Damage Detection in Cantilever Beams using Vibration Based Methods

More info about this article: http://www.ndt.net/?id=21240 Damage Detection in Cantilever Beams using Vibration Based Methods Santosh J. Chauhan, Nitesh P Yelve, Veda P. Palwankar Department of Mechanical Engineering Fr. C. Rodrigues Institute of Technology Vashi, Navi- Mumbai E-mail: santosh.jpc@gmail.com, niteshyelve@fcrit.ac.in, vedapalwankar22@gmail.com

Abstract Beam structures are used in various applications and thus have become an important element to be studied for noise and vibration reduction. Damages can change the dynamic behavior of beam and thus by examining this change, the size and location of damage can be identified. The present study focuses on damage localization by observing the changes in natural frequencies and mode shapes of the beam structures. In this study modal analysis is performed by simulation and experimentation procedures. In simulation ANSYS is used as a tool for modal analysis. For experimentation FRF measurements are made under controlled conditions, where the test structure is artificially excited by using an impact hammer. The polynomial equations for the first three modes of the beam are formulated using MATLAB ; which can be used to evaluate the frequencies of the damaged beams. By using the fuzzy logic system, the location and size of the damage also has been inspected. The input parameters to the Fuzzy Controller are the first three natural frequencies. The output parameters of the fuzzy controller are the relative crack location and relative crack depth. Several Fuzzy rules have been trained to obtain the results for relative crack location and depth using MATLAB tool box and have been compared with the results obtained from Finite Element analysis. It is observed that the fuzzy controller can predict the depths and locations accurately close to the finite element analysis. Keywords damage detection, modal analysis, fuzzy logic, membership function, fuzzy controller introduction Structures must work safely during its service life. Damages, if any, present may initiate breakdown period in structure. The quantification of damage and prediction of the remaining lifetime are the most difficult issues, particularly the latter [1]. Thus, it becomes important to diagnose changes in dynamic behavior of damaged and undamaged structures[2]. A crack must be detected in the early state, as it may cause serious failure of the structures with due course of time. It is difficult to recognize damage by visual inspection techniques, when it is too fine [3]. Damage detection methods can be classified as destructive or non-destructive. (NDE) techniques include visual inspection, x-ray, ultrasonic, eddy current, and thermal field methods. These methods are local in nature and need knowledge of the damage location before the damage identification process starts in any structure [4]. Non-destructive methods are preferred over destructive methods such that the system could remain in function during and after testing [5]. In recent years there has been an increasing awareness of importance of damage prognosis systems in civil, mechanical and aerospace structures. Damage identification system commonly classifies four levels of damage assessment [6]. Studies [7], [8] throw light on the damage detection through lamb wave based techniques on composite materials and by the use of ultrasonic sensors respectively. Damage detection in beams is although 100years old, the need to be able to detect in early stage, the presence of damage has led to increase in development of new techniques. Chaudhari et al [2] used experimental modal analysis to identify natural frequencies and

frequency response functions. The study also gives relationship of change in natural frequency and mode shape. Rizos et al. [9] studied a method based on assumption of transverse surface crack extending along the width of the structure. Cam et al. [10] in their paper studied cracked beam structure using impact echo method. Beams with cracks of varying depth have been tested in their study. Orhan [11] did analysis of cracked cantilever beams using free and forced vibration, by finite element program. The change in natural frequency and harmonic response corresponding to change in crack depth and location were evaluated. Doebling [12] gave formulation to detect damage in beams using frequency shifts. The modal based methods utilize the information from modal parameters to detect and access structural damage. Ratcliffe [13] presented a technique for locating a delamination in composite beams. Parhi and Choudhary [14] have presented nondestructive method for detection of crack in terms of crack depth and crack location considering natural frequency as a parameter using Fuzzy logic system and finite element analysis. A lot of research has been done on the vibration analysis using modal parameters. The objective of this paper is to carry out modal analysis of pristine and various damaged specimens in ANSYS and to fit equations which co-relate changes in natural frequency and to experimentally verify the obtained results by modal analysis using impact hammer test. The analysis of damaged specimens to find damage depth has been carried out using fuzzy logic technique in MATLAB. 2 damage detection using changes in natural frequency Three approaches have been considered to analyze the effect of change of natural frequency on structure. In theoretical analysis, the natural frequencies have been carried out using the exact method. In simulation study, a rectangular notch extending across the width of the beam was made and extruded in Pro-E version 4.0. ANSYS was used as a tool to carry out modal analysis. A 3-D 20-node structural solid element SOLID95 was used to model the beam. The depth of the damage is considered to be constant (4mm), whereas the location of the damage is varied at each 10mm along the length of beam. The modal analysis is carried out for the 49 locations along the length of the beam and the changes in natural frequencies are tabulated. Experimentation procedure has been carried out on undamaged and various damaged specimen using impact hammer test in an open environment. 2.1 Theory A cantilever beam model representing a continuous system based on Euler- Bernoulli beam theory has been used for deriving the necessary formulation. The governing equation for free vibration is given by: The natural frequencies of the beam are given by (2) 4 4, + 2, =0 (1) 2

