Analysis of magneto-aerothermal load effects on variable nonlocal dynamics of functionally graded nanobeams using Bernstein polynomials

Abstract This study explores the relationship between the variable nonlocal parameter and material variations in functionally graded (FG) nanobeams incorporating the influence of unsteady aero thermal and magnetic load defined by the first-order Piston theory. The governing equations of FG Euler nanobeams are derived using Eringen’s nonlocal elasticity theory. These equations are then numerically tested using the Bernstein-based Rayleigh-Ritz method. A comparison with previously published results is conducted to validate the accuracy of the findings. Additionally, the study investigates the effects of nonlocal ceramic, nonlocal metal parameters, Mach number, and aerodynamic force on various physical parameters of FG nanobeam.