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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of …

International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.

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  • 1. R.J.V. Anil Kumar, Dr Y.Venkata Mohana Reddy, Dr. K.Prahlada Rao / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1453-14591453 | P a g eCritical Review On Structural Dynamic Modification On BeamStructuresR.J.V. Anil Kumar, Dr Y.Venkata Mohana Reddy, Dr. K.Prahlada RaoLecturer, Dept of Mech. Engg., JNTUA College of Engg., AnantapurProf. and HOD, GPREC, Kurnool.Professor, JNTUA College of Engg., Anantapur.Abstract:The present paper illustrates the variousdevelopments in the field of structural dynamicmodification (SDM). SDM techniques can bedefined as the methods by which the dynamicbehavior of a structure is improved by predictingthe modified behavior brought about by addingmodifications like those of lumped masses, rigidlinks, dampers, beams etc or by variations in theconfiguration parameters of the structures itself.The theory of SDM started in the late 70s.But intensive research has taken place only after adecade and subsequently light has been put on thissubject in recent years. The contribution of manyresearchers to this field has taken the subject to anew era of investigation. The modification in anystructure to improve its natural frequencies hasreceived a lot of attention in many areas asstructure response is heavily influenced by itsnatural frequencies. FEM is a basic tool that isused for analysis of such structures, whichsimplifies the laborious calculationsKeywords: Beam Analysis, Eigen Values, Naturalfrequencies, SDMAbbreviations:SDM : Structural Dynamic Modification3D : 3 DimensionalDOF : Degrees of FreedomIMAC : International Modal AnalysisConferenceEM : Eigen value ModificationLEMP : Local Eigen Value ModificationprocedureFRF : Frequency Response FunctionLMM : Linear Modification MethodDMM ; Direct Modification MethodMUCO: Modal updating using constrainedoptimizationFEA : Finite Element AnalysisMAC : Modal Assurance CriterionEMA : Experimental Modal AnalysisIESM : Iterative method or inverse Eigensensitivity MethodI. Introduction:The first useful structural element in theSDM process to be considered was a general 3Dbeam element (useful for beam and rib types ofmodification studies). However, there was aninherent problem when these realistic structuralelements were used in conjunction with modal dataobtained from a modal test. The Lack of rotationalDOF was a major obstacle at the introduction of theSDM technique and still presents unique obstacles toefficient implementation. A great deal of researcheffort was expended in the 1980s to developtechniques for the estimation of rotational DOF aswell as the development of structural elementsSince rotational measurements may not exist or beavailable, efforts were focused on approximations ofgeneral 3D structural elements using only availabletranslational information. Beam approximations using3-point bending equations were the first estimates tobe used. These provided reasonably good results forsystems that behaved with beam-like responses in themodified system characteristics. In general, the firstten years of the International Modal AnalysisConference (IMAC) were seen to be the birth anddevelopment of the Structural Dynamic ModificationTechnique. The development of the proportional andcomplex mode Eigen value modification techniquewith the computationally efficient Local Eigen valueModification Technique (LEMP) was the subject ofmany papers in the early years of IMAC. This wasfollowed by the development of more realisticstructural elements for component modificationstudies as well as system models from componentmodes. The development of tools to estimaterotational DOF was evident during the same period.II. Origin for research -1980Around in 1980s research was done by B.P.Wang etal on S.D.M. on some existing structures andpresented the paper, ‘Structural DynamicModification using Modal Analysis Data [1]. TheFrequency Response Functions (FRF) of the modifiedstructure was studied using the frequency responsedata of the existing structure. An experiment wasperformed on a 31 cm square Aluminum plate.Graphs were plotted with frequency on X axis andmagnitude of transfer function on Y axis. For every
