Modal Analysis Of Beam Type Structures
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015Modal Analysis of Beam Type StructuresPankaj Kumar, Tejas Vispute, Anurag Sawant,Rohit JagtapGirish DalviAsst. Professor,Department of Mechanical Engineering,Fr. C. Rodrigues Institute of Technology,Vashi, Navi Mumbai 400 703, IndiaStudents,Department of Mechanical Engineering,Fr. C. Rodrigues Institute of Technology,Vashi, Navi Mumbai 400 703, IndiaAbstract : The purpose of this project is to study Modalbehaviour of Beam type structures. Beams under study includeCantilever, Simply Supported and Fixed beam. Mode shapesand natural frequencies of these three types of beams areobtained using Theoretical analysis, Simulation in ANSYS andExperiment using FFT analyser. Finally natural frequenciesobtained from Simulation and Experiment are compared withTheoretical values of natural frequency. The mode shapesobtained from simulation and experiment are matching closelywith analytical ones. Natural frequencies obtained by simulationare within 6% deviation when compared to theoretical resultswhereas for experimental natural frequencies the maximumdeviation from theoretical values is 19.31%.Keywords—Modal Analysis, Beam type structure, FFTAnalyzer, Natural Frequency, Mode ShapesI.INTRODUCTIONModal analysis is the study of the dynamic properties ofstructures under vibration excitation. The goal of modalanalysis in structural mechanics is to determine the naturalmode shapes and frequencies of an object or structure duringfree vibration.The various research papers studied are based onevaluation of specific properties or characteristics ofvibration of beams by various techniques. L.Rubio‟s [4] workfocuses on crack identification by means of modalparameters. P.Šuránek et.al[6] work is on decaying rate ofvibration in cantilever beam for which they used analuminum frame as an accessory to increase decay rate.Farooq and B. Feeny‟s[5] work is on new approach intheoretical modal analysis where they have used andevaluated the results experimentally for validity. H.Auweraer[2] has adopted a black box approach and evaluatedthem on industrial application. S. Mahalingam[1] has foundchanges occurring in modal parameters when supportchanges its position at an instance. A. Cusano et.al[3] usedBragg grating sensors instead of conventional accelerometerin experimental modal analysis and results were evaluated byexperiment and simulation.The literature survey shows that lot of efforts have beentaken for determining the modal properties of beam typestructures using numerous methods. Industry is focusing onreducing noise and vibration level for betterment ofperformance of various products. Beam type of structures areused in various application, hence it becomes an importantstructure to be studied for noise and vibration reduction.Mode shapes of beam type structures may provide moreinformation to control vibration. The present study willIJERTV4IS040847attempt to conduct experimental modal analysis of beam typestructures namely Cantilever, Simply Supported and FixedBeam. Thus, the scope involves:- Determination of Mode Shapes of Beam type structuresanalytically.- Simulation of Beam type structure in ANSYS.- Experimental Modal Analysis.II. THEORETICAL ANALYSISBeams are slender members used for supporting transverseloading. It is a basic structural element that is capable ofwithstanding load primarily by resisting bending. Simplysupported, cantilever and fixed beam are considered foranalysis and description of them are given below.Cantilever beam:A beam which is supported on the fixed support andhaving the other end free is termed as a cantilever beam:Fixed support is obtained by building a beam into a brickwall, casting it into concrete or welding the end of the beam.Such a support provides both the translational and rotationalconstrain to the beam, therefore the reaction as well as themoments appears, as shown in the figure below.Fig 1 Cantilever BeamSimply supported beam:The beams are said to be simply supported if their supportscreates only the translational constraints. When both thesupports of beams are roller supports or one support is rollerand the other hinged, the beam is known as a simplysupportedbeam.Fig 2 Simply Supported Beamwww.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)650
