This study explores the influence of varying nonlocal parameters on the free vibration of axially functionally graded (FG) nanobeams. The nanobeams are modeled using the Euler-Bernoulli beam theory, and the nonlocal effects are examined using Eringen’s nonlocal elasticity theory. The nonlocal parameter is varied linearly along the axial direction, while the structural properties of the nanobeam are assumed to vary continuously following a power-law distribution. The frequency parameter values of this problem are obtained using the Rayleigh-Ritz method. 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 boundary conditions across a range of power-law exponents and nonlocal parameter values. The results offer valuable insights into the dynamic behavior of axially FG nanobeams and demonstrate the robustness and accuracy of the Rayleigh–Ritz method for analyzing such advanced nanostructures.