  • 2. R.J.V. Anil Kumar, Dr Y.Venkata Mohana Reddy, Dr. K.Prahlada Rao / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1453-14591454 | P a g estep of the increase in mass it was seen that theaccuracy of the synthesized function decreased.Later B.P.Wang [2] studied the limitationof the local modification on the distribution of naturalfrequencies. For finite element models, it was shownthat the distribution of natural frequencies cannot bealtered arbitrarily by local modifications. Threecomponents were taken for analysis viz, 1) 5 DOFsystem, 2) Truss Members and 3) Spring MassSystem. In all the systems, it was seen that thefundamental frequency could not be raised afterreaching a saturation point even by modifying thestiffness of the system.In 1985, Fabrizo Pimazio andLucion Ricciardiello [3] studied the effects ofstructural variations on the dynamic behavior of asystem. Two structures were studied. The firststructure was simple; as was used to correlate theenergy of an area with the efficiency of amodification in the area itself. The second structurewas more complex to permit analysis of perturbationformulae. The analysis revealed that even a smallchange to area of any structure having high energycontent; brought a notable variation in the frequencyand if the energy of the modified area is higher, theforecast and reference frequencies have less error.This error increased when the degree of modificationwas increased.. The dynamic behavior of structureis usually modeled using the below equation,------------------- (1)Where ‘f’ is the excitation applied to the structure,‘x’ is the instantaneous deformation andm, k and c represent the capacity of thestructure to store kinetic and strain energy anddissipate energy viscously respectively.The homogeneous form of equation (1) issolved in terms of an Eigen value problem2m+The research work carried out by J.ABrandon etal [4] presents the analysis of the aboveequations in terms of matrix algebra where matricesare of the order ‘n’. It is the utilization of the knownsolution of an existing problem to deduce the solutionto a modified model.A new modification approach was presentedby A.Sestieri and W.D’Ambrogio [5]. The methodmay be used to handle useful applications and allowsthe achievement of optimal modificationsaccomplished with different dynamic requirementslike FRF Modulas, response power spectral densityand response mean square value. The structuralmodifications that can be accounted for are lumpedmasses, springs, viscous dampers, dynamic absorbersand stiffening rods.The method devised by them involves 3steps viz,.(a) Synthesis of the modified structure: Here theFRF was used to express the dynamic behavior of themodified structure which is called as FRF matrix with‘N’ degrees of freedom of order NxN.(b) Definition of structural modification goals: Goalof structural modification is to limit the key responseparameters with in established boundaries.(c) Formation of the mathematical of structuralmodification: The problem stated above was putunder non linear programming technique and isdefined as a constrained optimization problem.A further step in the area ofoptimization was presented by the same author in thepaper- SDM Variables Optimization [6]. Here theinverse of optimization problem was presented andFRFs were used and not the modal parameters todefine the dynamic behavior.Two cases were examined viz considering a)Deterministic forces and b) Random ForcesIt is to be noted that, when there is no sufficientinformation on the existing forces, the estimate of thedynamic behavior of the structure may be performedby means of the FRF. By it, it is possible to determinethe response in several points of the structure startingfrom a general estimate of the existing force.If the existing forces are known, it ispossible to estimate the dynamic behavior of thestructure by considering the response to such forces.The author also defines sensitivity analysis andapplies it to the non linear optimization problems toreduce the number of design variables. By sensitivityanalysis one can determine the effectiveness inperforming the required goals.` The applications of SDM were studied byA.Sesteiri [7]. The method as applied to two real lifestructures viz a) Reduction of kinematic vibrationtransmission path in case of engines and b) loweringof peaks of spindle drive point on a flexiblemanufacturing cell.As the engine element is designed for staticcriteria, it is chosen for modification. Hence additionof small amount of masses at a few points on theengine showed significant sensitivity i.e. it reducedthe vibration transmission. It was seen that the highfrequency range is mass controlled and stiffnessmodification gave more negligible results.In the latter case structural modificationtechnique was applied on the Flexible ManufacturingCell. The aim of this case was to improve thedynamic behavior of the machine by somemodifications to it without hindering the normalmachine operation. The sensitivity analysis wasperformed by considering effects of adding a singlemass of increasing magnitude.At first masses were added to the back of themachine. Only a very slight effect on the spindlerelated FRFs was seen. Then masses on the spindlehousing were examined. The effect was notencouraging. Finally the effect of a dynamic absorber