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015Fixed beam:A beam which is supported on the fixed support on boththe ends is termed as a fixed beam. It provides both thetranslational and rotational constrain to the beam at both theends.Simulation of modal analysis is done on FEA software„ANSYS‟ for three different types of beam structures whichare cantilever, simply supported and fixed beam.Fig 3 Fixed BeamCantilever BeamThe following parameters have been used in simulation.Young‟s Modulus 2.1 1011 N/mm2Poisson‟s ratio 0.3Density 7886 kg/m3The Grid size has been gradually increased from 20 to 85to reach a point where Natural frequencies obtained insimulation matches very closely with that of Analyticalresults. As the results best match at a mesh size of 85 allbeam elements are further given a mesh size of 85 foranalysis.The natural frequencies of cantilever beam are found withthe help ANSYS software and shown in the following table 3Calculation of Natural FrequencyNatural frequencies for first five mode shapes ofcantilever, simply supported beam and fixed beam arecalculated in this section.Using modified expression,III. SIMULATIONfn fnCgEIwlTable 3 Natural Frequency of Cantilever beamSet12345 natural frequency constant acceleration due to gravity young‟s modulus moment of inertia weight per unit length length of beamThe value of constant (C) is different for different beamtypes which have been enlisted in Table 1.Natural Frequency(Hz)16.75105.02294.05575.09952.08Mesh model of cantilever beam is shown in fig 5 and firstfive mode shapes obtained using Ansys are shown in figure 6,7, 8, 9 and 10.Table 1: Values of c for different type of 431.81Simply 31.8147.52Fig 5 Meshed Model of Cantilever BeamThe dimensions of beam considered for all types of beamstructures are shown in figure 4.Length 0.5 mWidth 0.04 mDepth 0.005 mFig 6 First mode shapeFig. 4 Dimensions of BeamNatural Frequencies of three types of beam are calculated andlisted in following table 2.Table 2 Theoretical natural frequenciesBeam Type 948.211168.21384.99FixedFig 7 Second mode shapeFig 8 Third mode shapeIJERTV4IS040847www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)651
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015Fig 9 Fourth mode shapeFig 12 Combined Setup for Simply Supported & Fixed BeamFig 10 Fifth mode shapeSimilarly mode shapes and natural frequencies are foundout for Simply Supported and Fixed beam. Naturalfrequencies obtained by simulation for different beamstructures are given in Table 4.C. Fixed BeamFixed beam can be made by restricting all degrees offreedom of beam at ends as shown in figure 5.1. Fixed beamarrangement consists of two identical I-sections, two platesand mild steel strip of dimensions 70 4 0.5 cm. Two Isections are welded to base, which is in the form of Csection, at 50 cm. Ends of strip are sandwiched betweenupper flange of I-section and plate and then bolted tightly.The setup is shown in figure 13.Table 4 Natural Frequencies of Beam Type StructureNatural FrequenciesBeam 6293.97575.20952.201422Fig 13 Fixed Beam SetupIV. EXPERIMENTAL SETUPIn this chapter, the various types of beams studied in theproject are realized. Natural frequencies and mode shapes ofdifferent beams are obtained using FFT analyzer.V. EXPERIMENTAL ANALYSISExperimental analysis is performed on three types of beamusing FFT analyzer. Modes shapes and Natural Frequenciesof Cantilever Beam are shown in this section. Figure 14shows five peaks corresponding to five natural frequencies.Figure 15 to 19 represents first five mode shapes obtainedexperimentally.A. Cantilever BeamA Cantilever beam can be made by restricting all degreesof freedom of beam‟s one end only. This arrangement can berealized using the same setup of fixed beam by eliminating itssecond support as shown in figure 11.Fig 14 Peaks obtained for Cantilever Beam(m/s²/Newton)25.0000EWaterfall H1 .00008.0000Fig 11 Cantilever Beam Setup6.00004.00002.0000B. Simply Supported BeamSimply supported beam can be made if the supports createonly translational constraint at one end and only verticalreaction at other end. The set up prepared is shown 05.006.007.008.009.00Time (seconds)Freq 25.00 HzFig 15 First mode shape for Cantilever Beamwww.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)652
