graphically at different values of thermal relaxation times.
PL
Celem pracy jest zaprezentowanie zaburzeń wywołanych punktowym obciążeniem termicznym przyłożonym do jednorodnej, poprzecznie izotropowej półprzestrzeni w ogólnym sformułowaniu zagadnieniu termosprężystości. Do wyznaczenia równań układu zastosowano kombinację transformaty Fouriera i Hankela. Przy odwracaniu tak otrzymanych transformat użyto metody Cagniarda dla krótkich przedziałów czasowych. Rezultaty analizy pod kątem wyznaczenia temperatury i naprężeń otrzymano w drodze symulacji numerycznej dla przypadku cynku jako materiału badawczego. Wykazano, że oscylacje poziomu naprężeń i temperatury są szczególnie wyraźne dla krótkich przedziałów czasu i gasną z jego upływem. Wyniki badań zilustrowano graficznie dla różnych czasów relaksacji termicznej.
9
Content available remote Circular crested waves in thermoelastic plates bordered with viscous liquid
Sharma J. N., Sharma P. K., Pathania S.
International Journal of Applied Mechanics and Engineering
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2012
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Vol. 17, no. 2
513-534
EN
In this paper the propagation of thermoelastic waves in a homogeneous, transversely isotropic, thermally conducting elastic plate bordered with layers (or half-spaces) of a viscous liquid on both sides is investigated in the context of non classical theories of thermoelasticity. Complex secular equations for symmetric and antisymmetric wave motion of the circular plate, in completely separate terms, are derived. The regions of the secular equation, waves of short and long wavelength are also discussed. Finally, in order to illustrate the analytical results, the numerical solution is carried out for a transversely isotropic plate of cobalt material bordered with water by using the functional iteration method. The results are deduced and compared with the existing ones in relevant publications available in the literature at various stages of this work.
10
Content available remote Propagation of waves in a micropolar transversely isotropic generalized thermoelastic half-space
Kumar R., Gupta R. R.
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 3
671-681
EN
Rayleigh waves in a half-space exhibiting microplar transversely isotropic generalized thermoelastic properties based on the Lord-Shulman (L-S), Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories are discussed. The phase velocity and attenuation coefficient in the previous three different theories have been obtained. A comparison is carried out of phase velocity, attenuation coefficient and specific loss as calculated from the different theories of generalized thermoelasticity along with the comparison of anisotropy. The amplitudes of displacements, microrotation, stresses and temperature distribution are also obtained. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.
11
Uogólnione zagadnienie boussinesqa w przypadku transwersalnie izotropowej półprzestrzeni warstwowej
Szwed A., Jemioło S., Tybura A.
Logistyka
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2009
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nr 6
CD-CD
PL
W pracy przedstawiono rozwiązanie uogólnionego zadania Boussinesqa, w którym układ transwersalnie izotropowych warstw sprężystych na transwersalnie izotropowej półprzestrzeni sprężystej jest obciążony siłami powierzchniowymi równomiernie rozłożonymi na powierzchni koła. Zaprezentowano rozwiązanie metodą funkcji naprężeń. Wyniki porównano z odpowiadającym zadaniem w przypadku materiałów izotropowych.
EN
In the paper the generalized Boussinesq problem is presented. The system of transversely isotropic elastic layers on the top of transversely isotropic elastic half-space is subjected to uniform load on the circular area. Using stress function method solution of the problem is presented. The obtained results are compared to corresponding results for the problem of layered system made of isotropic material.
12
Wave propagation at the imperfect boundary between transversely isotropic thermoelastic diffusive half-space and an isotropic elastic layer
Kumar R., Chawla V.
Journal of Technical Physics
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2009
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Vol. 50, no 2
121-146
EN
The present investigation is devoted to a study of the surface wave propagation at imperfect boundary between a homogenous, transversely isotropic thermoelastic diffusive half-space and an isotropic elastic layer of finite thickness. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness, and then deduced for normal stiffness, tangential stiffness and welded contact. The dispersion curves for these quantities are illustrated to depict the effect of stiffness and thermal relaxation times. The amplitudes of displacements, temperature and concentration are computed numerically at the free plane boundary. Specific loss of energy is obtained and depicted graphically. Special cases of interest are also deduced and compared with known results.
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