  • 3. R.J.V. Anil Kumar, Dr Y.Venkata Mohana Reddy, Dr. K.Prahlada Rao / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1453-14591455 | P a g eon the spindle housing was examined which showed asignificant improvement in the spindle FRFs. But thecost of modification on the back was assessed to beten times lower than the cost of modifications on thespindle housing. This demonstrated that theoptimization technique based on FR is effective alsoon complex structures like machine tools.H.N. Ozguven [8] showed that when themodification does not alter the DOF of the structure,then the computational speed is also increased. Themethod was applicable to complex systems andseveral inaccuracies were also eliminated.III. After a decade- 1990The dynamic behavior of a vibrating systemafter modification was studied by Y.M.Ram and J.J.Bleech [9]. A mass was freely attached to a vibratingsystem through a spring. This decreased all thenatural frequencies of the modified system. Thelowest Eigen value of this system determines thetrend on which the Eigen values of the first systemchange and conversely.S.Lammens etal [10] studied the modalupdating and structural optimization of a tennisracket. Changes were applied to the AluminumTennis Racket and the dynamic characteristics werecalculated. An experimental modal analysis test wasperformed. With the updated model, the structuraloptimization calculation was performed. Finally theresults of the optimization were verified on the realstructure. Ten iterations were done. The frequencydifferences between calculated and measuredfrequencies were less than 5%.The effect of SDM was studied on thedamped beam elements by R.K. Srivatsava and T.K.Kundra [11]. They formulated an algorithm usinghysterically damped beam elements. Considering anumerical example it was observed that the modaldamping is increased with increased damping of theadded beam. Also there is a decrease in trend ofvibration levels with increased damping.In the event that a vibration problem exists,the question arises as to how the characteristics of thestructure may be modified in such a manner as tominimize the problem. Staneley G.Hutton [12]presented a paper restricting to the case in which it isrequired to modify a natural frequency of thestructure. For the modification of the structure twobasic approaches were available. The author throwsthe light on these two approaches firstly Forwardmodification using modal truncation which is a trialand error method and an iterative procedure. Initiallythe change is made to the structure and the resultingequations are solved to check if the prescribedchanges had the desired effect if not, further changesare made and the progress is repeated. In the secondapproach, algorithms are developed in which theprescribed changes to the natural frequency arespecified as input data and the output defines the massand stiffness changes required to the effect of therequired modification. Such procedures are called asInverse Modification Procedures. Here it is requiredto determine what structural changes will produce aprescribed changed in a given frequency. Thisproblem is complicated by the fact that, in generalthere is no simple relationship between frequencychange and structural change.Structural Dynamic Modifications are themethods to obtain the modified system dynamiccharacteristics due to structural modifications withoutgoing for a repeated analytical solution orexperimentation. Among the various methods ofSDM, the perturbation method is very useful andgives reasonably accurate estimates of the dynamiccharacteristics. There are two methods in theperturbation,1) Multistep Perturbation Method (also called asModal Perturbation Method),2) Single Step Perturbation Method.S.S.A. Ravi, T.K. Kundra and B.C.Nakra[13] proposed a single step perturbation method foran Aluminum beam. The experiment was conductedon a simply supported beam for full constraineddamping layer treatment. It was found that single stepperturbation method is more accurate, has a fasterconvergence and computationally more efficient ascompared to the multi step perturbation. The singlestep perturbation method gives more accurate resultsin case of very large modifications also except forpartial coverage.In 2000 A.Sestieri [14] gave a detaileddescription of SDM. Two different problems wereusually considered i.e., 1) direct problem and 2)inverse problemThe direct problem consists in determining the effectof already established modifications.Inverse problem is a typical designingproblem and is complex.Various relations were derived for the direct problemand inverse problem. Detailed descriptions of themodifications are dealt.The considered elementary modifications areconcentrated masses, springs, viscous dampers,dynamic absorbers and continuous rods.It was concluded that when dealing withstructural modifications either a direct problem or anoptimistation problem could be considered Thus bothmodal and the FRF approaches were successful. Butuse of FRF data base was particularly appropriate,giving a satisfactory solution.Later T.K.Kundra [15] gave a detaileddescription of SDM for an F type structure involvingvarious mathematical models namely mass, stiffnessand damping matrices of the equations of motion of astructure. Various mathematical equations wereframed for the mass modifications and tuned absorbermodifications.
