Memory effect analysis of magneto-thermoelastic response of viscoelastic rotating nanobeams based on nonlocal and modified coupled stress elasticity theories

Abstract

As a basic constituent of micro- and nanoelectromechanical systems, the analysis of the thermodynamic properties of rotating nanobeams is crucial for the safe operation of the systems. However, the classical continuum mechanics theory and Fourier’s law of heat conduction can no longer accurately predict the size-dependent effect in the elastic deformation of micro- and nanostructures and the thermal hysteresis effect in the heat transfer process of micro- and nanostructures, respectively. Therefore, in this paper, a new mathematical model based on the concept of memory derivatives is proposed to analyze the properties of viscoelastic rotating nanobeams surrounded by a magnetic field as well as excited by a heat source. The size-dependent effects of this rotating nanobeam are characterized using the nonlocal modified coupled stress theory, and the controlling equations are constructed in the context of generalized thermoelasticity taking into account the memory-dependent effects using the concepts of the Euler–Bernoulli beam theory, Maxwell electromagnetic equations, and fractional-order Kelvin–Voigt viscoelasticity model. The rotating nanobeam deflection, thermodynamic temperature, displacement, and bending moment are numerically solved using the Laplace transform and its inverse transform technique. The effects of time-delay factors, kernel functions, nonlocal parameters, and internal characteristic parameters of the material on the dimensionless field quantities of the rotating nanobeam are also investigated and characterized graphically.