(2) Where, i =constant L = length of the beam (0.5 m) ρ = density of beam (7780kg/m 3 ) E = Young s modulus (β.1 10 11 N/m 2 ) A = Cross sectional area (2.1 10-4 m 2 ) I= moment of inertia (bd 3 /12) The theoretical first three natural frequencies of the damage-free beam for the above specifications are found to be 23.4968Hz, 147.388Hz and 412.382Hz respectively. 2.2 Simulation Study The modal analysis of the cantilever beam requires the completion of following steps: (a) modeling of beam (b) meshing the geometry (c) assigning boundary conditions (d) studying results. Block Lanczos method is used for the extraction of modes. The natural frequencies by the simulation method are 24.657, 154.41 and 431.81 respectively. For the study of damaged specimens, a rectangular notch extending along the width of the beam is made and extruded. The geometry is as shown in fig 1. Fig.1. Geometry of the damaged specimen 2.3 Experimental Verification The purpose of this section is to study the effect of damage on modal parameters experimentally. To validate the results, experiments are carried out in an open environment. The simulation and experimental results are analyzed and compared. Experimentation is carried out using an impact hammer, shear accelerometer, ultraportable dynamic signal analyzer and RT photon+ software. The beam is divided in ten equal parts and the accelerometer is placed at 6 th position i.e. at 300mm from the fixed end. If it is placed at the exact center of the beam, we cannot get the 2 nd mode shape. The actual experimental setup is as shown in Fig 3.

Fig.2. Actual experimental setup 2.4 Fuzzy logic technique Fuzzy logic is a tool for embedding human structured knowledge. P. L. Zadeh says, įfuzzy logic may be viewed as a bridge over the excessively wide gap between the precision of classical crisp logic and imprecision of both the real world and its human intervention. Fuzzy logic in MATLAB can be dealt very easily due to existing new fuzzy logic toolbox. Parhi and Choudhary [14] in their paper have presented a nondestructive method for detection of cracks in terms of crack depth and crack location with the consideration of natural frequency. The fuzzy inference system is formulated with three inputs (first three natural frequencies) and two outputs (damage location and depth).the proposed fuzzy logic based system for damage detection is compared with the results obtained from FEA. Specific terms are to be used for the specification of the membership functions. First natural frequency= fnf Second natural frequency= snf Third natural frequency= tnf Relative damage depth= rcd Relative damage location= rcl The respective weights for each rule are given as 1. A factor W ijk is defined for the rules as follows: W ijk = µfnfi (freqi) snfj (freqj) tnfi (freqk) Where freqi, freqj and freqk are the first, second and third natural frequency of the cantilever beam with damage respectively; by Appling composition rule of interference (Das et al 2008) the membership values of the relative crack location and relative crack depth µrclijk (location) = Wijk rclijk (location) length ωl µrclijk (depth) = Wijk rclijk (depth) depth CD 3 damage detection using changes in strains corresponding to mode shapes The mode shapes of healthy structures is smooth and continuous, if any damage is present on the surface, it will introduce an irregularity to the smooth mode shape [13]. To verify the statement, analysis is carried out by using the data extracted from the simulation using ANSYS. The strain

values against the location of the nodes of an edge are plotted and analyzed for comparison study. Fig 3.The edge selected and the plotted nodes of the edge 4 rsesults and discussions After extensive theoretical, simulation and experimental investigation, results are to be compared for the different methods that are used for damage detection. 4.1 Curve fitting technique The verification for the equations obtained using MATLAB and various experimentations have been performed on pristine and damaged specimens. The fig 3 shows the fitted mathematical equations for the first three modes of vibration. 1.02 Fitted quation for first mode shape 1.02 Fitted equation for second mode 1.02 Fitted equation for third mode 1 y = 0.5719*x 4-1.141*x 3 + 0.504*x 2 + 0.2393*x + 0.8393 1 y = 23.34*x 6-71.77*x 5 + 79.36*x 4-36.08*x 3 + 4.753*x 2 + 0.5234*x + 0.8877 1 y = - 532.1*x 9 + 3032*x 8-7081*x 7 + 8782*x 6-6242*x 5 + 2549*x 4-563.3*x 3 + 57.25*x 2-1.588*x + 0.9453 0.98 0.96 0.98 0.98 frequency ratio 0.94 0.92 0.9 frequency ratio 0.96 0.94 frequency ratio 0.96 0.94 0.88 0.92 0.86 0.84 simulation data fitted curve 0.9 simulation data fitted curve 0.92 simulation data fitted curve 0.82 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 damage ratio (a/l) 0.88 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 damage ratio (a/ L) 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 damage ratio (a/l) Fig.3 Fitted equation for 1 st, 2 nd and 3 rd mode respectively. The simulation and experimental results have been compared and the percentage error has been calculated. The cases with min errors are considered. Table shows comparison of results and calculated % error. Table 1 Comparison of simulation and experimental results Location Mode Simulation Experimental % Error 50 1 21.417 21.2402 0.8255 2 148.23 143.555 3.15 3 429.28 402.832 6.16 75 1 22.01 20.5078 6.825 2 152.58 144.287 5.435 3 431.31 433.594-0.5295 135 1 22.722 21.2402 6.521

