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FRF, FBA and TPA Capability in MD Nastran R2.1

by

Dr. P. R. PamidiPrincipal Development Engineer

Joe MaronickLead Application Engineer

MSC.Software Corporation

MSC N&V SymposiumDetroit, MichiganOctober 10, 2007

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Outline of the FRF, FBA and TPA Capability Description

New NVH Analysis Technique in NastranFRF ConceptFBA ConceptTPA ConceptDistinction Between External Superelement (EXTSEOUT) and FRF Based Approaches for Frequency Response AnalysisAdvantages of FRF Based ApproachFRF/FBA Implementation in MD Nastran R2.1FRF/FBA Usage ProcedureIllustrative ExamplesLimitations of the FBA Process Implementation in MD Nastran R2.1FRF/FBA/TPA Enhancements Planned for Future Releases of MD Nastran

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New NVH Analysis Technique in Nastran

Frequency Response Functions (FRFs) represent responses at desired DOFs of a component due to unit loads at specified DOFs of that componentFRFs can be used to represent componentsFRFs of these components can then be employed for calculating the FRFs of assemblies of such components. This process is referred to as FBA (FRF Based Assembly).FRF/FBA represents an alternative to external superelement (EXTSEOUT) based frequency response analysis.

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New NVH Analysis Technique in Nastran (cont‘d)

The technique also lends itself to tracking load paths or energy flows through a structure. This procedure is referred to as Transfer Path Analysis (TPA).TPA represents an alternative to mode participation studies and is particularly well suited for vibration isolation, N&V mount studies and component design.

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FRF / FBA / TPA Schematic

Single Component FRFs One-shot FRF analysis(eg. mobility studies)

Single componentTPA

Full model or component loads

Multi-component FRFsAssembly or System

FRFs (FBA)

Multi-componentTPA

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FRF ConceptEquation of Motion for Frequency Response Analysis:

(1)where is the dynamic stiffness matrix

Solving for response displacement,(2)

where is the receptance matrix of the system. is also referred to as the FRF (Frequency Response Function) of the system.

Note that the FRF of a system is a function of the forcing frequency . Thus, there is a different FRF for the system for each forcing frequency.

[ ] [ ] [ ]( ){ } [ ]{ } { }PuZuKBiM ==++− ωω 2

{ } [ ] { } [ ]{ }PHPZu == −1

[ ]Z

[ ]H [ ]H

ω

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FRF Concept (cont’d)

The FRF matrix at any forcing frequency represents the response of the system due to unit loads at that frequency.The rows of the FRF matrix represent response DOFs while its columns represent DOFs where unit loads are applied.In practice, the FRF matrix is computed by solving the system for a series of unit loads.The general FRF matrix is square because it assumes that responses are computed at all DOFs and also that unit loads are applied at at all DOFs.In most practical cases, responses are computed at only a subset of the total points in a system and loads are applied to only a small subset of the total DOFs in a system. Thus, in practice, the actual FRF matrix to be considered for analysis purposes is rectangularwhere the number of rows is equal to the number of actual response DOFs and the number of columns is equal to the number of actual excitation DOFs.

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FRF Concept (cont’d)

Definition of FRFs

(Source: “Modal Testing: Theory, Practice and Application,” by D. J. Ewins)

Apparent MassAcceleranceInertance

AccelerationMechanical ImpedanceMobilityVelocity

Dynamic StiffnessReceptanceAdmittance

Dynamic ComplianceDynamic Flexibility

DisplacementInverse FRF: F(orce)/RStandard FRF: R/F(orce)Response Function R

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FBA ConceptThe FRFs of an assembly of components can be computed from the FRFs of the individual components by employing conditions of equilibrium and compatibility at the connected DOFs. This process is referred as FRF Based Assembly (FBA). Some people refer to this as FRF Based Substructuring (FBS).

Displacement Compatibility Condition

Response displacement at a connected DOF must be the same for all components connected at that DOF.

Force Equilibrium Condition

The forces at a connected DOF must be the sum of the forces from all components connected at that DOF.

Using the above two conditions, the FRFs of an assembly of components are computed in Nastran solely from the FRFs of its constituent components and the connection information between and among these components. No other information is needed for the FBA process.

The FBA process assumes that the FRFs of all FRF components are generated at the same forcing frequencies and that these are also the forcing frequencies at which the FBA process is performed.

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TPA ConceptIf the load {P} is specified, then the partial response displacements due to the load on the j-th DOF is given by

(3)

where is the j-th column of the FRF matrix [H]

The total response displacements {u} due to the load {P} is given by

= [H]{P} (4)

The TPA of a component involves the examination of the partial and total response displacements defined above due to the load {P}.

The TPA of an assembly of components involves the examination of the partial and total response displacements for all of the constituent components as well as the computation and examination of the forces between and among the components due to specified loads.

