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1
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.
2
Content available remote Propagation of thermal disturbance due to thermal load in thermoelasticity with thermal relaxation time
Verma K. L.
Studia Geotechnica et Mechanica
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2009
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Vol. 31, nr 2
35-50
EN
In this article, an attempt is made to study the fracas due to a thermal line load in a homogeneous transversely isotropic half-space in linearized theory of generalized thermoelasticity. A combination of the Fourier and the Laplace transform techniques is applied to obtain the solutions of governing equations. The transformed solutions are then inverted using the Cagniard technique for small times. The results obtained theoretically for temperature and stresses are computed numerically for a crystal of zinc, and it is found that variations in stresses and temperature are more prominent at small times and decrease with the passage of time. The results obtained theoretically are represented graphically.
PL
Podjęto próbę analizy zaburzeń spowodowanych obciążeniem termicznym w jednorodnej, poziomo uwarstwionej półprzestrzeni w ramach uogólnionej liniowej termosprężystości. Zastosowano kombinację transformacji Fouriera i Laplace'a w celu uzyskania rozwiązań równań konstytutywnych. Otrzymane transformaty rozwiązań były następnie odwracane za pomocą procedury Cagniarda dla małych odcinków czasowych. Rozwiązania teoretyczne wykorzystano do numerycznego obliczenia temperatur i naprężeń dla przypadku kryształu cynku. Stwierdzono, że wahania naprężeń i temperatur są większe w małych odcinkach czasowych, a zanikają w miarę upływu czasu.
3
Content available remote On the matrix techniques for modeling of thermoelastic waves in layered structures
Verma K. L.
International Journal of Applied Mechanics and Engineering
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2006
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Vol. 11, no 3
655-669
EN
The development of a general purpose model for thermoelastic wave propagation in Cartesian system for heat conducting isotropic layered plates is illustrated, the model can account for elastic and visco-elastic isotropic materials, single or multi-layered structures, and free or leaky systems. Theoretical treatment is presented for calculating the displacements, temperature, thermal stresses and temperature gradient within a multilayered plate in generalized theories of thermoelasticity, using the matrix transfer technique. Rigidly bonded and smooth interface condition is also considered as a special case to stimulate de-bonding of two materials layers. The model developed will be of value in material characterization and others quantitative information on thermo-mechanical, strength related properties of advanced materials. Relevant results of previous investigations and coupled thermoelasticity are deduced as special cases.
4
Content available remote Flexural and extensional waves propagation in transversely isotropic plates in generalized thermoelasticity
Verma K. L., Verma S. C., Hasebe N.
International Journal of Applied Mechanics and Engineering
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2004
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Vol. 9, no 3
587-606
EN
In this paper, the boundary value problem concerning the propagation of plane harmonic thermoelastic waves in flat infinite homogeneous transversely isotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations for a heat conducting thermoelastic plate corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. The horizontally polarized SH wave gets decoupled from the rest of motion and propagates without dispersion or damping, and is not affected by thermal variations on the same plate. A numerical solution to the frequency equations for an aluminum plate (isotropic) and zinc plate (transversely isotropic) is given, and the dispersion curves are presented. The three motions namely, longitudinal, transverse and thermal of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves is modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.
5
Content available remote On the dynamic responses with and without energy dissipation in the thermoelastic rotating media
Verma K. L., Hasebe N.
International Journal of Applied Mechanics and Engineering
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2002
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Vol. 7, no 4
1329-1348
EN
The generalized dynamical theories of thermoelasticity with and without energy dissipation are applied to study the propagation of thermoelastic waves in an infinite, homogenous, isotropic medium rotating uniformly with constant angular velocity. A generalized characteristic equation is derived to investigate the effects of rotation, the relaxation time constants and thermomechanical coupling on the dispersion behavior of thermoelastic waves. Results of earlier works are deduced as particular cases of the more general results obtained here.
6
Content available remote On the propagation of generalized thermoelastic vibrations in plates
Verma K. L., Hasebe N.
Engineering Transactions
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1999
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Vol. 47, iss. 3
300-319
EN
The heat conduction equation in the context of generalized theories of thermoelasticity is used to study the propagation of plane harmonic waves in a thin, flat, infinite, homogeneous, thermoelastic isotropic plate of finite width. The frequency equations corresponding to the symmetric and antisymmetric modes of vibration of the plate are obtained, and some limiting cases of the freguency equations are then discussed. The comparison of the results for the theories of generalized thermoelasicity have also been made. The results obtained have been verified numerically and are represented graphically for aluminum epoxy composite plate.
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