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1

Deformation of modified couple stress thermoelastic diffusion in a thick circular plate due to heat sources

Kumar R., Devi S.

Computational Methods in Science and Technology

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2019

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Vol. 25, No. 4

167--176

EN

The aim of this study is to present a mathematical model for predicting the results for displacements, stress components, temperature change and chemical potential with considering independently a particular type of heat source. The general solution for the two-dimensional problem of a thick circular plate with heat sources in modified couple stress thermoelastic diffusion has been obtained in the context of one and two relaxation times. Laplace and Hankel transforms technique is applied to obtain the solutions of the governing equations. Resulting quantities are obtained in the transformed domain. The numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of time on the resulting quantities are shown graphically.

2

Eigenvalue approach to nanobeam in modified couple stress thermoelastic with three-phase-lag model induced by ramp type heating

Kumar R., Devi S.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

1067--1079

EN

This article deals with the study of a thermoelastic nanobeam in a modified couple stress theory subjected to ramp-type heating. The mathematical model is prepared for the nanobeam in thermoelastic three-phase-lag. The Laplace transform and the eigenvalue approach are used to find the displacement component, lateral deflection, temperature change and axial stress of the thermoelastic beam. The general algorithm of the inverse Laplace transform is developed to compute results numerically. The comparison of three-phase-lag, dual-phaselag and GN-III (1993) models are represented, and their illustration is depicted graphically. This study finds the applications in engineering, medical science, sensors, etc.

3

Interaction due to Hall Current and Rotation in a Modified Couple Stress Elastic Half-Space due to Ramp-type Loading

Kumar R., Devi S.

Computational Methods in Science and Technology

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2015

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Vol. 21, No. 4

229--240

EN

The present investigation is to focus on the effect of Hall current and rotation in a modified couple stress theory of elastic half space due to ramp-type loading in a homogeneous, isotropic, thermoelastic diffusive medium. The mathematical formulation is prepared for different theories of thermoelastic diffusion, including the Coriolis and centrifugal forces. The Laplace and Fourier transforms techniques are applied to obtain the solutions of the governing equations. The components of displacement, stresses, temperature change and mass concentration are obtained in the transformed domain. The numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of Hall current and rotation are shown on the resulting quantities. Some particular cases are also discussed in the present problem.

4

Deformation in a generalized thermoelastic material with voids under the dependence of modulus of elasticity and thermal conductivity on reference temperature

Kumar R., Devi S.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 3

747-767

EN

The present investigation is to determine the displacement component, change in the volume fraction field and temperature distribution in a generalized thermoelastic half space with voids with a variable modulus of elasticity and thermal conductivity subjected to mechanical and thermal boundary conditions. The formulation is applied to the coupled as well as the generalized theories of thermoelasticity: the Lord-Shulman theory (with one relaxation time), Green-Lindsay theory (with two relaxation times), and Chandrasekhariah-Tzou theory (with dual phase lag). The Laplace transform technique has been used to solve the problem. An application of concentrated (mechanical/thermal) and continuous (mechanical/thermal) sources has been considered to illustrate the utility of the approach. The transformed solutions are inverted using a numerical inversion technique to obtain the displacement component, change in the volume fraction field and temperature distribution in the physical domain and illustrated graphically for a particular model. Various special cases of interest have been deduced from the present investigation.

5

Reduction of linear discrete time systems in frequency domain using continued fraction expansions

Prasad R., Devi S.

Systems Science

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2004

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Vol. 30, no 1

65-76

EN

The continued fraction expansions (CFE) approach coupled with several powerful stable reduction methods is proposed for the reduction of high order z-transfer functions. These methods include the advantages of stability preservation methods (SPM), such as Routh approximation, Routh Hurwitz array and stability equation method etc., with those of the method based on continued fraction expansions. The high order z-transfer functions are transformed in w-domain using bilinear transformation and the denominator of the reduced models are found in w-domain. The numerators of reduced order models are determined by matching the quotients of continued fraction expansions in w-domain. Finally, the reduced z-transfer functions are determined using reverse bilinear transformation. In this paper, combined features of SPM and CFE have been utilised to reduce the linear discrete time systems. To match the initial value of the original step response the bilinear transformation is applied in the high order z transfer function in such a way that the numerator and denominator polynomials of original system are separately expressed in w domain. And, to remove any steady error between the system and model responses, steady state values of original, and reduced systems are matched. The method proposed preserves the time domain and frequency domain characteristics and gives stable models for stable systems. An example illustrates the method.