{ } { } jjj HPu =

{ } { } { } jj

n

jj

n

jHPuu

11 ==Σ=Σ=

{ } jH

{ }jujP

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Distinction Between External Superelement (EXTSEOUT) and FRF Based Approaches for Frequency Response

Analysis

Limited connectionsGeneral structureResidualAssembly of the component FRFsAssembly of component boundary

matrices (including those of residual, if any)

Assembly

FRF Case Control commandEXTSEOUT Case Control commandComponent processing trigger

Load path analysis (TPA) and optimization (future)

Mode participation studies and optimization

Analysis goals

For the assembled configuration and for specified output requests of

upstream components

For the assembled configuration and for specified output requests of

upstream components

Data recovery

Computation of the FRFs of the assembly by the FBA process

Frequency response analysis of the assembled system via SOL108 or SOL

111 (preceded by computation of system modes for SOL 111)

Solution

FRFs (via a complete SOL 108 or SOL 111 execution)

Boundary matricesComponent processing results

Component mode synthesis (CMS) may be performed, but it is NOT a

requirement

Component mode synthesis (CMS) is a REQUIREMENT

Component processing procedure

FRF Based ApproachEXTSEOUT Based Approach

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Advantages of FRF Based Approach

Provides an alternative to external superelement (EXTSEOUT) based approach for understanding system dynamic responseCan point to attachments through which energy travels (TPA)Facilitates investigation of the dynamics of coupling between components to understand how to improve isolation

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Advantages of FRF Based Approach (cont’d)

May be an attractive option for repetitive frequency response analyses involving multiple components wherein the time taken for the frequency response calculations represents a significant portion of the total time taken for the calculations

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Advantages of FRF Based Approach (cont’d)

Can be used to attach FE based models with test based models

FE models of certain components may have FRFscomputed analyticallyTest based models of other components may have FRFs determined by testsFRFs of the above components can be combined together to yield FRFs of their assemblies

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FRF/FBA/TPA Implementation in MD Nastran R2.1

Provides an elegant way of computing FRFs of a componentUseful for stand-alone FRF studies like performing mobility analysis

Provides a convenient way of calculating the FRFs of an assembly of components from the FRFs of the individual components (FBA)The above FRF generation and FBA process capabilities are implemented for both Direct Frequency Response Analysis (SOL 108) and Modal Frequency Response Analysis (SOL 111).The above features represent a major enhancement to the dynamic analysis capability in Nastran.

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FRF/FBA Usage Procedure

The procedure involves the following two steps:

Step 1 – FRF GenerationGenerate the FRFs of an one shot configuration or of a component via the use of the FRF Case Control command in SOL 108 or SOL 111

If this involves an one shot configuration, no Step 2 is needed. This is useful for stand-alone FRF studies like performing mobility analysis.Otherwise, the user should define the points at which this FRF component is to be connected with other FRF components in a subsequent FBA processFRFs and other information for the component will be saved on the medium specified by the FRF command (database or OP2 file) and an assembly punch (.asm) file will be generated with a single (new) FRFCOMP Bulk Data entry on it for subsequent use in Step 2.Unit loads - Simple specification via new FRFXIT/FRFXIT1 Bulk Data entries - No need any more for cumbersome specification of unit loads via multiple subcaseswith multiple DLOADs pointing to multiple RLOADi Bulk Data entriesUser defined loads - Specification via the standard DLOAD Case Control command pointing to DLOAD/RLOADi Bulk Data entries

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FRF/FBA Usage Procedure

Step 1 – FRF Generation (cont’d)FRFs are generated for the following points:

All points specified via DISP, VELO or ACCE output requestsAll points associated with elements for which STRESS/FORCE requests are specifiedAll grid points associated with PLOTEL entriesAll points where unit loads / user defined loads are appliedAll connection points

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FRF/FBA Usage Procedure (cont’d)

Step 2 – FBA ProcessCombine the FRFs of the components from Step 1 and compute the FRFs of an assembly of these components using the FBA process via the use of the FRF Case Control command in SOL 108 or SOL 111FRF components to be combined in the FBA process are specified via FRFCOMP Bulk Data entries (resident on the .asm files generated by the FRF generation runs and INCLUDEd in the FBA job)Connections between and among the FRF components are determined automaticallyUnit loads – Already defined by the constituent FRF components User defined loads - Specification via the new FBALOAD, FBADLAY and FBAPHAS Bulk Data entries – These entries essentially define complex scale factors by which the unit load responses will be multiplied in order to get responses to user defined loads

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FRF/FBA Usage Procedure (cont’d)

Alternate Step 2 – FRF Generation of a Component and FBA Process in Same Execution

Generate the FRFs of a component via the use of the FRF Case Control command in SOL 108 or SOL 111 and, in the same execution, combine these FRFs with the FRFs of other components from Step 1 to compute the FRFs of an assembly of these components using the FBA process

This scenario is particularly useful for design iterations or design alternatives involving the last FRF component.

