Abstract
The phenomena of sub- and super-harmonic responses make up one of the prominent nonlinear characteristics of a beam with a breathing crack. In order to fully understand the behaviors of sub- and super-harmonic resonances, it is necessary to analyze the nonlinear vibration of a beam-like structure with a breathing crack. In this study, a new stiffness model that considers the influence of the partial crack closure is proposed to model the stiffness variation of the cracked beam. Based on the finite element model of a beam with a breathing crack, the multiple-scale method is proposed to analyze the nonlinear vibration of a cracked beam subjected to harmonic excitation, and the relation between the nonlinear vibration of the cracked beam and the system parameters is obtained. An experiment is conducted to validate the analytical results. The study shows that the nonlinear responses of a beam with a breathing crack are affected by both the structural parameters and the crack parameters.
Highlights
Beams are one of the basic structural members and are widely used in various fields, such as aerospace, machinery, automobile and structure industries [1,2,3,4]
Owing to the advancement of reliable fault detection and diagnosis techniques, vibration-based damage identification methods have been developed for various engineering applications, such as the rotating blades of engines [11], submarine pipes [12], rotating rotors [13] and atomic force microscope (AFM) probes [14]
The main reason for this is that the nonlinear vibration of a beam with a breathing crack is not fully understood, and that the inherent relation between the sub- and super-harmonic resonance responses and the parameters of the cracked beam require further investigation
Summary
Beams are one of the basic structural members and are widely used in various fields, such as aerospace, machinery, automobile and structure industries [1,2,3,4]. Experimental approaches [23,24] Their studies showed that nonlinear vibration characteristics have a higher sensitivity to breathing cracks, especially the presence of sub- and super-harmonic resonances [25]. The main reason for this is that the nonlinear vibration of a beam with a breathing crack is not fully understood, and that the inherent relation between the sub- and super-harmonic resonance responses and the parameters of the cracked beam require further investigation. Chondrous et al [31] developed a dynamic model of a cracked beam with a breathing crack by using consistent one-dimensional theory Their results showed that the natural frequencies obtained from analysis are in accordance with the experimental results. May be used as a qualitative damage indicator for crack detection
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