  • 4. R.J.V. Anil Kumar, Dr Y.Venkata Mohana Reddy, Dr. K.Prahlada Rao / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1453-14591456 | P a g eRaleigh’s method was widely used for Eigenvalue reanalysis. The following was the equation forsmall modifications,For any changes of [dM] and [dK] changesin Ω can be approximately and readily calculated. Theoptimization aspect of SDM was also highlighted bythe author.B.C. Nakra [16] applied Perturbation methodbased on FEM to the structural systems in which PVCwas used as the damping material. The modulasproperties of this PVC increases with frequency anddecreases with temperature. Sensitivity analysis canprovide the ratio of the change of modal parameterssuch as natural frequency, mode shape etc withrespect to that of design parameter such as mass,stiffness or damping.In the research carried out by Nobuyukiokubu and Takeshitoi [17], the theoretical backgroundof sensitivity analysis was described followed byverification using simple structures. The differentsensitivity parameters considered are naturalfrequency, mode shape, operational deflection shape,relative motion, transmitted force, servo sensitivityand acoustic sensitivity. The first two sensitivitieswere described and applied to simple structure forverification of its effectiveness. By these methods thepoint of modification in the structure was identified tosuppress the vibration. Later 5 sensitivities were alsoanalysed and practical examples were illustrated.R.K.Srivatasava [18] studied the SDMtechniques as applied to various applications. Thecase of undamped and damped was also studied withthe help of relevant equations. The differentapplications under study were SDM using spatialmodels, modal models, tuned absorber, using FRFand optimal SDM.The solution for inverse problem forstructural modification was studied by Tao Li Jimin[19]. Among the dynamic properties, changing anatural frequency was perhaps the most commonobjective of structural modification. The theoreticaldescription of structural modification was explainedand equations for mass and stiffness modificationwere presented along with a set of linear simultaneousequations for mass and stiffness; equations for massunder linear modification method (LMM) andstiffness modification by direct modification method(DMM) were also given which derives the answersexplicitly by linear transformation. The validity andfeasibility of LMM and DMM was verified by theauthor who revels that the DMM is a convenientapproach as it reduces the numerical calculations tominimum than LMM as there was only one input forDMM.IV. SDM for beams after 2000:For the uncoupled beam structures thestructural optimization method was applied usingonly FRF matrices by Hwa Park and Youn Sik Park[20]. The optimal structural modification wascalculated by combining the results obtained by theEigen value sensitivities and reanalysis throughseveral iterations. Also a comparison of this was donewith perturbation method. The comparison shows anadvantage of the proposed experimental method overperturbation method as applied to the complex realstructures. Inspite of the advantages extra efforts areneeded for the measurements of FRFs to construct thefull FRF valuesThe author gives a key equation for the aboveconclusions vizWhere H (ω) is the modal force matrix,Hb(ω) is the FRF matrix of the baselinestructure andHm(ω) is the FRF matrix of the modificationstructure.A comparative study of SDM and sensitivitymethod approximation was done by KengC.yap and David C.Zimmerman [21]. A numericalanalysis was performed to compare the Eigen solutionestimation accuracy of SDM and sensitivity method.The following observations are derived by theauthors:1) SDM may be more feasible than sensitivity methodfor applications involving Eigen value estimatesespecially when stiffness perturbation is predominant.2) The natural frequencies are better with SDMmethod and mode shapes are better with sensitivitymethod.A further research in the above area wasenhanced by F.Aryana and H.Bahai`[22] studyingsensitivity analysis and modification of Structuraldynamic characteristics using second orderapproximation in Taylor expansion. The methodproposed by the authors was based on a matrixtreatment procedure for modifying stiffness and massof the finite elements.An algorithm was developed and four casestudies were conducted. The four case studies are aplane truss structure, a plane stress model of acantilever, plane stress mode of a bracket and a planestrain model of a dam. For a plane truss structure andplane stress cantilever the second derivative of thefirst Eigen vector showed good accuracy. Plane StressBracket and Plane strain Dam: The comparisonbetween the first order and second order approachesfollow the same pattern as the previous studies forthese two case studies also.Large modifications of frequencies can be conductedvery efficiently with an acceptable level of accuracy.It was found that the proposed model always yieldsthe exact Eigen frequencies with minimized
