On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Abstract This paper presents an investigation of the dynamic behavior bi-directionally functionally graded (BDFG) micro/nanobeams excited by a moving harmonic load. The formulation is established in context surface elasticity theory and modified couple stress to incorporate effects energy microstructure, respectively. Based on generalized parabolic shear deformation beam theory, nonclassical governing equations problem are obtained using Lagrange’s equation accounting for physical neutral plane concept. material properties smoothly change along both axial thickness directions according power-law distribution, gradation length scale parameter parameters, i.e., residual stress, two elastic constants, mass density. Using trigonometric Ritz method (TRM), trial functions denoting transverse, deflections, rotation cross sections expressed sinusoidal form. Then, with aid equation, system motion derived. Finally, Newmark employed find responses BDFG subjected To validate present solution method, some comparisons fundamental frequency response those available literature performed. A parametric study performed extensively explore impact key parameters such as gradient indices directions, speed, excitation acting load nanobeams. results can serve guideline assessing multi-functional optimal design acted upon