Exact Solutions for Forced Vibration of Non-Uniform Rods by Laplace Transformation

Longitudinal forced vibration behavior of non-uniform rods subjected to dynamic axial load is studied. Exact displacement solutions are obtained using the Laplace transformation method. Free vibration behavior is readily obtained in the analysis. Natural frequencies available in the literature for the cases considered are fully recovered. Inverse transformation into the time domain is performed using calculus of residues. Closed-form displacement expressions are tractable and efficiently implemented. Their efficiency is demonstrated by comparing the results with those obtained using Mode Superposition Method.