Vibration characteristics of a cracked multi-bay frame with moving oscillatory loads

This research focuses on analyzing the resonance behavior of a cracked multi-bay frame structure under the influence of moving oscillatory loads, specifically examining vibrations in both axial and vertical directions. To model the system, the finite element approach, integrated with Lagrange’s formulation, was applied, utilizing the Bernoulli-Euler beam assumptions to derive the in-plane motion equations. The dynamic structural response was calculated using the Newmark integration algorithm. For damaged elements, stiffness characteristics were formulated based on principles from fracture mechanics. A three-dimensional graph showing the interdependence of crack position, oscillator speed, and peak displacement was developed to visualize the effect of crack location. The findings revealed that the initial resonant frequency corresponds to the first vibrational mode, which is predominantly horizontal, while the second resonant condition aligns with vertical mode dominance. © The Author(s) 2025