Investigation of Modal and Damage Parameters of Isotropic Cantilever Beam under Double-Sided Crack

Abstract

In this study, the modal and damage parameters of isotropic mild steel cantilever beam under double-sided crack are studied. Static, modal and harmonic analyses for un-cracked and cracked cantilever beams have been carried out using finite element analysis software ANSYS. The natural frequencies and mode shapes for both un-cracked and cracked cantilever beams for the first five modes of bending vibration have been extracted using block Lanczos method through modal analysis. Harmonic analysis for both un-cracked and cracked cantilever beams has been performed, and deformation response in Y-direction in the range of 0–80 Hz has been plotted to determine the reduction in natural frequencies for the cracked beams by noticing the shifts in the natural frequencies. The results show that the amount of shifts in the natural frequencies of the cracked beam depends on pattern of mode shape and its deviation with respect to that of un-cracked beam. Rotational stiffness and flexibility at crack location have been analytically calculated, and the results show that by increasing the crack depth rotational stiffness decreases and flexibility increases. Zero frequency deflections for un-cracked and cracked beams have been determined through static analysis using ANSYS, and stiffness ratios for cracked beams were calculated. As the crack depth increases and the crack position from fixed end decreases, then the stiffness ratio for the cracked beam decreases. The evaluation of modal and damage parameters of cracked cantilever beams is crucially important to monitor the condition of the beams to eliminate the sudden failure.