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Displacement analysis of cantilever beam using fem package
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  • 1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME75DISPLACEMENT ANALYSIS OF CANTILEVER BEAM USING FEMPACKAGEJN Mahto1, SC Roy2, J Kushwaha3, RS Prasad41,2Department of Mechanical Engineering, BIT, Sindri3Department of Mechanical Engineering, KIET, Ghaziabad4Department of Mechanical Engineering, RKGIT, GhaziabadABSTRACTIn the present investigation, efforts have been made to characterize behaviour of beamunder longitudinal stress. Specimens were modelled and analysed with the extensive use ofFEM package (Autodesk Inventor). Analysis was done by setting maximum load value as1100 N. The value of displacement and stress computed for the cantilever beam through FEMpackage were tabulated and graphs were drawn to observe pattern. Dimensions of specimenwere initially selected as length 500mm, width as 50mm and thickness as 12mm. By keepinglength of specimen fixed the thickness of specimen, width of specimen and force applied tothe specimen were varied to observe its effect on the behaviour of the beam. Aluminum,Copper and Steel were selected as three different materials for analysis.Keywords: Displacement Analysis; FEM Package; Structural Analysis; Mode-I Vibration.1. INTRODUCTIONIt is very important if it is known that how a beam under a load will behave when itscross section varies in a particular fashion. Also it is important to know the effect of changein the load applied to a beam. In the earlier work done it was found that cantilever beamwhen subjected to a cyclic transverse load frequency for the mode of vibration decreases asthe poisons ratio of the material increases. Modal parameters such as natural frequencies,mode shapes, were key information in determining the dynamic performance of the structure.Also, it was found that stress, strain energy, displacement gets affected if property of materialINTERNATIONAL JOURNAL OF MECHANICAL ENGINEERINGAND TECHNOLOGY (IJMET)ISSN 0976 – 6340 (Print)ISSN 0976 – 6359 (Online)Volume 4, Issue 3, May - June (2013), pp. 75-78© IAEME: www.iaeme.com/ijmet.aspJournal Impact Factor (2013): 5.7731 (Calculated by GISI)www.jifactor.comIJMET© I A E M E
  • 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME76changes. However, the accuracy of these quantities depends on the accuracy of the modalparameters used in the analysis. For this reason the present investigation was made so that thebehavior of beam under longitudinal load can be observed. FEM packages are adequatelyavailable to simulate and analyze. The data obtained can be further analyzed in order to knowbehavior of structure.2. LITERATURE REVIEWFrequency response of the vibration is very sensitive to the inhomogenity present inthe structure and can be used to determine location of crack and crack growth rate in astructure under vibration [1,2].Frequency response of a material is not only utilized to know about construction materials,but it has also been utilized to develop sensors. A cantilever sensor can be operated in twodifferent modes: the static mode, where the cantilever deflection is monitored, and thedynamic mode, where the cantilever resonance is monitored. The deflection of a cantilevercan be due to number of processes such as molecular adsorption, thermal effects, electric andmagnetic fields, and fluid flow. Cantilevers shorter than 10 µm in length with sub-attogramsensitivity were demonstrated in 2004 [3,4,5], enabling the detection of single virus particlesof femtogram mass [6].3. FEM ANALYSISThree materials are selected as steel, copper, aluminium because of their differentvalue of Young’s Modulus (E). The value of Young’s Modulus of the three materials are,ESteel=210e09, ECu=117.2e09, EAl=68.95e09. Density (ρ) and poison’s ratio (υ) of thematerials were taken as ρSteel=7800 kg/m3, ρCu=8960 kg/m3, ρAl=2700 kg/m3and υSteel=0.3,υCu=0.36, υAl=0.33.For the analysis of aluminium bar as a cantilever beam, a rectangular bar withdimensions 500m*50mm*12mm was modelled and material of model was defined asaluminium by taking value of Young’s Modulus of Elasticity as 68.95e09 N/m2, density as2700 kg/m3and poison’s ratio of aluminium as 0.33. The size of elements taken was 0.011,number of elements as 225 and number of nodes as 552.The maximum force value selected was 1100N for which the maximum displacementwas observed in each case. In case of aluminium, total mass of model calculated as 0.81 kg.At the force 1000N, width 50mm and thickness 12mm the displacement value underlongitudinal load was 4.75e-04inch.In case of the analysis of the rectangular bar of copper, value of Young’s Modulus ofElasticity was 117.2e09 N/m2, density as 8960 kg/m3and poison’s ratio as 0.36. Throughanalysis the total mass of model was calculated as 2.688 kg. At the force 1000N, width 50mmand thickness 12mm the displacement value under longitudinal load was 2.79e-04inch.For the analysis of the rectangular bar of steel, value of Young’s Modulus ofElasticity was taken as 210e09 N/m2, density as 7800 kg/m3and poison’s ratio of steel as 0.3.Total mass of model was observed as 2.34 kg. At the force 1000N, width 50mm andthickness 12mm the displacement value under longitudinal load was 1.56e-04inch.