  • 5. R.J.V. Anil Kumar, Dr Y.Venkata Mohana Reddy, Dr. K.Prahlada Rao / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1453-14591457 | P a g enumerical effort. Model was more computationallyeconomical and optimization was carried in one stepwith no iterations.In 2003 a review paper by Peter Avitable[23] was presented giving a detailed textualknowledge of SDM. The authors start from the basisof SDM. Inherent problems that are encounteredwhen using these techniques are discussed withexamples. Two approach1) Eigen Value Modification (EM)2) Local Eigen Value Modification Procedure(LEMP)With the Eigen value modification approachonly single modification could be performed. So thiswas replaced by LEMP.The author describes various conditions for StructuralDynamic modification using response functions,rotational DOF, mode shape scaling, rigid bodymodes and damping conditionsA case study on dynamic design of DrillingMachine was done by Rajiv Singh Bais etal [24]Using Direct Method Based Updated F.E. model.Two aspects were studied for modal testing viz testsusing instrumentation impact hammer and randomnoise generator & modal exciter. The updatedanalytical FE models from both studies had been usedfor SDM which predicted a fair degree of accuracy toobtain desired modal frequencies. Results show thatnatural frequencies are close to each other. The modeshape at II mode shows a good level of correlationthan at I, III and IV mode.Along with the above 3 authors A.K.Gupta[25] studied the FE formulation of the drillingmachine. It includes the FE model updating usingdirect and indirect method. In the direct method theresults obtained using FEM were compared with theexperimental ones using mode shape comparison andMAC values. The indirect method is an iterativemethod. The updated FE model closely represents theactual machine tool structure. An improvement isseen in the MAC values over initial MAC values.Both studies predict that effect of modifications onthe dynamic characteristics of the machine with a fairdegree of accuracy and the procedure can be usedwith confidence in order to obtain desired modalfrequencies.Studies on Dynamic Design using updatedmodels and its subsequent use for predicting theeffects of structural modifications were done byS.V.Modak etal [26]. The two methods of modelupdating are:a) Modal updating using constrained optimization(MUCO) and 2) Iterative method or inverse Eigensensitivity Method (IESM) is briefly presented. InMUCO, the error between measured and analyticalnatural frequencies and the mode shapes isminimized.In IESM the updating parametercorresponding to an analytical model are corrected tobring the analytical modal data close to that of theexperimentally derived. Thus is an iterative method.The process is repeated until convergence is obtained.In SDM, the number of finite elements, the number ofnodes and consequently the size of the modifiedmodel will be higher than that for the unmodifiedmodel.Let [Km] and [Mm ] be the stiffness matrixand mass matrix of the modified model. Eigen values[λm] and Eigen vectors [Φm] can be obtained byresolving the Eigen value problem.i.e. [Km] [Φm]= [Mm ] [Φm] [λm]Models like a fixed-fixed beam and Fstructure were considered for updation. Comparisonof natural frequencies before and after modificationshowed that the values are very close to the actualchanges. To improve the correlation the FE model isupdated. First updating is carried out for matchingonly the first five natural frequencies and updating thethree stiffness parameters. It is seen that thecorrelation of the natural frequencies had significantlyimproved. It was also seen that there is a very goodmatch between the updated model FRF and themeasured FRF. For the case of updating usingMUCO, the mode shapes were included in the formof MAC based constraints. The results show that theMUCO updated model had given reasonablepredictions of both the natural frequencies and themode shapes for the case of mass modifications.A beam modification was