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Challenges in HighChallenges in High

Frequency VibrationFrequency Vibration

DesignDesign

Kulkarni Satish S.Kulkarni Satish S.Sr. Lecturer, Textile and Engineering Institute,Sr. Lecturer, Textile and Engineering Institute,Ichalkaranji 416115. INDIAIchalkaranji 416115. INDIA

kulsat@indiatimes.comkulsat@indiatimes.com

Dr. Padte J. C.Dr. Padte J. C.Director, FIE Research Institute, IchalkaranjiDirector, FIE Research Institute, Ichalkaranji416115. INDIA416115. INDIA

International Conference onResource Utilization and Intelligent

Systems

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Topics for DiscussionTopics for Discussion

Why Vibration Design?Why Vibration Design?

Present TrendsPresent Trends Deterministic TechniquesDeterministic Techniques

Modal AnalysisModal Analysis

Domain DecompositionDomain Decomposition

Energy Finite Element MethodEnergy Finite Element Method

Probabilistic TechniquesProbabilistic Techniques

Statistical Energy AnalysisStatistical Energy Analysis

ComparisonComparison

Challenges at High FrequencyChallenges at High FrequencyVibration DesignVibration Design

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Modal AnalysisModal Analysis

Modal TestingModal Testing

Finite Element Model UpdatingFinite Element Model Updating Co-relation techniquesCo-relation techniques

Structural Dynamic ModificatioStructural Dynamic Modificatio

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Description of Structure Response Levels

Description of StructureResponse Levels

Vibration Modes Vibration Modes

Spatial Model

SpatialModel

ModalModel

ModalModel

ResponseModel

ResponseModel

Routes of Modal Analysis

Mass, Stiffness,Damping

Frequency/ImpulseResponse

NaturalFrequency, Mode

Shapes

Experimental Modal

Analysis

Analytical Modal

Analysis

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Co-relation techniquesCo-relation techniques

Orthogonality CheckOrthogonality Check

single indicator for coupled errors inthe analytical model development, the

reduction of the analytical model and

the estimated modal vectors and was

not best approach

Modal Assurance CriteriaModal Assurance Criteria To provide a measure of consistency

(degree of linearity) between

estimates of a modal vector.

Interpretation of MACInterpretation of MAC

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Modal Assurance CriteriaModal Assurance Criteria

Interpretation of MACInterpretation of MAC MAC UnityMAC Unity((the modal vectors are consistent.)

The modal vectors have been incompletelymeasured.

The modal vectors are the result of a

forced excitation other than the desiredinput.

The modal vectors are primarily coherentnoise.

The modal vectors represent the samemodal vector with different arbitrary

scaling.

MAC Zero (MAC Zero (modal vectors are not consistent.)

The system is non-stationary.

There is noise on the reference modalvector.

The modal parameter estimation is invalid.

The modal vectors are from linearlyunrelated mode shape

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Finite Element Model

Updating

Sources of Error in FE Model

Nature and Distribution of damping in theStructure cannot be obtained theoretically

Accurate stiffness and damping modeling of

joints in complex structure

Type of mesh and Nature of finite element and

Co-ordinates of interest in FE model

Basic SDM Approach Orthogonality check- Comparison of

measured mode shapes with theoretical mass

Adjustments of measured mode shapes

Adjustments of Theoretical Stiffness Matrices

System Error matrices

Inverse Mass and Stiffness

Mass and Stiffness

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Structural DynamicStructural Dynamic

ModificationModificationORIGINALTATE

MODIFIED STATE

Modification

OriginalMass, Stiffness ModifiedMass, Stiffness

OriginalModes

Change in Mass Stiffness

ModifiedModes

ModalTrans

formations

ModalTrans

formations

Change in Modal Displacements

Physical Space

N Physical DOF

Modal Space

M Modal DOF

N

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Other DeterministicOther Deterministic

TechniquesTechniques

Domain DecompositionDomain Decomposition Component Mode Synthesis (CMS)Component Mode Synthesis (CMS)

Craig Bampton DecompositionCraig Bampton Decomposition

Automated Multilevel Sub structuringAutomated Multilevel Sub structuringMethod (AMLS)Method (AMLS)

Energy Finite Element MethodEnergy Finite Element Method It predicts mechanical energy basedIt predicts mechanical energy based

on energy equilibrium equationson energy equilibrium equations able to model local effects like localable to model local effects like local

damping and localized power inputdamping and localized power input

Analysis of these components can beAnalysis of these components can be

obtained by existing FE codes ofobtained by existing FE codes ofthermal analysis.thermal analysis.

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Statistical EnergyStatistical Energy

AnalysisAnalysis

System 1E1

System 2E2

owernjected

PowerDissipated

owernjected

PowerFlow

Between

Systems

PowerDissipated

Two System SEA ModelTwo System SEA Model

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Terminologies Used in SEATerminologies Used in SEA

Modal DensityModal Density Minimum 3 to 4 modes in one third octaveMinimum 3 to 4 modes in one third octavebandband

Input PowerInput Power Dissipation of EnergyDissipation of Energy

Coupling Loss FactorCoupling Loss Factor Sub System (SS)Sub System (SS)

Group of similar energy storage modesGroup of similar energy storage modes(Flexural, Torsional acoustic cavities etc.)(Flexural, Torsional acoustic cavities etc.)

Assumption for SSAssumption for SS

Effect of boundary conditions on SS is small.Effect of boundary conditions on SS is small.This implies that number of modes in givenThis implies that number of modes in givenfrequency band to be high.frequency band to be high.