  • 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME77Fig. 1. Variation in the displacement value with the change in materialFig. 2. Variation in the displacement value with the change in material4. RESULTS AND DISCUSSIONSThe value for maximum displacement of cantilever beam along its length whensubjected to the longitudinal load for the three materials were computed using FEM package.The graphs were drawn with the data obtained using FEM package for displacement is asshown in Fig. 1. The effect of material change on the stress value of beam is as shown in Fig.2.Fig. 3. Frequency Value of Materials at Mode-I
  • 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME785. CONCLUSIONSFrom Fig. 1 it was observed that displacement value of a rectangular bar undercantilever beam condition increases when poisons ratio varies from 0.3 to 0.33and thendecreases when poison’s ratio varies from 0.33 to 0.36. From Fig. 2 it can also be observedthat as the poison’s value increases the value of stress increases when subjected tolongitudinal load. But, from Fig. 3 it can be observed that value of poison’s ratio varies from0.3 for steel to 0.36 for copper where as the value of frequency at mode-I of vibration variesfrom 4.1943 Hz for steel to 2.8583 Hz for copper [7].REFERENCES[1] Prasad RS, Roy SC, Tyagi KP, Analysis and Comparison of Pattern of Crack GrowthRate along Vibrating Cantilever Beam using FEM Package, International Journal ofApplied Engineering Research, Vol. 5(12), pp 2091-2095, 2010.[2] Prasad RS, Roy SC, Tyagi KP, Effect of Crack Position along Vibrating CantileverBeam on Crack Growth Rate, International Journal of Engineering, Science andTechnology. Vol. 2(5), pp 837-839, 2010.[3] Ilic B, Craighead HG, Krylov S, Senaratne W, Ober C, Neuzil P, Attogram Detectionusing Nano-electromechanical Oscillators, Journal of Applied Physics, Vol. 95(7), pp3694-3703, 2004.[4] Yang JL, Ono T, Esashi M, Energy Dissipation in Submicrometer Thick Single-crystalSilicon Cantilevers. Journal of Microelectromechanical Systems, Vol. 11(6), pp 775-783,2002.[5] Burg TP, Manalis SR, Suspended Microchannel Resonators for Biomolecular Detection.Applied Physics Letters, Vol. 83(13), pp 2698-2700, 2003.[6] Gupta A, Akin D, Bashir R, Single Virus Particle Mass Detection using Microresonatorswith Nanoscale Thickness. Applied Physics Letters, Vol. 84(11), pp 1976-1978, 2004.[7] Mahto JN, Roy SC, Prasad RS, Material of Structure affecting the Frequency Analysisusing FEM Package, International Journal of Mechanical and Industrial Engineering,Vol. 1(4), 2012, pp 76-78.[8] K. Srinivasulu Reddy, “Canister Testing Chamber Design & Analysis using Fem”,International Journal of Design and Manufacturing Technology (IJDMT), Volume 4,Issue 1, 2013, pp. 68 - 73, ISSN Print: 0976 – 6995, ISSN Online: 0976 – 7002.[9] Sharad V. Kshirsagar and Dr. Lalit B. Bhuyar, “Signature Analysis of CrackedCantilever Beam”, International Journal of Advanced Research in Engineering &Technology (IJARET), Volume 1, Issue 1, 2010, pp. 105 - 117, ISSN Print: 0976-6480,ISSN Online: 0976-6499.