Analysis of the dynamic characteristics of a slant-cracked cantilever beam

Abstract

In this study, the dynamic characteristics of a slant-cracked cantilever beam are studied based on a new finite element (FE) model where both plane and beam elements are used to reduce the computational costs. Simulation studies show that the proposed model has the same system natural frequencies and vibration responses as those in the pure plane element model but is computationally more efficient. Based on the new model, the effects of loads such as gravity Fg, excitation force amplitude F0 and direction angles of excitation force φ, and crack parameters including slant crack angle θ, dimensionless crack depth s and dimensionless crack location p, on system dynamics have been analyzed. The results indicate that (1) the gravity has a more significant effect on the sub-harmonic resonance responses than on the super-harmonic resonance and resonance responses; (2) The amplitudes of the system responses at both excitation force frequencies fe and its harmonics such as 2fe and 3fe increase almost linearly with the increase of the excitation force amplitude F0; (3) Under the constant excitation force in the flexural direction, the tensile and compressive forces along the longitudinal direction can lead to opposite breathing behaviors of the crack within the super-harmonic and sub-harmonic resonance frequency regions; (4) Vibration is most severe under the straight crack angle (θ=90°) and near the straight crack angle such as θ=100° and 110°, and the vibration responses under smaller or larger crack angles such as θ=30° and θ=150° become weaker; (5) The resonance at 2fe is sensitive to the faint crack signals when s is small and p is large. In addition, the significant vibration responses at the multiple frequency of 3fe and the fractional frequency of 0.5fe can be regarded as a distinguishable feature of the serious crack with large s and small p.