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• Present study derives a new mathematical model with the definition of memory dependent derivative. • Nature of the thermo-viscoelastic micro-beams influenced with the longitudinal magnetic field is analyzed. • The analytical solutions of the deflection, displacement, temperature, thermal stress are determined. • Effects of constituents of MDD and intensity of laser pulse have been analysed through graphical results. • This new model supports the low dissipation of energy and become a nice model. The concept of the memory-dependent derivative has been found to be more intuitive for understanding the physical meaning of real-world problems. The attractiveness of the memory-dependent derivative can be understood in such a way that its important components can be freely chosen according to the requirements of the problem. Linear viscosity theory plays a critical role in the study of solids and polymers when they are subjected to thermodynamic loading. The current study presents a new mathematical model based on the concept of memory-based derivative to analyze the nature of the thermoviscoelastic micro-beams surrounded by a magnetic field considering the effects of temperature change. The governing equations are constructed in the context of generalized thermoelasticity with two delay times using the concept of Euler-Bernoulli beam theory, Maxwell's electromagnetic equations and the Kelvin-Voigt viscosity model. The proposed model has been applied to study a micro-beam fixed at both ends and exposed to a laser pulse type heat source. The analytic solutions of the physical fields have been determined using the Laplace transform technique. In order to show the efficiency of the new thermal conductivity model, a comparison has been made between the results in the presence or absence of the memory-dependent derivative. In addition, the significant effects of influencing parameters such as memory-dependent derivative, kernel function and time delay as well as the intensity of the laser pulse on the physical fields have been analyzed. [ABSTRACT FROM AUTHOR]

In recent decades, microelectromechanical system (MEMS) technology has aroused great interest from researchers in the fields of science and technology, electromechanics, chemistry, and bioengineering. Rotary systems are also used in a variety of sectors, from a space station with a spinning wheel to a small turbine in smartphones. In this paper, the thermoviscoelastic interactions of rotating microbeams were investigated using the modified couple stress theory (MCST) to examine the size-dependent effect. Also, the governing equations were derived within the framework of the Lord and Shulman generalized thermoelastic theory and the Euler–Bernoulli beam model. In addition, the Kelvin–Voigt approach is used to calculate the properties of viscoelastic materials. By applying the proposed model, an axially compressed microbeam that rotates at a constant angular velocity and is exposed to a femtosecond laser pulsed heat source was studied To solve the equations of motion in the space domain, the well-known Laplace transform technique is utilized. The inverse Laplace transform is calculated numerically using a well-established and reliable approximation approach. The effect of the length scale parameter, laser pulse duration, and angular velocity on the heat and elastic waves of a rotating thin beam is explored and discussed. The effect of the viscous damping factor on different physical fields of the microbeam was also studied. • The thermoviscoelastic interactions of rotating microbeams based on the modified couple stress theory are studied. • The governing equations are derived based on generalized thermoelasticity and Euler–Bernoulli beam theories. • This microbeam is axially compressed and rotated at a consistent angular speed and subjected to a heat source. • The influence of the effective parameters on the thermal and mechanical waves was depicted and explored in depth. [ABSTRACT FROM AUTHOR]

Memory-dependent derivative (MDD) has become a new hot spot in many fields, including vibration mechanics, particle physics and thermoelasticity due to its simple formulation and high expressive force. In this study, a new generalized mathematical thermoelastic model that includes a high-order heat transfer law with different phase delays is developed based on the MD derivatives. The time delay in this new concept represents the duration of the memory influence, while the kernel function represents the dependent weight. A problem of an infinite thermoelastic half-space whose surface is stress-free and periodically heated by a laser-pulse is described in order to validate the proposed model. The system of equations is solved using Laplace transforms technique as well as its inversion is applied based on an appropriate numerical technique. Changes in thermophysical fields are obtained with several values of higher-order time derivatives. The effects of kernel function, time delay parameters and laser pulse duration are also investigated and explained by giving some graphs and tables. Moreover, certain comparisons are made taking into account the various unique features of the current model as well as when the memory effect is ignored. The results indicate that MDD is more suitable for modeling thermoelasticity. [ABSTRACT FROM AUTHOR]