Thermoelastic damping in nonlocal rod using three-phase lag heat conduction model

2021 ◽  
pp. 1-15
Author(s):  
N. Satish ◽  
S. Gunabal ◽  
K. Brahma Raju ◽  
S. Narendar
Keyword(s):  
Heat Conduction ◽  
Phase Lag ◽  
Thermoelastic Damping ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Three Phase

scholarly journals A generalized heat conduction model of higher-order time derivatives and three-phase-lags for non-simple thermoelastic materials

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Ahmed E. Abouelregal ◽  
K. M. Khalil ◽  
F. A. Mohammed ◽  
M. E. Nasr ◽  
Adam Zakaria ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Higher Order ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Three Phase ◽  
Phase Lags ◽  
Generalized Heat Conduction

Some theorems on linear theory of thermoelasticity for an anisotropic medium under an exact heat conduction model with a delay

2016 ◽  
Vol 22 (5) ◽  
pp. 1177-1189 ◽  
Author(s):  
Bharti Kumari ◽  
Santwana Mukhopadhyay
Keyword(s):  
Heat Conduction ◽  
Anisotropic Body ◽  
Spatial Behavior ◽  
Inhomogeneous Material ◽  
Phase Lag ◽  
Conduction Model ◽  
Delay Term ◽  
Heat Conduction Model ◽  
Thermoelasticity Theory ◽  
Equation Of Heat Conduction

The present work is concerned with a very recently proposed heat conduction model—an exact heat conduction model with a delay term for an anisotropic and inhomogeneous material—and some important theorems within this theory. A generalized thermoelasticity theory was proposed based on the heat conduction law with three phase-lag effects for the purpose of considering the delayed responses in time due to the micro-structural interactions in the heat transport mechanism. However, the model defines an ill-posed problem in the Hadamard sense. Subsequently, a proposal was made to reformulate this constitutive equation of heat conduction theory with a single delay term and the spatial behavior of the solutions for this theory have been investigated. A Phragmen–Lindelof type alternative was obtained and it has been shown that the solutions either decay in an exponential way or blow-up at infinity in an exponential way. The obtained results are extended to a thermoelasticity theory by considering the Taylor series approximation of the equation of heat conduction to the delay term and a Phragmen–Lindelof type alternative was obtained for the forward and backward in time equations. In the present work, we consider the basic equations concerning this new theory of thermoelasticity for an anisotropic and inhomogeneous material and make an attempt to establish some important theorems in this context. A uniqueness theorem has been established for an anisotropic body. An alternative characterization of the mixed initial-boundary value problem is formulated and a variational principle as well as a reciprocity principle is established.

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