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This article discusses changes in heat transfer resulting from laser pulses and magnetic fields produced in thermoelastic materials under initial stress. This paper introduces a novel approach to modeling generalized thermoelastic materials by including fractional time derivatives with Eringen's non‐local thermoelastic theory. This model incorporates both the Caputo–Fabrizio and the Atangana–Baleanu derivatives, which are novel forms of fractional derivatives in the domain of fractional calculus. Analytical formulations for system variables, such as temperature and thermal stress, were derived using the Laplace transform method. This was done considering the effects of laser pulses, non‐local actuators, and fractional actuators. The findings of these investigations are showcased through numerical illustrations and visual representations. The research also included comparisons between the acquired results and those derived from earlier theories, which may be regarded as a specific instance. Validating the suggested model and showing its correctness and applicability is seen as a crucial step. [ABSTRACT FROM AUTHOR]

The present work aims to study the influence of variable thermal conductivity in generalized thermoelastic solid with microstretch within the framework of the Green‐Naghdi theory. The analytical methodology is adopted for obtaining exact expressions of displacement components, stresses, couple stresses, micro stress distribution and temperature distribution. The effect of variable thermal conductivity is illustrated graphically in two and three dimensions for the above physical quantities by taking different values of thermal conductivity. [ABSTRACT FROM AUTHOR]

This article offers the first investigation into the thermoelectric vibration of microscale Euler‐Bernoulli beams resting on an elastic Winkler base. We developed the system of equations for thermoelastic microbeams using elastic basis theory and the generalized Moore–Gibson–Thompson (MGT) thermal transport framework with a single‐phase delay. At the front of the microbeam, a graphene strip connected to an electrical power source was employed to generate heat. In addition, the influence of an ultra‐short‐pulsed laser on the vibration of a microbeam is studied, taking into account its heating effect. The microbeam system variables were analyzed after solving the mathematical equations by applying the Laplace transform technique. Graphs showing how different inputs affect different mechanical fields, such as Winkler substrate stiffness, voltage, electrical resistance, and temperature modulus pulses, are also presented. An increase in the Winkler modulus and the shear modulus of the foundation was found to decrease the amount of deflection and axial deformation in the microbeams. The increased beam stiffness has resulted in this decrease. [ABSTRACT FROM AUTHOR]

In our study, we adapt certain basic results from the abstract theory of differential equations of the elliptic type with the purpose to deduce some basic results in the case of a concrete type of media. Namely, after the boundary values problem is formulated in the context of elasticity of Cosserat bodies with voids, some results on existence of a generalized solution and the uniqueness of this solution are proven. [ABSTRACT FROM AUTHOR]

We consider the mixed initial‐boundary value problem in the context of the Moore‐Gibson‐Thompson theory of thermoelasticity for dipolar bodies. We consider the case of heat conduction with dissipation. Even if the elasticity tensors are not supposed to be positively defined, we have proven both, the uniqueness and the instability of the solution of the mixed problem. In the case that the mass density and the thermal conductivity tensor are positive, we obtain the uniqueness of the solution using some Lagrange type identities. [ABSTRACT FROM AUTHOR]

We consider a time differential model for dual-phase-lag thermoelastic dipolar material. For the heat flux with dual-phase-lag we introduce a time differential equation to describe the thermal effects, and this is coupled with elastic deformation. Some qualitative results on solutions of the mixed initial boundary value problem, associated with this model, are obtained under mild constitutive restrictions. We will deduce an identity of Lagrange type and will use a conservation law in order to prove the uniqueness of solution, whereas the result of continuous dependence of solution is established by using a Gronwall type inequality and a conservation law. [ABSTRACT FROM AUTHOR]