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FRF/FBA Usage Procedure (cont’d)

Results for user defined loads from both FRF and FBA jobsThis is a very powerful feature of the implementation.If the user specifies a dynamic load in a FRF / FBA job (SOL 108 or SOL 111) via a DLOAD Case Control request and the load involves loads on N DOFs in the model, the program automatically generates results for (N+1) load cases. The first N of these load cases represent loads on each of the N DOFsseparately and individually and the (N+1)th load case represents the total applied load. On option, the user can also obtain the output only for the (N+1)th load case.The above scenario is in contrast to standard SOL 108 / SOL 111 jobs wherein the output is generated only for the total applied load, corresponding to the (N+1)th load case mentioned above.The output for user defined loads from FRF / FBA jobs described above is perfectly suited for TPA studies since it allows for the examination of the effects on the response of the system due to loads on individual DOFs as well as due to the total applied load.

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Examples to Illustrate FRF/FBA Implementation in MD Nastran R2.1

Three ExamplesExample 1. A rectangular plateExample 2. A double flyswatter modelExample 3. A trim automobile body and suspension system

All of these models have been analyzed using the FRF/FBA implementation outlined earlierThe results show that the FRFs of the assembled components computed from the FRFs of the individual components match the FRFs of the models computed using a single shot full model analysisThe results establish the validity and correctness of the implementation

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FRF/FBA Example 1Rectangular Plate - Full Model

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FRF/FBA Example 1 (cont’d)Rectangular Plate – 8 FRF Components

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FRF/FBA Example 1 (cont’d) FRF/FBA Results vs Single Shot Results

Displacement at Grid 884(T3) Due to User Load at Grid 812(T3)

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FRF/FBA Example 2Double Flyswatter - Full Model

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FRF/FBA Example 2 (cont’d) Double Flyswatter – 8 FRF Components

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FRF/FBA Example 2 (cont’d) FRF/FBA Results vs Single Shot Results

Displacement at Grid 36(T3) Due to User Load at Grid 104(T3)

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FRF/FBA Example 3Detailed Trim Body (with Acoustic Cavity)

ResponsesAcoustic driver’s earSteer Wheel Ctr X Y Z= 4 response DOFs

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FRF/FBA Example 3 (cont’d)Detailed Trim Body + Suspension System &

Idle Engine Torque Loads

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FRF/FBA Example 3 (cont’d) Detailed Trim Body FRF

• 2 Mdofs• 20 – 300 Hz FRF• 3,300 struct modes to 450 Hz• 150 fluid modes to 600 Hz• 26 attachment points – 6 DOFs each – 156 FRFs• 281 excitation frequencies• 1.4 hrs smp=2 (one-time)

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FRF/FBA Example 3 (cont’d)FRF Assembly Analysis – Suspension System

+ Trim Body FRF

• 156 trim body attachment FRF’s• 4 trim body output resp xformations

• Suspension system FRF internally generated• TB + Suspension FBA analysis (same run)

• Equal & Opposite Engine Torque (user loads)• 12 suspension / tb boundary responses• 4 spindle suspension interior responses• 4 interior TB full user load responses recovered

• 45 minute run (for multiple suspension & mount case studies)

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FRF/FBA Example 3 (cont’d)Driver Ear Acoustic Response

Sound Pressure Level

– Full model acms sol 111– FRF combined model

Frequency (Hz)

dB

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FRF/FBA Example 3 (cont’d)Steering Wheel Vibration

Resultant Velocity

– Full model acms sol 111– FRF combined model

Frequency (Hz)

Velo

city

(mm

/s)

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Limitations of the FBA Process Implementationin MD Nastran R2.1

The FBA process connects a particular grid point in an FRF component with grid points in other FRF components only if such points are coincident (that is, their basic coordinates are the same). There is no provision to allow for connection of scalar points.All connections between and among FRF components are considered as rigid. There is no provision to allow for non-rigid (that is, spring, damper or release) connections.There is no provision to allow for connection of non-coincident grid points.

The above limitations will be removed in future releases of MD Nastran.

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FRF/FBA/TPA Enhancements Planned for Future Releases of MD Nastran

Feature EnhancementsAllow for general (spring, damper or release) connections between and among FRF componentsAllow for connections of scalar points of the FRF componentsAllow for constraining (or grounding) of connection DOFs in the FBA processCompute interface forces (or force transmissibilities) between FRF components

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FRF/FBA/TPA Enhancements Planned for Future Releases of MD Nastran (cont’d)

Feature Enhancements (cont’d)

Support combination of FE based FRF components with test based FRF components in the FBA process

Ability to handle different types of FRF data for FRF components in the FBA processFRF output from FE based FRF components are displacementsFRF output from test based FRF components may be displacements, velocities or accelerations

Handling numerical problems related to “noise” when dealing with test based FRF componentsAbility to interpolate/extrapolate FRFs for different forcing frequenciesNeed more input from customers about their needs and requirements regarding this feature before it can be effectively implemented

Support loads inputFrom testsFrom vehicle dynamics simulations (MD Adams)From user defined load data (to be determined by customer preferences)

Support optimization

Support user-specified FRF “trees” or FRF paths

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FRF/FBA/TPA Enhancements Planned for Future Releases of MD Nastran (cont’d)

TPA Visualization EnhancementsX-Y plots (cumulative, incremental)Bar chartsPolar diagramsEnhancements to Simx/Patran to provide above support

Efficiency and Performance EnhancementsExtend technique to include DMP featureSupport efficient restarts