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Keywords = viscothermoelastic materials

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13 pages, 5264 KB  
Article
Study of Transversely Isotropic Visco-Beam with Memory-Dependent Derivative
by Kulvinder Singh, Iqbal Kaur and Eduard-Marius Craciun
Mathematics 2023, 11(21), 4416; https://doi.org/10.3390/math11214416 - 25 Oct 2023
Cited by 3 | Viewed by 1274
Abstract
Based on the modified Moore–Gibson–Thompson (MGT) model, transversely isotropic visco-thermoelastic material is investigated for frequency shift and thermoelastic damping. The Green–Naghdi (GN) III theory of thermoelasticity with two temperatures is used to express the equations that govern heat conduction in deformable bodies based [...] Read more.
Based on the modified Moore–Gibson–Thompson (MGT) model, transversely isotropic visco-thermoelastic material is investigated for frequency shift and thermoelastic damping. The Green–Naghdi (GN) III theory of thermoelasticity with two temperatures is used to express the equations that govern heat conduction in deformable bodies based on the difference between conductive and dynamic temperature acceleration. A mathematical model for a simply supported scale beam is formed in a closed form using Euler Bernoulli (EB) beam theory. We have figured out the lateral deflection, conductive temperature, frequency shift, and thermoelastic damping. To calculate the numerical values of various physical quantities, a MATLAB program has been developed. Graphical representations of the memory-dependent derivative’s influence have been made. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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11 pages, 3771 KB  
Article
Generalized Thermoelastic Interactions in an Infinite Viscothermoelastic Medium under the Nonlocal Thermoelastic Model
by Tareq Saeed
Mathematics 2022, 10(23), 4425; https://doi.org/10.3390/math10234425 - 24 Nov 2022
Cited by 3 | Viewed by 1891
Abstract
The wave propagation in viscothermoelastic materials is discussed in the present work using the nonlocal thermoelasticity model. This model was created using the Lord and Shulman generalized thermoelastic model due to the consequences of delay times in the formulations of heat conduction and [...] Read more.
The wave propagation in viscothermoelastic materials is discussed in the present work using the nonlocal thermoelasticity model. This model was created using the Lord and Shulman generalized thermoelastic model due to the consequences of delay times in the formulations of heat conduction and the motion equations. This model was created using Eringen’s theory of the nonlocal continuum. The linear Kelvin–Voigt viscoelasticity model explains the viscoelastic properties of isotropic material. The analytical solutions for the displacement, temperature, and thermal stress distributions are obtained by the eigenvalues approach with the integral transforms in the Laplace transform techniques. The field functions, namely displacement, temperature, and stress, have been graphically depicted for local and nonlocal viscothermoelastic materials to assess the quality of wave propagation in various outcomes of interest. The results are displayed graphically to illustrate the effects of nonlocal thermoelasticity and viscoelasticity. Comparisons are made with and without thermal relaxation time. The outcomes show that Eringen’s nonlocal viscothemoelasticity theory is a promising criterion for analyzing nanostructures, considering the small size effects. Full article
(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)
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