This record contains the accepted author manuscript (AAM) of the paper: "Approximate Fundamental Frequency Formula for Cantilevers with Weakly Non-Uniform Sections and Verification with Experiments and Other Studies in the Literature", Journal of Sound and Vibration, 2024. DOI: 10.1016/j.jsv.2024.118813 The paper proposes an analytical approximation for the fundamental frequency of weakly non-uniform Euler–Bernoulli beams and validates the formulation with multiple experimental configurations including point masses, thin films, and etched structures. The results demonstrate average errors below 0.17% compared to experimental measurements. This version is provided for open-access dissemination in accordance with the publisher’s self-archiving policy.