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015Table 6 % Deviation of Simulation and Theoretical values(m/s²/Newton)88.000075.0000EWaterfall H1 2,1(f)Natural Frequencies60.000045.0000Beam .002.003.004.005.006.007.008.009.00Time (seconds)Freq 160.00 HzFig 16 Second mode shape for Cantilever Beam(m/s²/Newton)240.0000Table 7 % Deviation of Experimental and Theoretical valuesEWaterfall H1 2,1(f)200.0000160.0000120.0000Natural Frequencies80.0000Beam 006.007.008.009.00Time (seconds)Freq 443.00 HzFig 17 Third mode shape for Cantilever Beam(m/s²/Newton)34.0000EWaterfall H1 2,1(f)28.0000It is observed that maximum percentage deviation is 5.78for theoretical analysis and simulation and that for theoreticaland experimental results it is from 19.31. For experimentalanalysis larger deviation are -4.0000-8.0000-12.0000-16.0000-20.0000-24.0000VII. 09.00Time (seconds)Freq 897.00 HzFig 18 Fourth mode shape for Cantilever Beam(m/s²/Newton)650.0000600.0000EWaterfall H1 0024.0000 080.0000Time (seconds)Freq 1446.00 HzFig 19 Fifth mode shape for Cantilever BeamSimilarly mode shapes and natural frequencies are foundout for Simply Supported and Fixed beam. Naturalfrequencies obtained experimentally for different beamstructures are given in Table 5.Table 5 Natural Frequencies of beams by ExperimentNatural FrequenciesBeam .3276520903Simply Supported572173667581195Fixed842385469111367VI. RESULTS AND DISCUSSIONThis chapter compares results obtained by simulation andexperimental analysis with theoretical values. Percentagedeviation of experimental and simulation values fromtheoretical value is calculated and listed in following twotables. Table 6 gives percentage deviation of simulationvalues from theoretical and table 7 gives percentage deviationof experimental values from theoretical values.IJERTV4IS040847Based on theoretical, analytical & experimental results it ishereby concluded that: Results obtained by simulation are matching closely withtheoretical values. The maximum percentage deviation is5.78%. Results obtained by experimental analysis deviate morefrom theoretical analysis compared to simulation. Themaximum percentage deviation is 19.13%. In experimental analysis of Simply Supported Beam andFixed Beam some extra peaks are observed along withpeaks corresponding to natural frequencies. Modes shapes obtained from simulation and experiment arein agreement with the theoretical ones.ACKNOWLEDGEMENTWe would like to take this opportunity to thank all those whohave whole heartedly lent their support and contributed inthis project.We are sincerely thankful to our HOD, Dr. S. M. Khot andour principal, Dr. Rollin Fernandes for giving us anopportunity to work on this project.We are sincerely thankful to our guide, Prof. Girish Dalvi forhis valuable, inspiring and timely guidance and assistancethroughout the course of the project.We would like to sincerely thank Mr. K. P. Rajesh and Mr.Moreshwar Kor for helping us in preparation of experimentalsetup of the beam structures.Lastly, we would like to thank all those people whoknowingly and unknowingly contributed to our project.www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)653
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 4 Issue 04, April-2015REFERENCES[1] S. Mahalingam(1965) “Effect of a change in position of asupport on the natural frequencies and modes of vibration of asystem”, Journal Mechanical Engineering Science, Sri Lanka[2] Herman Van der Auweraer(2001) “Structural DynamicsModelling using Modal Analysis: Applications, Trends andChallenges”, IEEE, Technology Conference, Belgium[3] Andrea Cusano, Patrizio Capoluongo, S. Campopiano,Antonello Cutolo, Michele Giordano, Ferdinando Felli,Antonio Paolozzi, and Michele Caponero (2006) “ExperimentalModal Analysis of an Aircraft Model Wing by Embedded FiberBragg Grating Sensors” IEEE sensors journal, Italy[4] L. Rubio(2009), “an efficient method for crack identification insimply supported Euler Bernoulli beams”, Journal of Vibrationand Acoustics, Department of Mechanical Engineering,University Carlos III of Madrid, Spain.