Nonlinear vibration analysis of a cantilever beam with a breathing crack and bilinear behavior

Nonlinear phenomena widely occur in practical engineering applications. A typical example in aerospace structures is the creation of a breathing crack that opens and closes under cyclic loads, which causes bilinear behavior in the structural response. Late detection of such cracks can lead to a catastrophic failure that results in extensive structural damage. Therefore, analyzing the behavior of the structure because of the presence of a breathing crack is very important and needs to be investigated in detail. In this article, the nonlinear response of a single-degree-of-freedom nonlinear cantilever beam with a transverse breathing crack and bilinear behavior was studied. To investigate the nonlinear behavior, bilinear functions of the beam stiffness and nonlinear geometric stiffness were converted to polynomial functions. The proposed model is validated by comparing the time history responses of the approximated polynomials with the bilinear model of the cracked beam. Moreover, by considering damping changes because of the presence of the breathing crack, the nonlinear behavior was investigated. The results indicated that the proposed method is sensitive to the presence of a breathing crack. Also, the nonlinearity increases with an increase in the crack depth and location ratios associated with the jump phenomenon in the vibration response of the cracked beam.

Vibration and Stability Analysis of a Bearing–Rotor System with Transverse Breathing Crack and Initial Bending

This paper focuses on the stability and nonlinear response of a bearing-rotor system affected by a transverse crack and initial bending which was thought to be part of an unbalance or had been neglected before. The differences of breathing functions for the transverse breathing crack caused by initial bending is presented here, and the calculation of time-varying finite elements stiffness matrix of the cracked shaft is improved by replacing traditional the approximate crack segment with an exact area. After establishing the dynamic model of the cracked rotor with initial bending, vibrational characteristics such as amplitude-speed diagram, frequency spectrogram and bifurcations are investigated in detail. The eigenvalues of the transition matrix are calculated and analyzed as an indicator of dynamic stability with the growths of crack depth and initial bending. Many differences are found between the two cases of dynamic response of rotor system by numerical simulation. The frequency change with the growth of initial bending is opposite to the change with the growth of crack depth, and the shapes of amplitude-speed also having great different features. Stable regions are reduced and extended laterally by initial bending. All these results obtained in this paper will contribute to identify the bending fault and assess the stability of the bearing-rotor systems.

Breathing crack damage diagnostic strategy using improved MFCC features

In this paper, a new two-stage damage diagnostic technique for breathing crack identification in using improved Mel frequency Cepstral Analysis is proposed for engineering structures. The improvements such as the centre frequencies of Mel-filter bank around the resonant frequencies and the automatic selection of cut-off frequency for frequency conversion (i.e. from Mel-scale to frequency-scale) based on the energy of the response is employed in the present work to customise the estimation of Mel-frequency Cepstral Coefficients (popularly being used for speech signals) for structural vibration responses. In the first stage of the proposed improved Mel-frequency Cepstral Coefficients (MFCC) approach for breathing crack identification, the measured acceleration time history responses are converted into Mel-frequency Cepstral Coefficients using improved Mel frequency Cepstral Analysis. The Mahanabolis distance-based measure between the improved Mel-frequency Cepstral coefficients of the healthy structure and the structure with localized damage is used for confirming the presence of breathing crack using ambient vibration data during online monitoring. In the second stage, the spatial location of breathing crack is established through offline monitoring, by exciting the structure with bitone harmonic excitation. The improved Mel-filter bank energy measured spatially across the structure is used to identify the spatial location(s) of breathing crack. The effectiveness of the proposed approach is verified using the synthetic datasets of the benchmark simply supported beam with a breathing crack, provided by Helsinki Metropolia University of Applied Sciences and a numerically simulated cantilever beam with varied spatial locations and different depths of breathing crack. Finally, experimental investigations have been carried out to demonstrate the practical viability of the proposed MFCC approach. Numerical and experimental studies concluded that the proposed damage diagnostic approach is capable of detecting and localising multiple and also subtle cracks even under varying environmental conditions with noise-contaminated measurements.

Use of Bispectrum Analysis to Inspect the Non-Linear Dynamic Characteristics of Beam-Type Structures Containing a Breathing Crack

A breathing crack is a typical form of structural damage attributed to long-term dynamic loads acting on engineering structures. Traditional linear damage identification methods suffer from the loss of valuable information when structural responses are essentially non-linear. To deal with this issue, bispectrum analysis is employed to study the non-linear dynamic characteristics of a beam structure containing a breathing crack, from the perspective of numerical simulation and experimental validation. A finite element model of a cantilever beam is built with contact elements to simulate a breathing crack. The effects of crack depth and location, excitation frequency and magnitude, and measurement noise on the non-linear behavior of the beam are studied systematically. The result demonstrates that bispectral analysis can effectively identify non-linear damage in different states with strong noise immunity. Compared with existing methods, the bispectral non-linear analysis can efficiently extract non-linear features of a breathing crack, and it can overcome the limitations of existing linear damage detection methods used for non-linear damage detection. This study’s outcome provides a theoretical basis and a paradigm for damage identification in cracked structures.