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JOURNALS // Prikladnaya Mekhanika i Tekhnicheskaya Fizika // Archive

Prikl. Mekh. Tekh. Fiz., 2016 Volume 57, Issue 4, Pages 91–106 (Mi pmtf817)

This article is cited in 23 papers

Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags

R. Karmakar, A. Sur, M. Kanoria

University of Calcutta, 92 A.P.C. Road, 700009, Kolkata, West Bengal, India

Abstract: The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord–Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained for at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord–Shulman and dual-phase-lag models.

Keywords: two-temperature generalized thermoelasticity, dual-phase-lag model, state-space approach, vector-matrix differential equation.

UDC: 539.3

Received: 03.02.2014
Revised: 12.08.2014

DOI: 10.15372/PMTF20160409


 English version:
Journal of Applied Mechanics and Technical Physics, 2016, 57:4, 652–665

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