[5] Umar Farooq, Brian F. Feeny (2012) “An ExperimentalInvestigation of State-Variable Modal Decomposition forModal Analysis”, Journal of Vibration and Acoustics,Department of Mechanical Engineering, Michigan StateUniversity, pp. 021017-1 - 021017-8[6] Pavel .Šuránek, Miroslav Mahdal, Jaromír Zavadil(2013) “Modal Analysis of the Cantilever Beam”, IEEE, VSB .–Technical University of Ostrava, Faculty of MechanicalEngineering, Czech Republic, 14th International CarpathianControl Conference (ICCC) pp. 367 – 372[7] Rao S.S., “Mechanical Vibration” ISBN 978-0-13-212819-3[8] Singh V.P., “Mechanical Vibration” ISBN 9788177000313[9] C. Harris, A. Piersol “Harris‟ shock and vibration handbook”ISBN-10: 0071508198[10] Roy B., “Natural Frequencies to Transverse Vibrations”, 2013,http://www.roymech.co.uk/Useful Tables/Vibrations/NaturalVibrations derivation.html[11] “Free Vibration of Cantilever Beam (Continuous System)”,Sakshat VirtualLabs,http://iitg.vlab.co.in/?sub 62&brch 175&sim 1080&cnt 1[12] “Beam(structure)–Wikipedia, the free encyclopedia” ,http://en.m.wikipedia.org/wiki/beam (structure)[13] “Design Data – Data Book of engineers by PSG college oftechnology – Kalaikathir Achchagam- Coimbatore”[14] Sharma Satish C.,”LECTURE 21- Members Subjected toFlexural %20&%20picts/image/lect21/lecture21.htm[15] Klang E., “MAE 533 – Finite Element Analysis I”, NC ses/mae533/Reference/Convergence.htm[16] Brown David L., Allemang Randall J., “The Modern Era ofExperimental Modal Analysis”, University of Cincinnati,Cincinnati, ERTV4IS040847www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)654
with analytical ones. Natural frequencies obtained by simulation are within 6% deviation when compared to theoretical results whereas for experimental natural frequencies the maximum deviation from theoretical values is 19.31%. Keywords—Modal Analysis, Beam type structure, FFT Analyzer, Natural Frequency, Mode Shapes . I. INTRODUCTION
In this paper are given basic steps of the modal analysis simulation. The modal analysis is carried out on the titan cantilever beam. The cantilever beam is designed in the graphical environment of the ANSYS and SolidWorks. The cantilever beam was fixed on one end and all degrees of freedom on this end were taken, beam cannot move and rotate.
Experimental Modal Analysis (EMA) modal model, a Finite Element Analysis (FEA) modal model, or a Hybrid modal model consisting of both EMA and FEA modal parameters. EMA mode shapes are obtained from experimental data and FEA mode shapes are obtained from an analytical finite element computer model.
Fig. 3 (a): Mode 1 of cantilever beam (b) Mode 2 of cantilever beam (c) Mode 3 of cantilever beam III. MODAL ANALYSIS OF CANTILEVER BEAM (ANALYTICAL) For a cantilever beam Fig. (12), which is subjected to free vib
LANDASAN TEORI A. Pengertian Pasar Modal Pengertian Pasar Modal adalah menurut para ahli yang diharapkan dapat menjadi rujukan penulisan sahabat ekoonomi Pengertian Pasar Modal Pasar modal adalah sebuah lembaga keuangan negara yang kegiatannya dalam hal penawaran dan perdagangan efek (surat berharga). Pasar modal bisa diartikan sebuah lembaga .
the finite element method is known for computing modal analysis; if will be collected through the test of system input and output signal through the parameter identification obtained modal parameters, known for experimental modal analysis. Computational modal analysis method has been applied in many product developments, espe-
ANSYS User Meeting . November 2014 . Modal Analysis Correlation . Modal analysis and more--- QSK95 Generator set development--- 11/19/2014 Gary Sandlass CAE Specialist . A modal analysis will be correlated with a test when the frequency and the mode shape is correlated. The tool used to compare shapes is the MAC (modal assurance .
BC1 Page 41 BEAM CLAMP BD1 Page 41 BEAM CLAMP BF1 Page 42 BEAM CLAMP BG1 Page 42 BEAM CLAMP BH1 Page 42 BEAM CLAMP BF2 Page 42 BEAM CLAMP BG2 Page 42 BEAM CLAMP BL FLANGE CLAMP Page 43 GRATE FIX Page 44 BEAM CLAMP GRATING CLIP Page 45 BEAM CLAMP FLOORFIX HT Page 46 FLOORFIX Page
This work is devoted to the modal analysis of a pre-stressed steel strip. Two different complementary ap-proaches exist in modal analysis, respectively the theoretical and experimental modal analyses. On the one hand, the theoretical modal analysis is related to a direct problem. It requires a model of the structure.
