Magneto-thermoelastic vibration analysis to a FG aluminum-based microbeam reinforced by GPLs based on nonlocal strain gradient theory and MGT generalized thermoelasticity

Abstract

To realize easy production and optimize the overall performances, nanocomposite structures made of graphene platelets (GPLS)-reinforced materials are usually functionally graded (FG). The FG distribution patterns of the fillers are commonly categorized into FG-A, FG-X and FG-O types. To promote engineering applications, a series of investigations on structural responses of FG nanocomposite structures have been conducted. Nevertheless, of them, the studies within the generalized thermoelastic theories remain limited, especially for microstructures. To bridge this gap, the magneto-thermoelastic vibration of a FG multilayer microbeam composed of an aluminum matrix reinforced by GPLs is considered in this study. The problem is formulated by incorporating the Euler–Bernoulli beam model, the Moore–Gibson–Thompson (MGT) generalized thermoelastic theory, the surface elasticity theory, and the nonlocal strain gradient theory along with the Maxwell’s equations. To assess the effective elastic modulus as well as other material properties, the Halpin–Tsai micromechanics model, and the mixture law are employed. Then, the governing equations are solved by using Navier’s method and the frequency of the microbeam is obtained. In calculation, parametric studies are carried out to examine the influences the distribution patterns of GPLs, the material length-scale parameter, the surface effect, the nonlocal elasticity parameter, the GPLs mass fractions, and the magnetic field parameter on the vibrational response. The FG-X material distribution achieves the highest vibration frequency due to optimal reinforcement. The inclusion of material length-scale parameter and surface effect greatly improves microbeam stiffness and vibration performance. An external magnetic field further increases the frequency by enhancing structural rigidity.