Papers by Keyword: Breathing Crack

Abstract: Transverse cracks affect the stiffness and consequently the dynamic behavior of beams, by altering the natural frequencies. Actual cracked beam models are not able to explain in-deep the vibration mechanism and, therefore, no mathematical relation able to predict frequency changes due to damage exist. This paper proposes a new damage model which better explain the dynamic behavior of beams with open and closed cracks and a mathematical relation able to predict the frequency changes due to damage. In contrast to actual models, a global approach is used, by considering the influence of the stored energy distribution for each transversal vibration mode. Since the energy loss globally quantifies the state change due to damage, it was possible to replace the cracked beam with an equivalent one having constant but reduced stiffness. Based on it, a relation indicating the frequency drop damage was contrived and tested, by means of the finite element analysis, for various damage types and locations along the beam. Simulations have shown that accurate prediction about the natural frequency shifts can be made with the proposed relation.

Abstract: Cracking is a common type of failure in machines and structures. Cracks must be detected at an early stage before catastrophic failure. In structural health monitoring, changes in the vibration characteristics of the structure can be utilized in damage detection. A fatigue crack with alternating contact and non-contact phases results in a non-linear behaviour. This type of damage was simulated with a finite element model of a simply supported beam. The structure was monitored with a sensor array measuring transverse accelerations under random excitation. The objective was to determine the smallest crack length that can be detected. The effect of the sensor locations was also studied. Damage detection was performed using the generalized likelihood ratio test (GLRT) in time domain followed by principal component analysis (PCA). Extreme value statistics (EVS) were used for novelty detection. It was found that a crack in the bottom of the midspan could be detected once the crack length exceeded 10% of the beam height. The crack was correctly localized using the monitoring data.

Abstract: The coupling effect of vibration and fatigue crack propagation for a cracked cantilever beam is studied in this paper. The dynamic characteristics and fracture mechanics parameters are calculated by using 2D 8-nodes elements in FEM code. The nonlinear dynamic behavior of breathing crack is described by a frictionless contact FEM model. Linear fracture mechanics theory is used to calculate the stress intensity factor. At resonant state, coupling effect is significant between vibration and crack propagation. The response of beam under harmonic excitation is extremely sensitive to the structure natural frequency decrease which is caused by crack length growth. An approach of sweeping crack length analysis is proposed in resonant response evaluation of cracked beam. Two numerical tests are calculated to investigate coupling effects at resonant state: crack arrest problem and crack unstable propagation problem.

Abstract: Damage identification for a cantilever beam with a breathing crack was presented based on instantaneous frequency(IF). One time-varying stiffness model was introduced by considering the breathing effect of the crack in vibration. A simplified single-degree-of-freedom(SDOF) time-varying dynamic differential equation was built. Relationships between the structural instantaneous frequencies (IFs) and damage location and degree were analyzed. IFs of the free vibration displacements were estimated by using phase difference and Teager energy operator (TEO).Moreover the influence of noise on IFs estimation was discussed. Damage indices were built by IFs and the damage degree was identified. Structural IFs are two-dimension function of damage location and degree and the intra-wave phenomenon of IFs verified the non-linearity of damaged structure. The damage indices based on IFs are more reliable than traditional frequency on identifying damage degree and have some anti-noise properties.

Abstract: This paper presents a method for the vibration of a beam with a breathing crack under harmonic excitation. The infinitely thin crack is characterised by a parameter that takes into account the shape and the depth of the crack. The closed- and open-crack states are both modelled by a modal approach: two sets of equations of motion cast in the modal coordinates of their individual mode shapes. The state change (from closed to open or vice versa) involves the calculation of the modal coordinates associated with the new state from the modal coordinates of the previous state. By imposing the continuity of displacement and velocity the beam at the instant of the state change, the matrix that transforms the modal coordinates from one state to the other is determined and proved to be the Modal Scale Factor matrix. This analytical approach takes advantage of exact nature and mathematical convenience of beam modes and is time-efficient. Forced vibration at various values of crack parameter is determined. It is found that as decreases (crack length increases) the vibration becomes increasingly erratic and finally chaotic.

Abstract: A novel approach for crack identification based on jointly time-frequency analysis is presented in the paper. A bilinear stiffness model for the breathing crack was introduced to represent the nonlinear dynamics of a cracked beam. The nonlinearity of the dynamic responses due to the crack opening-closing is used to identify the occurrence of the crack. The Wigner-Wille distribution technique is applied to analyze the response signals and the instantaneous frequency is extracted as damage-sensitive feature. The numerical simulations of a breathing crack model were carried out to validate the possibility and effectiveness of the proposed approach. The effects of crack severity and sampling frequency on crack identification were also studied in the simulations respectively. The results show that the proposed method can effectively identify the crack with slight severity without any baseline model or data, and the better the identification obtains as the larger the sampling frequency. The study demonstrates that the proposed approach by using of jointly time-frequency analysis is a promising technique for crack identification.

Abstract: This paper describes initial results from a project expanding the field of rotor health monitoring by using Active Magnetic Bearings (AMBs) as actuators for applying a variety of known force inputs to a spinning rotor in order to monitor and evaluate response signals resulting from these inputs on-line. Similar to modal analysis and other nondestructive evaluation (NDE) techniques which apply input signals to static structures in order to monitor responses; this approach allows for the measurement of both input and output response in a rotating system for evaluation. However, unlike these techniques, the new procedure allows for multiple forms of force input signals to be applied to a rotating structure. This technique is being developed for use on rotating equipment supported in conventional bearings where an AMB actuator is added to a system for improved health monitoring. This paper presents initial results from this project including a demonstration of the system identification capability of the procedure during the commissioning of a test rig, and a summary of a technique developed for identifying breathing-cracks in rotors using the new technique.