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

2021 ◽  
pp. 107754632110183
Author(s):  
Masoud Kharazan ◽  
Saied Irani ◽  
Mohammad Reza Salimi
Keyword(s):  
Cantilever Beam ◽  
Structural Damage ◽  
Crack Depth ◽  
Structural Response ◽  
Time History ◽  
Nonlinear Behavior ◽  
Nonlinear Phenomena ◽  
Breathing Crack ◽  
Cracked Beam ◽  
Practical Engineering

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.

Dynamic Instability Analysis of a Cantilever Beam With Breathing Crack

2017 ◽  
Author(s):  
Vigneshwaran Krishnaswamy ◽  
Manoj Pandey
Keyword(s):  
Cantilever Beam ◽  
Dynamic Instability ◽  
Crack Depth ◽  
Harmonic Balance Method ◽  
Equation Of Motion ◽  
Instability Region ◽  
Breathing Crack ◽  
Cracked Beam ◽  
Stability Boundaries ◽  
Cracked Structure

In this paper, dynamic characteristics of a beam with breathing crack is considered. Breathing crack is modeled as a bilinear oscillator. The stiffness of the cracked beam is estimated by using influence coefficients based on castigliano’s theorem and strain energy release rate (SERR). The equation of motion of breathing cracked beam is formulated using finite element method using Hamilton’s principle. The equation of motion of breathing cracked beam is converted into Mathieu-Hill type equation to obtain the regions of dynamic instability of beam using Harmonic balance method and it is further solved for Eigen frequency of the cracked beam. The increase in breathing crack depth increases the instability region and it is found that the effect of the crack location near to the fixed end is more for the cantilever beam, and this also increases the instability region. It is found that increase in dynamic instability index increases the instability regions of the cracked structure. In addition to that, the effect of static and dynamic loads are also investigated and discussed. The study has been conducted for the first two instability boundaries of the cracked structure only. It is hence seen that assuming the crack to remain open underestimates the stability boundaries of the system. Permitting the crack to open and close (breath) yields a stability boundaries in between the open and uncracked beam.

Effect of a breathing crack on the damping changes in nonlinear vibrations of a cracked beam: Experimental and theoretical investigations

2020 ◽  
pp. 107754632096031
Author(s):  
Masoud Kharazan ◽  
Saied Irani ◽  
Mohammad Ali Noorian ◽  
Mohammad Reza Salimi
Keyword(s):  
Nonlinear Vibrations ◽  
Crack Depth ◽  
Beam Theory ◽  
Experimental Tests ◽  
Damping Coefficient ◽  
Crack Identification ◽  
Breathing Crack ◽  
Cracked Beam ◽  
Identification Method ◽  
Nonlinear Crack

The attempts to identify damping changes in a cracked beam can improve the accuracy of the nonlinear crack identification method. For the purpose of this aim, a parametric nonlinear equation of motion is obtained using the Euler–Bernoulli beam theory and parametric nonlinear breathing crack assumptions. Several experiments were conducted to identify the effect of breathing cracks on changing the damping value in nonlinear vibrations of a cracked beam. Experimental tests have revealed that increasing the crack depth and the level of excitation enlarges the damping coefficient in a vibrating beam. For this reason, the effects of the excitation force and crack depth on the structural damping coefficient are investigated. The obtained results indicated that considering the nonlinear response of a cracked beam and measuring the value of the damping changes can significantly improve the accuracy of the nonlinear crack identification method.

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

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1177
Author(s):  
Li Cui ◽  
Hao Xu ◽  
Jing Ge ◽  
Maosen Cao ◽  
Yangmin Xu ◽  
...  
Keyword(s):  
Damage Detection ◽  
Dynamic Characteristics ◽  
Structural Damage ◽  
Damage Identification ◽  
Crack Depth ◽  
Excitation Frequency ◽  
Breathing Crack ◽  
Engineering Structures ◽  
Linear Dynamic ◽  
Non Linear

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.

scholarly journals A Theoretical and Experimental Investigation on Free Vibration Vehavior of a Cantilever Beam with a Breathing Crack

2012 ◽  
Vol 19 (2) ◽  
pp. 175-186 ◽  
Author(s):  
M. Rezaee ◽  
H. Fekrmandi
Keyword(s):  
Cantilever Beam ◽  
Multiple Scales ◽  
Correction Term ◽  
Experimental Tests ◽  
Analytical Relation ◽  
System Response ◽  
Breathing Crack ◽  
Cracked Beam ◽  
Lumped Parameter ◽  
Intrinsic Nonlinearity

In this paper the free nonlinear vibration behavior of a cracked cantilever beam is investigated both theoretically and experimentally. For simplicity, the dynamic behavior of a cracked beam vibrating at its first mode is simulated using a simple single degree of freedom lumped parameter system. The time varying stiffness is modeled using a harmonic function. The governing equation of motion is solved by a perturbation method – the method of Multiple Scales.Results show that the correction term that is added to the main part of the response reflects the effect of breathing crack on the vibration response. Moreover, this part of response consists of the superharmonic components of the spectrum which is due to the system's intrinsic nonlinearity. Using this method an analytical relation is established between the system characteristics and the crack parameters in one hand and the nonlinear characteristics of system response on the other hand. Results have been validated by the experimental tests and a numerical method.

