Effect of Variable Nonlocal Parameter on the Free Vibration of Axially Functionally Graded Nanobeams

Abstract

This study explores the influence of varying nonlocal parameters on the free vibration characteristics of axially functionally graded (FG) nanobeams. The nanobeams are modeled using Euler-Bernoulli beam theory, with nonlocal effects analyzed based on Eringen’s nonlocal elasticity theory. The Young’s modulus and mass density are assumed to vary continuously according to a power-law distribution, while the nonlocal parameter is varied linearly along the axial direction. The Rayleigh-Ritz method is employed to determine the vibration frequency parameters. Convergence study is presented and the obtained results are validated with existing literature for specific cases. The analysis includes a detailed investigation of frequency parameters under Simply Supported - Simply Supported boundary conditions across a range of power-law exponents and nonlocal parameter values. The findings contribute to a deeper understanding of the dynamic behavior of axially FG nanobeams and demonstrate the effectiveness of the Rayleigh-Ritz method for understanding the dynamic behavior of such advanced systems.