introduced byattaching stiffener at the end of the horizontalmembers. The MUCO updated model gave goodreasonable predictions of both the natural frequenciesand the mode shapes for this case also.So it was concluded that selection ofupdating parameters during updating was veryimportant for making reliable predictions.Hua Peng Che [28] presented the efficientmethods for determining the modified modalparameters in SDM when the modifications wererelatively large. An efficient iterative computationalprocedure was proposed for determining the modifiedEigen values and corresponding Eigen vectors forcomplex structural systems. The iterative proceduregave exact predictions.relationship for modal updating. A high orderapproximation approach was also presented withoutiterative procedures which gave excellent estimates ofthe modified modal parameters.Brian Schwarz etali [28] presented FEAmodel updating using SDM. This paper gives a verydetailed basic ideas and definitions on SDM, FEA,Modal updating etc. Two examples of beamstructures were considered. In the first example abeam was taken and Modal analysis using FEA(analytical) and EMA (experimental) were performed.The results with FEA were less than its corresponding
  • 6. R.J.V. Anil Kumar, Dr Y.Venkata Mohana Reddy, Dr. K.Prahlada Rao / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1453-14591458 | P a g eEMA values. Next modal updating is done byincreasing the thickness of a back plate. There is aclear improvement in FEA modal frequencies andMAC values show negligible change in mode shapes.In example 2, an aluminum cantilever beam wastaken. FEA and EMA tests were performed andresults tabulated. It is evident that both the modalfrequencies and shape are more closely matchedfollowing model updating.This tool shows much promise for closingthe gap between FEA and EMA results.Experiments on the dynamic characteristicsof a tube collector were conducted using reanalysis byNatasa Trisovic [29]. Reanalysis is a method bywhich the dynamic behavior is brought about byadding modifications like those of lumped masses,rigid links, dampers, beams etc. The study deals withimproving of dynamic characteristics (of the ringcross section) by changing the boundary conditionsand geometry. It was proved that the change ofboundary conditions was the most efficient way toincrease the natural frequencies. The ideal case wouldbe to have both ends of the beam fixed, which wastechnically impossible. Only one fixed end and theother hinged gives improved dynamic characteristics.SDM of vibrating system was studied byM.Nad [30]. The design and technological treatmentswere considered to achieve suitable vibration andacoustical properties of vibrating system. A shortsummary of the structural dynamic modificationtechniques and the general mathematical theory of themodification process was presented. Two case studieswere also dealt viz i) SDM of a cantilever beam bythe constraining visco elastics layers and ii) SDM ofcircular disc by in plane residual stresses.The results obtained confirm that SDM is avery effective tool to change the dynamic propertiesof vibratory system.Very often natural frequencies and modeshapes (i.e. Eigen values and Eigen vectors) of a FEmodel do not match very well with experimentalmeasured frequencies and mode shapes obtained froma real life vibration test. Thus the FE model updatingproblem is how to incorporate the measured modaldata into the FE model to produce an adjusted FEmodel with the modal properties that closely matchthe experimental modal data. Then the updated modelmay be considered to be a better dynamicrepresentation of the structure.Yong Xin Ynan presented a new method forFE model updating problem using minimizationtheory [31] and [32].Two problems in the matrices wereconsidered and theorems were developed. Analgorithm was also generated. There was no iterationor Eigen analysis. The approach is demonstrated by a10 DOF cantilever beam. Numerical results areproduced which are reasonably good.Later Vikas Arora etal [33] studied DampedFE model Updating using Complex UpdatingParameters and its use for dynamic design. Here theF shaped structure which resembles the skeleton of adrilling machine was used to evaluate theeffectiveness of complex parameters based onupdating methods for accurate prediction of thecomplex FRFsThe experimental data is valid and moreaccurate modal updating aims at reducing theinaccuracies present in the analytical model in thelight of measured test data. Surprisingly most of theupdating