2 153.26 148.682 2.987 3 404.24 380.127 5.965 200 1 23.589 23.4375 0.6422 2 144.88 150.146-3.6347 3 417.39 417.48-0.0215 362 1 24.672 21.9297 11.11 2 147.15 143.555 2.443 3 389.91 431.396-10.64 400 1 24.761 23.4375 5.345 2 151.57 150.879 0.455 3 402.72 388.916 3.2835 4.2 Fuzzy logic technique: Using the designed fuzzy logic controller system and defining the set of rules, using the triangular membership functions, the damage depth and location can be predicted. The results of the fuzzy logic can be seen as below: Table 2 results of the fuzzy logic technique Sr.no. Natural frequency (Input) Actual Predicted FNF SNF TNF RCL RCD RCL RCD 1 24.657 154.41 431.81 - - 0.015 0.08 2 24.76 151.6 402.12 0.8 1 0.858 0.957 3 24.13 154.5 429.7 0.2 0.5 0.5 0.4 4 24.177 149.98 424.82 0.4 0.15 0.5 0.65 5 22.2 154.5 420.3 0.1 1 0.15 0.959 6 24.631 151.78 427.37 0.6 0.5 0.5 0.65 7 24.743 153.13 417.91 0.8 0.75 0.85 0.7 8 24.689 154.25 429.96 08 0.25 0.5 0.4 9 23.193 150.63 405.03 0.32 1 0.5 0.65 10 24.002 141.28 431.45 0.48 1 0.5 0.65 4.2 changes using strain values corresponding to mode shapes

The mode shapes of the damage- free beam is a smooth surface, whereas the damaged beams show abruptness or irregularities. The modes shapes of the damage free beam and the damage test specimen under study is as shown below in fig strain 0.00E+00-2.00E-02-4.00E-02-6.00E-02 0 0.1 0.2 0.3 0.4 0.5 length mode shape 1 strain 5.00E-02 0.00E+00-5.00E-02-1.00E-01-1.50E-01 beam span (m) 0 0.5 damage depth=1m m damage depth=2m m Fig 4 comparison of mode shape corresponding to damage-free and damaged specimen VI conclusions The damage detection using changes in natural frequency and changes in mode shapes is studied using modal analysis by simulation and experimentation procedures. The maximum errors lie in the range of 9-10%. It can be concluded that as the location goes on increasing, the frequency of vibration also goes on increasing. Also as the depth of damage goes on increasing, the frequency of vibration decreases, but the amplitude of vibration increases. The prediction of damage location and depth is studied by using fuzzy logic technique. Thus, the damage detection in cantilever beams using vibration methods is successfully implemented. References [1] P. Shm, įstructural Health Monitoring A overview of an evolving research area, Struct. Heal. Monit., vol. 2. [2] ω. ω. ωhaudhari, J. A. Gaikwad, V. R. ψhanuse, and J. V Kulkarni, įexperimental Investigation of Crack Detection in Cantilever Beam using Vibration Analysis, no. 1, pp. 1γ0 134, 2014. [3] S. Engineering and A. Priyadarshini, įidentification of ωracks in ψeams Using Identification of ωracks in ψeams Using, no. β11, β01γ. [4] S. Gerist, S. S. Naseralavi, and E. Salajegheh, įdamage Detection of Beam-like Structures Using an Improved Genetic Algorithm, no. March, pp. β 10, 2012. [5] ω. J. Schallhorn, įlocalization of vibration-based damage detection method in structural applications, β01β. [6] M. S. Prabhakar, įvibration Analysis of Cracked beam Vibration Analysis of Cracked beam Department of Mechanical Engineering National Institute of Technology, β00λ. [7] S. S. Kessler, S. M. Spearing, and ω. Soutis, įdamage detection in composite materials using Lamb wave methods, Smart Mater. Struct., vol. 11, no. 2, pp. 269 278, 2002.

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