Structural Damage Detection by Fuzzy Logic Technique

2014 ◽  
Vol 592-594 ◽  
pp. 1175-1179 ◽  
Author(s):  
Rabinarayan Sethi ◽  
S.K. Senapati ◽  
Dayal R. Parhi
Keyword(s):  
Fuzzy Logic ◽  
Cantilever Beam ◽  
Structural Damage ◽  
Fuzzy Controller ◽  
Crack Depth ◽  
Crack Location ◽  
Novel Approach ◽  
Vibration Parameters ◽  
Fuzzy Logic Technique

In this paper, a novel approach for detecting crack location and its intensity in cantilever beam by Fuzzy logic techniques is established. The analysis has been done by using ANSYS FE software. The fuzzy controller with Bell shaped membership functions are used here which consists of three input parameters are relative deviation of first three natural frequencies and two output parameters are relative crack depth and relative crack location respectively. A series of fuzzy rules are resulting from vibration parameters which are finally used for prediction of crack location and its intensity. This method provides the knowledge towards the detection, location and characterization of the damage in the cantilever beam.

scholarly journals Impulsive Signals Produced by Earthquakes in Italy and Their Potential Relation with Site Effects and Structural Damage

Geosciences ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 261
Author(s):  
Deniz Ertuncay ◽  
Petra Malisan ◽  
Giovanni Costa ◽  
Stefano Grimaz
Keyword(s):  
Structural Damage ◽  
Site Effects ◽  
Structural Response ◽  
Time History ◽  
Potential Influence ◽  
Directivity Effect ◽  
Step Effect ◽  
Fling Step ◽  
Seismic Records ◽  
2016 Amatrice Earthquake

Near fault seismic records may contain impulsive motions in velocity-time history. The seismic records can be identified as impulsive and non-impulsive depending on the features that their waveforms have. These motions can be an indicator of directivity or fling step effect, and they may cause dangerous effects on structures; for this reason, there is increasing attention on this subject in the last years. In this study, we collect the major earthquakes in Italy, with a magnitude large or equal to Mw 5.0, and identify the impulsive motions recorded by seismic stations. We correlate impulsive motions with directivity and fling step effects. We find that most earthquakes produced impulsive signals due to the directivity effect, though those at close stations to the 30 October 2016 Amatrice earthquake might be generated by the fling step effect. Starting from the analyzed impulses, we discuss on the potential influence of site effects on impulsive signals and suggest a characterization based on the main displacement directions of the impulsive horizontal displacements. Finally, we discuss on the damage of three churches in Emilia, which were subject to impulsive ground motion, underlying in a qualitative way, how the characteristics of the pulses may have had influences the structural response of the façades.

scholarly journals Static and Seismic Responses of Eco-Friendly Buried Concrete Pipes with Various Dosages of Fly Ash

2021 ◽  
Vol 11 (24) ◽  
pp. 11700
Author(s):  
Sayedali Mostofizadeh ◽  
Kong Fah Tee
Keyword(s):  
Fly Ash ◽  
Structural Response ◽  
Time History ◽  
Nonlinear Behavior ◽  
Vertical Displacement ◽  
Time Dependent ◽  
Optimal Time ◽  
Fe Model ◽  
Three Dimensional Model ◽  
Seismic Loadings

In this paper, an evaluation based on the detailed failure has been conducted for underground sewage Geopolymer concrete (GPC) pipes under static and seismic loadings with consideration of the optimal time steps in the time-dependent process related to nonlinear behavior of GPC pipes in static and dynamic analyses. The ANSYS platform is employed for improving an advanced FE model for a GPC pipe which can simulate the performance of underground GPC pipes containing various percentages of fly ash (FA) as a Portland cement (PC) replacement. Subsequently, the time-dependent model is used to assess the efficacy of this concrete admixture (FA) in the structural response of the unreinforced GPC pipe in FEM. Indeed, the generated GPC pipe with the three-dimensional model has the potential to capture the nonlinear behavior of concrete which depicts the patterns of tensile cracking and compressive crushing that occur over the applied static loads in the FE model. The main issue in this paper is the assessment of the GPC pipe response typically based on the displacement due to static and seismic loadings. The numerical results demonstrated that the optimal displacement was obtained when the structural response had typically the lowest value for GPC pipes containing 10–30% FA and 20% FA under static and seismic loadings, respectively. Indeed, a reduction by 25% for the vertical displacement of a GPC pipe containing 20% FA was observed compared to that without FA under time-history analysis.

scholarly journals Using a moving load to simultaneously detect location and severity of damage in a simply supported beam

2019 ◽  
Vol 25 (15) ◽  
pp. 2108-2123
Author(s):  
Mohsen Mousavi ◽  
Damien Holloway ◽  
J C Olivier
Keyword(s):  
Structural Damage ◽  
Moving Load ◽  
Time History ◽  
Static Deflection ◽  
Cracked Beam ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Damage Location ◽  
Wide Range ◽  
History Of

This paper demonstrates the feasibility of simultaneously identifying both the location and severity of structural damage in a beam by using two independent moving load experiments. First, a simple but sufficiently accurate single degree of freedom model is presented to simulate the structure efficiently over a wide range of relevant inputs. We then introduce a damage sensitive feature (DSF) based on the integral of the velocity time history of the beam at its midspan when the load moves over the beam. A critical velocity, a function only of the beam’s first natural frequency and length, is obtained for the proposed DSF, upon which the damage can be located more accurately. The only required data for the damage detection is the midspan velocity-time history of the cracked beam subjected to a moving load, and the midspan static deflection of the intact beam subjected to a load of the same magnitude. In the last section of this paper, the capability of the proposed DSF is examined in the presence of noise. The results demonstrate the capability of the proposed method to find both the damage location and severity successfully, and methods for further reducing the effects of noise are suggested.

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