Response doesnt vary largely over SS. ThisResponse doesnt vary largely over SS. Thisimplies that the damping in the system shouldimplies that the damping in the system shouldbe low and that the response of the system isbe low and that the response of the system isreverberant.reverberant.

Modes are randomly distributed over a range ofModes are randomly distributed over a range ofanalysis.analysis.

System contains equal energy at all frequencySystem contains equal energy at all frequencybands.bands.

Energy is stored in response of SS.Energy is stored in response of SS.

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ComparisonComparison

Deterministic TechniquesDeterministic Techniques

Experimental Modal AnalysisExperimental Modal Analysis

Co-relation and MACCo-relation and MAC

Structural Dynamic ModificationStructural Dynamic Modification

Analytical Deterministic TechniqueAnalytical Deterministic Technique

Probabilistic TechniquesProbabilistic Techniques

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Comparison :ExperimentalComparison :Experimental

Modal AnalysisModal Analysis

State of art instrumentationState of art instrumentation

and Analysis Softwares areand Analysis Softwares areavailableavailable

Unable to adjust theUnable to adjust theexperimental conditions withexperimental conditions with

that of Application.that of Application. Proper selection of sensorProper selection of sensor

locations and measuringlocations and measuringinstruments is needed forinstruments is needed for

avoiding loading effect ofavoiding loading effect ofsensors.sensors.

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Co-relation and MACCo-relation and MAC

validation of experimental results,validation of experimental results,correlation of analytical modelcorrelation of analytical modelwith experimental models, modalwith experimental models, modalvector error analysisvector error analysis

Misuse of MACMisuse of MACThe MAC is not an orthogonalityThe MAC is not an orthogonality

check.check.

The wrong mathematicalThe wrong mathematical

formulation for the MAC is used.formulation for the MAC is used.The MAC is sensitive to largeThe MAC is sensitive to large

values (wild points?) andvalues (wild points?) andinsensitive to small values.insensitive to small values.

The number of elements in theThe number of elements in the

modal vectors (space) is small.modal vectors (space) is small.The modal vectors have beenThe modal vectors have been

zero padded.zero padded.

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Comparison: StructuralComparison: Structural

Dynamic ModificationDynamic Modification Truncation of modes. Modal databaseTruncation of modes. Modal database

contain only few lower order modes.contain only few lower order modes.

Lack of rotational DOF for manyLack of rotational DOF for many

modifications that involve rotational DOF.modifications that involve rotational DOF.Even today, techniques available toEven today, techniques available tomeasure rotational DOF are costly andmeasure rotational DOF are costly andare unable to guarantee exactness of theare unable to guarantee exactness of theresults. Analytical approaches like splineresults. Analytical approaches like splinefits of measured data; analyticalfits of measured data; analytical

representations of curvature etc are usedrepresentations of curvature etc are usedas a substitute.as a substitute.

Rigid body modes are not included inRigid body modes are not included inmodal data. These are required to definemodal data. These are required to definethe inertial characteristics of thethe inertial characteristics of thecomponent.component.

Incorrect mode shape scaling. TheIncorrect mode shape scaling. Theprojected changes to the system in modalprojected changes to the system in modalspace will be directly affected due to this.space will be directly affected due to this.

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Comparison: AnalyticalComparison: Analytical

Deterministic TechniquesDeterministic Techniques

Suitable at low frequency.Suitable at low frequency. At high frequencyAt high frequency

element size is small and timeelement size is small and timerequired for analysis is prohibitivelyrequired for analysis is prohibitivelylarge.large.

modes are closely spaced and modemodes are closely spaced and mode

separation is not possibleseparation is not possible number of modes increases withnumber of modes increases with

frequency and hence analysis isfrequency and hence analysis isunable to provide any practicalunable to provide any practicalinformationinformation

structures are more sensitive tostructures are more sensitive tostructural modificationsstructural modifications

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Comparison: ProbabilisticComparison: Probabilistic

TechniquesTechniques

can handle large number of modes at onecan handle large number of modes at onetime and able to give practical resultstime and able to give practical results

regarding spatial variations of certainregarding spatial variations of certainparameters over wide frequency band.parameters over wide frequency band.

describe the system in much simpler waydescribe the system in much simpler way unable to give variation of them within theunable to give variation of them within the

elementelement

the local data is lostthe local data is lost useful for structures with low value ofuseful for structures with low value of

dampingdamping

required mode density is high and hencerequired mode density is high and hence

it is not useful at low frequency.it is not useful at low frequency.

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Challenges at HighChallenges at High

Frequency VibrationFrequency Vibration

AnalysisAnalysis Estimation of variability and confidenceEstimation of variability and confidence

intervals of SEA predictions andintervals of SEA predictions andparameters.parameters.

Study of transient behavior using SEA.Study of transient behavior using SEA.

Integration of FEA, SEA and EnergyIntegration of FEA, SEA and EnergyFlow Models.Flow Models.

To develop techniques to estimate SEATo develop techniques to estimate SEA

parameters in efficient and optimalparameters in efficient and optimalmanner from FE models.manner from FE models.

To develop experimental methods toTo develop experimental methods toestimate SEA parameters.estimate SEA parameters.

To develop SEA/Energy Flow Models forTo develop SEA/Energy Flow Models for

assembled structures.assembled structures. Estimation of parameters for uncertainEstimation of parameters for uncertain

structures.structures.

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