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The present study illustrates the thermoelastic vibrations of a rotating microbeam caused by a laser pulse heat source and sinusoidal heating in the context of three-phase thermoelasticity. Mathematical modeling of the problem was developed using the concept of the Euler–Bernoulli beam theory and the generalized theory of thermal conductivity with three relaxation coefficients of time. It was taken into account that the flexible beam suffers from initial stress at the beginning. The microbeam motion equation was derived by applying the assumptions of the Hamiltonian principle. The closed-form solutions of the studied domains are identified in the Laplace transform domain. After presenting the numerical inversion of the Laplace transform, the numerical results for the studied field variables, such as deflection and temperature, were developed. The influences of the angular velocity of rotation, the initially applied pressure, and the intensity of the laser pulse on the behavior of the physical fields have been demonstrated. In addition, the advantage of the current model has been verified by comparing the results of the field variables of the current model with the results of other thermal conduction theories, whether classical or generalized. It is believed that the results extracted from the present study may be useful for developing some high-quality electromechanical systems. [ABSTRACT FROM AUTHOR]

Mathematical models and numerical simulations are used to analyse and predict the behaviour of porous materials under coupled mechanical and thermal loading conditions in poroelastic thermoelastic studies. This field is crucial in understanding and designing systems involving porous media where mechanical and thermal factors are important. For this reason, this work aims to provide a theoretical study of porous elastic materials surrounded by a magnetic field using the dual phase lag (DPL) model of thermoelasticity. The significance of this study lies in its diverse range of applications across several engineering, and geophysical disciplines, encompassing soil mechanics, geomechanics, petroleum engineering, and civil engineering. An investigation was conducted on an indefinitely long, porous, solid circular cylinder subjected to a constant magnetic field to demonstrate the proposed theoretical framework. The outer surface of the cylinder was thermally shocked and maintained free from any stress or traction. To solve the problem, Laplace transforms and their inverse methods are used. Numerical examples of excess pore water pressure, temperature, displacement, induced magnetic field, and thermal stresses are given at different medium sites. Finally, graphical representations were created to depict the results of field variables across different thermal delays and porosity estimates. [ABSTRACT FROM AUTHOR]

Optical and photo-thermal effects have emerged in many fields, including thermal characterization, spectroscopy, transportation, and non-destructive examinations. In this study, the Moore-Gibson-Thompson (MGT) thermoelastic model is used to explore the photo-thermal coupling of an isotropic, homogeneous, semiconducting and thermomagnetic solid. The heat conduction law is modified to include the time derivative of fractional order and theoretically formulate the system of governing equations. Using the extended Mittag–Leffler functions as nonsingular kernels, the Atangana and Baleanu derivatives considers the features of fractional derivatives. As measured by an external reference frame, it is taken into account that the medium rotates with a constant angular velocity about the axis of symmetry. The cavity boundaries undergo thermal shock and time-varying heat flux. It has been shown that the Laplace transform method is a powerful technique for solving such problems that link the plasma and heat transfer with phase delays. It is finally aimed to describe the numerical results for changes in carrier density as a function of time and radial distance, temperature increment, strain, thermal stresses, and displacement using a photo-induced carrier with different values of physical relaxation time and fractional operator. [ABSTRACT FROM AUTHOR]