Analysis Of Crack Detection Of A Cantilever Beam Using Finite Element .
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015Analysis of Crack Detection of A Cantilever Beamusing Finite Element AnalysisNitesh A. MeshramProf. Vaibhav S. PawarStudent, ME (Machine Design)Pillai’s HOC college of Engineering and TechnologyRasayani, Raigad(MS), IndiaMechanical EngineeringPillai’s HOC college of Engineering and TechnologyRasayani, Raigad(MS), IndiaAbstract- This paper describes finite elemental analysis ofa cracked cantilever beam and analyzes the relation betweenthe modal natural frequencies with crack depth, modalnatural frequency with crack location. Also the relationamong the crack depth, crack location and natural frequencyhas been analyzed. Only single crack at different depth and atdifferent location are evaluated and the analysis revelsrelationship between crack depth and modal naturalfrequency. As we know when a structure suffers from damageits dynamic property can change and it was observed thatcrack caused a stiffness reduction with an inherent reductionin modal natural frequencies. Consequently it leads to changein dynamic response of the beam. The analysis was performedusing ANSYS software. The material of the beam is taken asaluminum. The proposed technique represents actually amodal analysis having great benefits for health monitoring ofstructures. For this 3D model of cantilever beam with singlecrack is created in ANSYS. Total 49 model of crack cantileverbeam has been analyzed. Thus result obtained from ANSYSsoftware we can draw the graph of modal natural frequencyVs crack depth for constant crack location and modal naturalfrequency Vs crack location keeping crack depth constant.And finally the value obtained from ANSYS is checked withresult obtained from analytical method.with a guess for the crack depth ratio and iterativelyestimates the crack location and crack depth until thedesired convergence for both is reached.Kew words: Free vibrations; crack; modal naturalfrequency; ANSYS software; cantilever beam.I.The basic premise in modal analysis based damagedetection is that damage will significantly change thestiffness, mass, or energy dissipation properties of asystem, which in turn, modifies the measured dynamicresponse of the system. One of the most challengingaspects of modal analysis based damage detection is thatdamage is typically a local phenomenon and may notsignificantly influence the lower-frequency response of thestructure that is normally measured during FFT analyzertests.INTRODUCTIONBeing very commonly used in steel construction andmachinery industries, health monitoring and the analysis ofdamage in the form of crack in Beam structures poses avital mean. Since long efforts are on their way to find afeasible solution for crack detection in beam structures inthis regard many approaches have so far being taken place.When a structure suffers from damages, its dynamicproperties can change. Crack damage leads to reduction instiffness also with an inherent reduction in naturalfrequency and increase in modal damping. The work givesa feasible relationship between the modal natural frequencyand the crack depth at different location. Since freevibration analysis has frequently become a topic of manystudies therefore attention is focused it only.Crack localization and sizing in a beam from the freeand forced response measurements method is indicated byKarthikeyan et al. [1]. In the beam Timoshenko beamtheory is used for modeling transverse vibrations.FEM isused for the free and forced vibration analysis of thecracked beam and open transverse crack is selected for thecrack model .Being iterative in nature the iteration startsIJERTV4IS041005In the most general terms, damage can be defined aschanges appearing in a system that may affect its current orfuture performance. From this definition of damage oncecan see that damage is not meaningful without acomparison between two different states of the system, oneof which is assumed to represent the initial (pristine) state,and the other the damaged state. The definition of damagecan also be limited to changes to the material and/orgeometric properties of the system, including changes tothe boundary conditions and system connectivity, whichadversely affect the current or future performance of thatsystem.II.LITERATURE REVIEWMany attempts for modeling and studying the dynamiccharacteristics of cracked beams have been conducted.Expressions for bending vibrations of an Euler–Bernoullicracked beam have been suggested by Matveev andBovsunovsky (2002). Ross and Matthews (1995) identifiedsome important cases and motives for SHM, in order tovalidate modifications to an existing structure, assess thesafety and performance of structures affected by externalinduced vibrations, as well as an assessment of ogonas(1998) used the Hu-Washizu-Barr variationa lanalysis to develop the differential equation and boundaryconditions for a cracked beam considered as a onedimensional (1-D) continuum. Qiao (2009) has applied asignal-based pattern-recognition method to detect structuraldamages with a single or limited number of input/outputsignals. This method is based on the acquisition ofsensitive features of the structural response under a specificexcitation that represents a unique pattern for any particulardamage scenario. Rao et al. (2010) have presented amethod for crack identification in beam structures bywww.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)713
