In this paper, we employ the Laplace Adomian Decomposition Method (LADM) to analyze harmonic force-induced vibrations in non-uniform beams. We begin by outlining the foundational principles, derivation, and governing equations. Using LADM, we solve the governing equations by transforming them into algebraic recursive relations. By applying boundary conditions and performing the inverse Laplace transformation, we ultimately obtain the beam’s deflection under forced vibration. The key strength of LADM lies in its ability to provide an analytical approximation to nonlinear differential equations without requiring linearization, approximation, or discretization, which typically leads to extensive numerical computations. The numerical methods demonstrate that when the structure’s natural frequency aligns with the frequency of forced oscillation, large-amplitude oscillations occur. Changing the intensity of the external force reveals that the force magnitude has minimal effect on the displacement during resonance. This means that even a small external force at the resonant frequency can cause displacement to increase indefinitely, potentially causing structural failure. Results confirm that LADM is well-suited for analyzing beam dynamics and properties.