Nonlinear Dynamics and Damage Assessment of a Cantilever Beam With Breathing Edge Crack

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Animesh Chatterjee
Keyword(s):  
Cantilever Beam ◽  
Crack Detection ◽  
Volterra Series ◽  
Fatigue Cracks ◽  
Harmonic Excitation ◽  
Crack Model ◽  
Open Crack ◽  
Breathing Crack ◽  
Vibration Testing ◽  
Polynomial Series

Failures in structures and machine elements can be prevented through early detection of fatigue cracks using various nondestructive testing methods. Vibration testing forms one of the most effective and recent one among these methods. There are mainly two approaches to crack detection through vibration testing: open crack model and breathing crack model. The present study is based on breathing crack model, in which the nonlinear vibration response under harmonic excitation is formulated through Volterra series and higher order frequency response functions. Bilinear stiffness characteristic of a cracked cantilever beam is approximated by a truncated polynomial series and response amplitudes of various harmonics are investigated for both qualitative and quantitative characterization. A new procedure is suggested whereby the presence of a breathing crack in a structure can be first identified and then the severity of the damage can be estimated through harmonic probing.

On the Modeling of Open and Breathing Cracks of a Cracked Rotor System

2010 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Eric A. Butcher
Keyword(s):  
Finite Element ◽  
Crack Detection ◽  
Linear Time ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Crack Model ◽  
Open Crack ◽  
Cracked Rotor ◽  
Critical Rotational Speed ◽  
Cracked Rotor System

The modeling of a cracked rotor system with an open or breathing transverse crack is addressed here. The cracked rotor with an open crack model behaves as an asymmetric shaft. Hence, the time-varying area moments of inertia of the cracked section are employed in formulating the periodic finite element stiffness matrix for both crack models which yields a linear time-periodic system. The harmonic balance method (HB) is used in solving the finite element (FE) equations of motions for studying the dynamic behavior of the cracked rotor system. The unique behavior of the whirl orbits during the passage through the subcritical rotational speeds and the sensitivity of these orbits to the unbalance force direction can be used for early crack detection of the cracked rotor for both crack models. These whirl orbits were verified experimentally for the open crack model in the neighborhood of 1/2 of the first critical rotational speed where a good match with the theoretical whirl orbits was observed.

Application of entropy in identification of breathing cracks in a beam structure: Simulations and experimental studies

2017 ◽  
Vol 17 (3) ◽  
pp. 549-564 ◽  
Author(s):  
Buddhi Wimarshana ◽  
Nan Wu ◽  
Christine Wu
Keyword(s):  
Cantilever Beam ◽  
Time Domain ◽  
Fatigue Cracks ◽  
Unit Length ◽  
Crack Depth ◽  
Experimental Studies ◽  
Sample Entropy ◽  
Breathing Crack ◽  
Engineering Structures ◽  
Vibration Signals

A cantilever beam with a breathing crack is studied to detect the crack and evaluate the crack depth using entropy measures. During the vibration in engineering structures, fatigue cracks undergo the status from close-to-open (and open-to-close) repetitively leading to a crack breathing phenomenon. Entropy is a measure, which can quantify the complexity or irregularity in system dynamics, and hence employed to quantify the bi-linearity/irregularity of the vibration response, which is induced by the breathing phenomenon of a crack. A mathematical model of harmonically excited unit length steel cantilever beam with a breathing crack located near the fixed end is established, and an iterative numerical method is applied to generate accurate time domain vibration responses. The steady-state time domain vibration signals are pre-processed with wavelet transformation, and the bi-linearity/irregularity of the vibration signals due to breathing effect is then successfully quantified using both sample entropy and quantized approximation of sample entropy to detect and estimate the crack depth. It is observed that the method is capable of identifying crack depths even at very early stages of 3% of the beam thickness with significant increment in the entropy values (more than 200%) compared to the healthy beam. In addition, experimental studies are conducted, and the simulation results are in good agreement with the experimental results. The proposed technique can also be applied to damage identification in other types of structures, such as plates and shells.

scholarly journals Effects of Crack on Vibration Characteristics of Mistuned Rotated Blades

2017 ◽  
Vol 2017 ◽  
pp. 1-18 ◽  
Author(s):  
Hailong Xu ◽  
Zhongsheng Chen ◽  
Yongmin Yang ◽  
Limin Tao ◽  
Xuefeng Chen
Keyword(s):  
Natural Frequency ◽  
Vibration Amplitude ◽  
Crack Detection ◽  
Vibration Characteristics ◽  
Lumped Parameter Model ◽  
Crack Model ◽  
Breathing Crack ◽  
Vibration Localization ◽  
Lumped Parameter ◽  
Amplitude Increase

Rotated blades are key mechanical components in turbine and high cycle fatigues often induce blade cracks. Meanwhile, mistuning is inevitable in rotated blades, which often makes it much difficult to detect cracks. In order to solve this problem, it is important and necessary to study effects of crack on vibration characteristics of mistuned rotated blades (MRBs). Firstly, a lumped-parameter model is established based on coupled multiple blades, where mistuned stiffness with normal distribution is introduced. Next, a breathing crack model is adopted and eigenvalue analysis is used in coupled lumped-parameter model. Then, numerical analysis is done and effects of depths and positions of a crack on natural frequency, vibration amplitude, and vibration localization parameters are studied. The results show that a crack causes natural frequency decease and vibration amplitude increase of cracked blade. Bifurcations will occur due to a breathing crack. Furthermore, based on natural frequencies and vibration amplitudes, variational factors are defined to detect a crack in MRBs, which are validated by numerical simulations. Thus, the proposed method provides theoretical guidance for crack detection in MRBs.