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015analyzing the fundamental mode of cracked cantileverbeam using continuous wavelet transform. The crack in thebeam is modeled as a combination of spiral and linearsprings under consideration of the coupling of bending andlongitudinal vibration of cracked cantilever beam. Rezaei(2010) has recorded critical data concerning the SH stateon a continuous or periodic basis through a sensoringsystem. The data are then processed and interpreted using aproper algorithm, e.g. Hilbert–Huang Transform (HHT), inorder to detect abnormalities and damages in the structure.A. specification Material Of Beam- Aluminum Span- 400mm Density Of Material- 2700 kg/m³ Cross-Section Of Beam- 16*16 mm² Young’s Modulus Of Elasticity- 70 GPa Crack Nature-Transverse to beam axis and opennature Poission’s ratio- 0.33Rezaee et al. (2010) proposed a new approach based onthe energy equilibrium method for free vibration analysisof a cracked cantilever beam taking into account bothstructural damping and damping due to the crack. Yazdi etal. (2009) presented transverse vibration of double crackedbeam using assumed mode method. Sinha et al. (2002)reported a new simplified approach to model cracks inbeams undergoing transverse vibration, in which they haveused a modeling approach based on Euler–Bernoulli beamelements with small modifications to the local flexibility inthe vicinity of cracks. Stephen (2009) has studied thevibration, aero-elasticity and crack detection of damagedcomposite wings. Wing damage has been considered as athrough thickness edge crack for all proposed theoreticalformulations and numerical investigation. Sanchez andCarlos (2006) examined structural damage identificationmethods based on changes in the dynamic characteristics ofthe structure and developed new approaches, which arebased on the modal curvature matrix, the FrequencyResponse Function (FRF), the curvature and the DiscreteWavelet Transform.B. Governing equation of motionThe free bending vibration of an Euler-Bernoulli beamof a constant rectangular cross-section is given by thefollowing differential equation as given in:In general, it can be stated that damage detectioncomprises five goals, each of which is gained withincreasing difficulty and complexity. The first is theexploration of damage in a specimen. The second is theestimation of the severity extent of damage. The third goalis the ability to differentiate between different types ofdamage. The fourth is the calculation of the damagelocations. The final is the estimation of the damage size. Inthe present paper it’s focused only on the first two goals.III.EQUATION OF MOTIONDynamic response of the structure affected by thefollowing aspects of the crack Position of crack(1)Where m is the mass of the beam per unit length (kg/m)wi is the natural frequency of the ith mode(rad/sec), E isthe modulus of elasticity (N/m²) and I is the moment ofinertia (m4). By definingequation (1) is rearranged as a fourth-order differentialequation as follows:(2)The general solution to equation (2) is(3)Where A, B, C, D are constants andis a frequencyparameter. Since the bending vibration is studied,edgecrack is modeled as a rotational spring with a lumpedstiffness. The crack is assumed open. Basedon thismodeling, the beam is divided into two segments: the firstand second segments are left andright-hand side of thecrack, respectively. Adopting Hermitian shape functions,the stiffness matrix of thetwo-noded beam element withouta crack is obtained using the standard integration based onthe variation Depth of crack(4) Number of crackswhere(5)H1(x), H2(x), H3(x), H4(x)(6)Hermitian shape functions defined asIJERTV4IS041005H1(x) 1 –3x2 /12 2x3/3 .(7)H2(x) x – 2x2/1 x3/12 .(8)H3(x) 3x2/12 – 2x3/13 (9)H4(x) -2x2/1 x3/12 (10)www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)714
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015Assuming the beam rigidity EI is constant and is givenby EI0 within the element, and then the element stiffness isWhere ωi0 is the ith mode frequency of the uncrackedbeam and ci is a constant depending on the mode numberand beam end conditions (for clamped-free beam, ci is3.516 and 22.034 for the first and second mode,respectively), ωi is the ith mode frequency of the crackedbeam. ri is the ratio between the natural frequencies of thecracked and uncracked beam. l is the length of the beam.IV. FINITE ELEMENT ANALYSISAssuming the stiffness reduction caused by as opencrack falls within a single element, and then the stiffnessmatrix of the cracked element can be written asIn this paper model preparation has been done in FEAsoftware. CAD model as follows(11)Where [ Kc] is the reduction in the stiffness matrix dueto the crack. According to Penet al. [8], the matrix is[ Kc](12)Fig. 1.Where K is the change in stiffness due to crack atdifferent location. It is supposed that the crack does notaffect the mass distribution of the beam. Therefore, theconsistent mass matrix of the beam element can beformulated directly asFigure I. Cantilever Beam In Ansys Nature(13)(14)In the dynamic analysis, the system matrix is usuallyrequired to be inverted. From this aspect, a diagonalizedmass matrix has a computational advantage. In this study, adiagonalized mass matrix is adopted, which is developedfrom the consistent mass matrix .The natural frequencythen can be calculated from the relationFig. 2.Cantilever Beam With Crack In Ansys NatureAlso, Analysis work has been done with FEA softwaremode shapes found as follows.(15)The natural frequency of the ith mode for uncracked andcracked beams is finally obtained as follows(16)Fig. 3.(17)IJERTV4IS041005Crack Meshingwww.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)715
