Memory response on magneto-thermoelastic vibrations on a viscoelastic micro-beam exposed to a laser pulse heat source.

• 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]