method neglect damping. But all structuresexhibit some form of damping, but despite a largeliterature on damping, it still remains one of the leastwell understood aspects of general vibration analysis.A model updating method should be able to predictthe changes in dynamic characteristics of the structuredue to potential structural modifications.The results of the complex parameter basedupdating were compared with FE model updatingwith damping identification method and also thecomplex FRFs were also predicted.The FRFs for the mass modified structure were thenacquired. It was observed that the predicted dynamiccharacteristics of complex parameter based updatedmodel are closer to the measured characteristics of themodified structure even at resonance and antiresonance frequencies.A beam modification increased the size ofmass and stiffness matrices. The mass and stiffnessmatrices for the modified structure were obtainedassuming there was a little effect of the beammodification. The dynamic characteristics predictedby complex parameters based on updated model werecloser to the measured characteristics of the modifiedstructure. It was noticed that:i) Complex parameter method was able to predictmore accurately,ii) Predicted FRFs for mass modification matchedbetter than beam modification andiii) Complex parameter based updated model could beused for dynamic design.V. Conclusion:Thus critical review on the StructuralDynamic Modification Techniques is done in thispaper. The SDM for the beam structures isconcentrated implementing it in various applications.All through the review the variables or parametersthat are accounted for SDM are lumped masses,springs, viscous dampers, dynamic absorbers andstiffening rods. Though a lot of work is carried in thearea of SDM, but research on the structures withdamping is much awaited.References:[1] Bo Ping Wang, Structural Dynamic Modificationusing Modal Analysis Data, pp 42-45, 1980
  • 7. R.J.V. Anil Kumar, Dr Y.Venkata Mohana Reddy, Dr. K.Prahlada Rao / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1453-14591459 | P a g e[2] Bo Ping Wang, G.Clark, F.H.Chu, TheLimitation of Local SDM, pp 53-55, 1980.[3] Fabrizo Pinazzi And Luciana Ricciardiello, TheEffect Of Structural Variations On The DynamicBehaviour Of A System, Computers & Structure,Vol. 20. No. 4, pp. 659-667, 1985.[4] J. A.Brandon, K. Sadeghipour and A. Cowley,Exact Reanalysis Techniques For Predicting TheEffects Of Modification On The DynamicBehaviour Of Structures, Their Potential AndLimitations, Int. J. Mach. Tools Manufac!. Vol.28. No.4. pp.351-357. 1988.[5] A. Sestieri And W. Dambrogio, A ModificationMethod For Vibration Control Of Structures,Mechanical Systems and Signal Processing Vol3(3), pp 229-253, 1989[6] A. Sestieri, SDM variables optimization,Mechanical Systems and Signal Processing, Vol3(3), pp 229-253, 1989.[7] A. Sestieri, SDM Applicatons To Machine ToolsAnd Engines, Mechanical Systems and SignalProcessing, Vol 49(1), pp 53-63, 1990.[8] H.Nevzat Ozguven, Structural ModificationsUsing Frequency Response Systems, Mechanicalsystems & signal processing Vol 49(1), pp 53-63, 1990.[9] Y. M. Ram and J. J. Blech, The DynamicBehaviour Of A Vibratory System AfterModification, Journal of Sound &Vibration, Vol150(3), pp 357-370, 1991.[10] S. Lammens, W. Heylen, And P. Sas, ModelUpdating And Structural Optimisation Of ATennis Racket, Mechanical Systems and SignalProcessing, Vol 6(5), pp 461-468, 1992.[11] R K Srivastava & T. K. Kundra, SDM WithDamped Beam Elements, Computers &Structures, Vol. 48,No. 5, pp. 943-950, 1993.[12] Stanley G. Hutton, Analytical Modification OfStructural Natural Frequencies, Finite Elementsin Analysis and Design, Vol 18, pp 75-81, 1994.[13] S.S.A.Ravi, T.K.Kundra and B.C.Nakra, SingleStep Eigen Perturbation Method for SDM,Mechanics Research Communication, Vol 22, No4, pp 363-369, 1995.[14] A. Sestieri, Structural Dynamic Modification,Mechanical Systems and Signal Processing, Vol3(3), pp 229-253, 1989.[15] T.K.Kundra, Structural Dynamic Modificationsvia models, Proceedings of IUTAM-IITDInternational Winter School on OptimumDynamic Design, pp 169-185, Dec 1997.[16] B.C. Nakra, SDM Using Additive Damping,Proceedings of IUTAM-IITD InternationalWinter School on Optimum Dynamic Design, pp187-204, Dec 1997.[17] Nobuyaki Okubo and Takeshi Toi, SensitivityAnalysis and its applications for dynamicimprovement, Mechanical Systems and SignalProcessing, Vol 3(3), pp 229-253, 1989.[18] R.K. 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