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015Fig. 4.First Mode Deformation Of Beam With Crack At 40mm AndDepth 4mmGraph 1. First Mode Natural Frequency Ratio In Terms Of VariousCrack PositionFig. 5.Second Mode Deformation Of Beam With Crack At 40mmAnd Depth 4mmGraph 2. Second Mode Natural Frequency Ratio In Terms Of VariousCrack PositionFig. 6.Third Mode Deformation Of Beam With Crack At 40mm AndDepth 4mmV.RESULT AND DISCUSSIONFrom theoretical and analysis data the curve-fittedresults were tabulated, and plotted (in a three dimensionalplot) in the form of frequency ratio (ωc/ω) (ratio of thenatural frequency of the cracked beam to that of the uncracked beam) versus the crack depth (a) for various cracklocation (X). This will show the variation of the frequencyratio as a function of the crack depth and crack location forbeams with fixed-free ends.Graph 3. Third Mode Natural Frequency Ratio In Terms Of VariousCrack PositionIJERTV4IS041005www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)716
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015Graph 4.Graph 8. Three Dimensional Plot For Second ModeFirst Mode Natural Frequency Ratio In Terms Of CrackPosition For Various Crack DepthsGraph 9. Three Dimensional Plot For Third ModeGraph 5.Second Mode Natural Frequency Ratio In Terms Of CrackPosition For Various Crack DepthsContour Plot Of Normalized First Frequency vs Crack Location,Crack Depth10C5 0.940.94 – 0.960.96 – 0.980.98 – 1.00 1.009CRACK DEPTH876543250100150200250300350CRACK LOCATIONGraph 10. Frequency Contour Plot Of Mode-1 For Normalized Frequency0.9761Contour Plot Of Normalized Second Frequency vs Crack Location,Crack Dep10Graph 6. Third Mode Natural Frequency Ratio In Terms Of CrackPosition For Various Crack Depths90.9650.9700.9750.980CRACK DEPTH87C5 –––– 00350CRACK LOCATIONGraph 7. Three Dimensional Plot For First ModeIJERTV4IS041005Graph 11. Frequency Contour Plot Of Mode-2 For Normalized Frequency0.9861www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)717
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015The following conclusions were drawn:-Contour Plot Of Normalized Third Frequency vs Crack Location,Crack Depth1090.9600.9650.9700.9750.9800.985CRACK DEPTH87C5 –––––– 1. With the presence of crack in the beam the frequencyof vibration 2. The above information can be used to predict thefailure of beam and preventive steps can be taken.654Crack Identification Technique By Using Frequency Contours1032501001502002503008.4350Crack Depth ( mm )CRACK POSITIONGraph 12. Frequency Contour Plot Of Mode-3 For NormalizedFrequency 0.9707DISCUSSION:-0.97610.98670.97076.85.23.6Graph 1, 2 and 3 shows the plots of the first threefrequency ratios as a function of crack depths for some ofthe crack positions. Graph 4, 5 and 6 shows the frequencyratio variation of three modes in terms of crack position forvarious crack depths respectively. From Graph 1 it isobserved that, for the cases considered, the fundamentalnatural frequency was least affected when the crack waslocated at 350mm from fixed end. The crack was mostlyaffected when the crack was located at 40mm from thefixed end. Hence for a cantilever beam, it could be inferredthat the fundamental frequency decreases significantly asthe crack location moves towards the fixed end of thebeam. This could be explained by the fact that the decreasein frequencies is greatest for a crack located where thebending moment is greatest. It appears therefore that thechange in frequencies is a function of crack location. FromGraph2 it is observed that the second natural frequency wasmostly affected for a crack located at the center for allcrack depths of a beam due to the fact that at that locationthe bending moment is having large value. The secondnatural frequency was least affected when the crack waslocated at 350mm from fixed end. From Graph3 it isobserved that the third natural frequency of beam changedrapidly for a crack located at 250 mm. The third naturalfrequency was almost unaffected for a crack located at thecenter of a cantilever beam; the reason for this zeroinfluence was that the nodal point for the third mode waslocated at the center of beamVI. CONCLUSION100150200250300350Crack Location ( mm )Graph 13. Crack Identification Technique By Using Frequency ContoursOf The First Three Modes Of Beam (Mode 1 NormalizedFrequency 0.9761; Mode 2 Normalized Frequency 0.9867; Mode 3Normalized Frequency 0.9707)VII. REFERENCES[1][2][3][4][5][6][7]In the given paper the effects of crack on the first threemodes of vibrating cantilever beams has been presented.From the results it is evident that