Green’s function technique for stepped beam vibrations

Abstract

The study investigates stepped heterogeneous beams fixed at two endpoints. The eigenfrequencies for both unloaded and axially loaded problems are derived through the transformation of classical eigenvalue problems into homogeneous Fredholm integral equations. These equations can numerically be solved by reducing them to algebraic eigenvalue problems. The study assesses the effects of step location, bending stiffness and, axial force on natural frequencies. Through a comprehensive exploration of these mathematical frameworks, the paper aims to contribute to the structural vibration analysis of stepped beams. The study’s outcomes confirm the suitability of the presented method.