An Open Crack Model for Vibration Simulation of Beam Structures by Transfer Matrix Method

2007 ◽  
Vol 348-349 ◽  
pp. 893-896
Author(s):  
Ke Ming Wang ◽  
Song Xiang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Crack Detection ◽  
Vibration Monitoring ◽  
Crack Model ◽  
Open Crack ◽  
Element Analysis ◽  
Beam Structures ◽  
Stiffness Reduction

Crack detection of critical beam structures such as bridges and aircraft wings by vibration monitoring is based on understanding how a crack affects the vibration characteristics of a beam structure. Transfer matrix method is a convenient, effective, and hence widely used approach to beam vibration analysis, but a crack in the beam makes this method ineffective. This paper proposes an open crack model that simulates the local stiffness reduction effect of a transverse crack by a rectangular slot to make the transfer matrix method able to analyze vibrations of a cracked beam. The depth of the slot is identical to the depth of the crack, and the equivalent width of the slot is obtained by comparison of stiffness reductions of finite element analysis results and the counterpart transfer matrix method results. Different dimensions of rectangular beams, different crack positions and loading conditions are considered and statistic method is used to improve the generality and accuracy of the model. A calculation example of a cracked cantilever beam is given and the validity of the proposed model is verified with available results of existing models.

Rotordynamic Crack Diagnosis: Distinguishing Crack Depth and Location

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Philip Varney ◽  
Itzhak Green
Keyword(s):  
Condition Monitoring ◽  
Crack Detection ◽  
Fatigue Cracks ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Forced Response ◽  
Contour Plot ◽  
Crack Model ◽  
Finite Width ◽  
Shaft Speed

The goal of this work is to establish simple condition monitoring principles for diagnosing the depth and location of transverse fatigue cracks in a rotordynamic system. The success of an on-line crack diagnosis regimen hinges on the accuracy of the crack model, which should account for the crack's depth and location. Two gaping crack models are presented; the first emulates a finite-width notch typically manufactured for experimental purposes, while the second models a gaping fatigue crack. The rotordynamic model used herein is based upon an available overhung rotordynamic test rig that was originally constructed to monitor the dynamics of a mechanical face seal. Four degree-of-freedom, linear equations of motion for both crack models are presented and discussed. Free and forced response analyses are presented, emphasizing results applicable to condition monitoring and, particularly, to diagnosing the crack parameters. The results demonstrate that two identifiers are required to diagnose the crack parameters: the 2X resonance shaft speed and the magnitude of the angular 2X subharmonic resonance. First, a contour plot of the 2X resonance shaft speed versus crack depth and location is generated. The magnitude of the 2X resonance along the desired 2X frequency contour is then obtained, narrowing the possible pairs of crack location and depth to either one or two possibilities. Practical aspects of the suggested diagnostic procedure are discussed, as well as qualitative observations concerning crack detection.

Modal Approach for Forced Vibration of Beams with a Breathing Crack

2009 ◽  
Vol 413-414 ◽  
pp. 39-46 ◽  
Author(s):  
Luis Baeza ◽  
Hua Jiang Ouyang
Keyword(s):  
Forced Vibration ◽  
Harmonic Excitation ◽  
The State ◽  
Mode Shapes ◽  
Exact Nature ◽  
Open Crack ◽  
State Change ◽  
Breathing Crack ◽  
Modal Approach ◽  
Modal Coordinates

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.

Fatigue crack detection method using analysis of vibration signal

2017 ◽  
Vol 1 (20) ◽  
pp. 63-74 ◽  
Author(s):  
Arkadiusz Rychlik ◽  
Krzysztof Ligier
Keyword(s):  
Crack Detection ◽  
Fatigue Cracks ◽  
Fatigue Cracking ◽  
Vibration Signal ◽  
Technical Condition ◽  
Visual Methods ◽  
Signal Characteristics ◽  
Fatigue Crack Detection ◽  
Sample Structure ◽  
Change Identification

This paper discusses the method used to identify the process involving fatigue cracking of samples on the basis of selected vibration signal characteristics. Acceleration of vibrations has been chosen as a diagnostic signal in the analysis of sample cross section. Signal characteristics in form of change in vibration amplitudes and corresponding changes in FFT spectrum have been indicated for the acceleration. The tests were performed on a designed setup, where destruction process was caused by the force of inertia of the sample. Based on the conducted tests, it was found that the demonstrated sample structure change identification method may be applied to identify the technical condition of the structure in the aspect of loss of its continuity and its properties (e.g.: mechanical and fatigue cracks). The vibration analysis results have been verified by penetration and visual methods, using a scanning electron microscope.

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yan-Shin Shih ◽  
Chen-Yuan Chung
Keyword(s):  
Governing Equation ◽  
Moving Boundary ◽  
Beam Theory ◽  
Crack Model ◽  
Breathing Crack ◽  
Connecting Rod ◽  
Bernoulli Beam ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Crank Mechanism

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

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