the vibration behavior ofthe beams is very sensitive to the crack location, crackdepth and mode number. A simple method for predictingthe location and depth of the crack based on changes in thenatural frequencies of the beam is also presented, anddiscussed. This procedure becomes feasible due to the factthat under robust test and measurement conditions, themeasured parameters of frequencies are unique values,which will remain the same (within a tolerance level),wherever similar beams are tested and responses measured.The experimental identification of crack location and crackdepth is very close to the actual crack size and location onthe corresponding test specimen.IJERTV4IS041005240[8][9]M. Karthikeyan, R. Tiwari, S. Talukdar (2006). “Crack localizationand sizing in a beam based on the free and forced responsemeasurements”. Mechanical Systems and Signal Processing 21(2007). pp. 1362–1385Salawu, O. S. and Williams, C., 1993, “Structural Damage DetectionUsing Experimental Modal Analysis–A Comparison Of SomeMethods,” in Proc. of 11thInternational Modal Analysis Conference,pp. 254–260Kim M-B, Zhao M. Study on crack detection of beam usingharmonic responses. Proceedings of the 2004internationalconference on intelligent mechatronics and automation, August2004, Chengdu, China, pp.72–6.Mohammad-TaghiVakil-Baghmisheh, Mansour Peimani, MortezaHomayoun Sadeghi, Mir Mohammad Ettefagh (2007). “Crackdetection in beam-like structures using genetic algorithms”. AppliedSoft Computing 8(2008). pp. 1150–1160.C.P. Ratcliffe, Frequency and curvature based experimental methodfor locating damage in structures, J. Vibration Acoustic. 122(2000).pp. 324–329.Sadettin Orhan (2007). “Analysis of free and forced vibration of acracked cantilever beam”. NDT & International 40 (2007). pp. 443–450.Chih-Chieh Chang, Lien-Wen Chen(2005). “Detection of thelocation and size of cracks in the multiple cracked beam by spatialwavelet based approach”. Mechanical Systems and SignalProcessing. Vol.19. pp.139–155Peng, Z. K., Lang, Z. Q., Billings, S.A.(2007), “Crack Detectionusing nonlinear output frequency response functions”. Journal ofSound and Vibration, 301, pp. 777-788.Prasad Ramchandra Baviskar, “Multiple Cracks Assessment usingNatural Frequency Measurement and Prediction of Crack Propertiesby Artificial Neural Network” International Journal of AdvancedScience and Technology Vol. 54, May, 2013.www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)718
IV. FINITE ELEMENT ANALYSIS In this paper model preparation has been done in FEA software. CAD model as follows Fig. 1. Cantilever Beam In Ansys Nature Fig. 2. Cantilever Beam With Crack In Ansys Nature Also, Analysis work has been done with FEA software mode shapes found as follows. Fig. 3. Crack Meshing
Crack repair consists of crack sealing and crack filling. Usually, crack sealing re-fers to routing cracks and placing material on the routed channel. Crack filling, on the other hand, refers to the placement of mate-rial in/on an uncut crack. For the purposes of this manual, crack sealing will refer to both crack filling and sealing.
crack growth as a mutual competition between intrinsic mechanisms of crack advance ahead of the crack tip (e.g., alternating crack-tip blunting and resharpening), which promote crack growth, and extrinsic mechanisms of crack-tip shielding behind the tip (e.g., crack closure and bridging), which impede it. The widely differing
vector fSg from the left side of the crack to the right side accord-ing to f SgRight ¼½F crack Left (4) where ½F crack is the crack transfer matrix provided in Part I [1], and summarized in Appendix A. The state vector fSg is fSg¼fu x h y M y V x u y h x M x V yg T (5) where the direction of the state vector quantity is indicated by the .
proposes an effective railway track crack detection using MEMS accelerometer. The proposed detection system is a cost effective yet robust solution to the problem of railway crack detection utilizing a method that is unique in the sense, that while its s
2.1 Crack closure method using two analysis steps Even though the virtual crack closure technique is the focus of this paper and is generally mentioned in the literature, it appears appropriate to include a related method: the crack closure method or two-step crack closure technique. The ter-minology in the literature is often inexact and this .
Crack in Radius of Flange 234 Cracked Lightening Hole Flange 237 Lateral Crack in Flange or Angle Leg 238 Drill Marks 240 Crack or Puncture in Interior or Exterior Skins 241 Crack or Puncture in Continuous or Spliced Interior or Exterior Skin — Flanged Side 245 Crack or Puncture in Continuous or Spliced Interior or Exterior Skin —
Crack filling is the placement of materials into nonworking or low movement cracks to reduce infiltration of water and incompressible materials into the crack. Filling typically involves less crack preparation than sealing and performance requirements may be lower for the filler materials. Filling is
As seen in Figure 2, crack maps are color coded by crack width. The block crack density determines severity of block and fatigue cracking. Block Crack density is a measurement of how tight or concentrated the cracks are over the area covered. Crack severity is summarized in Table 2.
