Modal AnalysisAdvanced TopicsModule 8

Module 8Modal Analysis - Advanced TopicsA. Learn how to do a prestressed modal analysisB. Learn how to take advantage of cyclic symmetry in a modal analysisC. Learn how to perform a modal analysis following a large deflection static analysis

A. Prestressed Modal AnalysisWhat is prestressed modal analysis and why?Modal analysis of a prestressed structure.Some structures show different dynamic behavior depending on their stress state.A guitar string or a drum head, for example, will vibrate at higher frequencies as its tension is increased.When a turbine blade spins, its natural frequencies tend to be higher because of the prestress caused by centrifugal forces.To properly design such structures, both stress-free and prestressed modal analyses may be required.

Prestressed Modal Analysis ProcedureThree main steps:Build the modelPrestress the model with a static analysisDo the modal analysis with prestressBuild the Model:Same considerations as a normal modal analysis.Remember to specify density with proper units.

Prestressed Modal Analysis ProcedureBuild the model

Priestess the model with a static analysisChoose analysis type & options: Be sure to activate prestress effects.Loading: Apply the loads causing the prestress.Postprocessing: Review the results to make sure that the proper loads have been applied.Solution > Unabridged Menu Solution > Analysis Type > Analysis Options

Prestressed Modal Analysis ProcedureElement Plot - Static Analysis of Prestressed ModalStress Plot - Static Analysis of Prestressed Modal

Prestressed Modal Analysis ProcedureBuild the modelPre-stress the model with a static analysis

Do the modal analysis with prestressSame procedure as a normal modal analysis except that prestress effects must be included when specifying analysis options.

Prestressed Modal Analysis ProcedureCompare:Prestressed plateWithout prestress

Prestressed Modal Analysis ProcedureBuild the modelPrestress the model with a static analysisDo the modal analysis with Pre-stress

B. WorkshopIn this workshop, you will Pre-stress the disc shown below and then determine its natural frequencies. If time permits, determine the natural frequencies and mode shapes of the disc without any Pre-stress and compare the results.See your Dynamics Workshop supplement for details (Pre-stressed Modal Analysis Workshop - Pre-Stressed Disc, Page W-61.).

C. Modal Cyclic SymmetryWhat is modal cyclic symmetry?A modal analysis that takes advantage of cyclic symmetry.You can model only one sector, then view mode shapes of the entire structure!Saves modeling time - no need to model all 360 degrees.Saves computer time and disk space - fewer elements and DOF.

ApplicationsAny structure that is cyclically symmetric: turbines, impellers, rotors, fans, etc.

Modal Cyclic Symmetry ProcedureSix main steps:Model the basic sectorIdentify cyclic symmetry planesAutomatic via CYCLIC commandManually by creating node componentsApply BCsSpecify modal analysis type and optionsSpecify cyclic solution options via CYCOPT command and solve using ANSYS SOLVE commandReview results by expanding to 360 degrees via /CYCEXPAND

Modal Cyclic SymmetryModel the Basic SectorBasic sectorMust be in a global or user-defined cylindrical system: X radial, Y along , Z axial.Cyclic symmetry planes (or edges):Node patterns can be matched or unmatched, but matched may provide more accurate solution.Can be curved.The sector angle modeled, , can be any number as long as the total number of sectors (360/) is an integer.

Modal Cyclic SymmetryIdentify Cyclic Symmetry PlanesModel the basic sector

Identify cyclic symmetry planes:Automatic Procedure:Issue the CYCLIC command to detect:the number of sectorsthe sector anglecyclic coordinate systemcyclic boundariesManual Procedure:Select nodes along the lowest angle.Create a component of nodes: Utility Menu > Select > Comp/Assembly > Create ComponentSelect nodes along the highest angle.Create a component of nodes: Utility Menu > Select > Comp/Assembly > Create ComponentIssue CYCLIC command specifying all fieldsBe sure to select everything when done!Components:DISC_M01LDISC_M01H

Modal Cyclic SymmetryApply BCsModel the basic sectorIdentify cyclic symmetry planes

Apply BCs:Mainly displacement constraints.Apply on nodes only, not on solid model entities (since the second sector contains only nodes and elements).Select nodes by location, not by numbers.No need to specify symmetry BC (unless you are doing a static analysis for prestress).

Modal Cyclic SymmetrySpecify Analysis Type & OptionsModel the basic sectorIdentify cyclic symmetry planesApply BCs

Specify analysis type Analysis Type ModalOptions:Block Lanczos method is recommended.Number of modes extracted (NMODE) is per nodal diameter (explained later).Expand as many modes as the number extracted.Main Menu > Solution > Analysis Type > New Analysis

Modal Cyclic SymmetrySolve using ANSYS SOLVE commandModel the basic sectorIdentify cyclic symmetry planesApply BCsSpecify analysis type & options

Specify cyclic options and solve using ANSYS SOLVE command:Issue CYCOPT,hindex, command to specify which harmonic indices to solve for. The default is to solve all applicable harmonic indices.Menu path is:Solution > Solve > Current LS

Modal Cyclic Symmetry Solve Nodal diameterA diametric line of zero displacement during vibration for a circular membrane (like a COSINE wave).Provides relationship to compute mode shape of entire model from the basic sector results.One nodal diameter typically causes one wave around the circumference , two nodal diameters cause two waves, and so on.Each nodal diameter has multiple modes of vibration.

Modal Cyclic Symmetry SolveOne nodal diameterNotice one diametric line of zero displacement in the UZ contour plot below. An end view of the mode shape is shown on the right.

Modal Cyclic Symmetry SolveTwo nodal diameters

Modal Cyclic Symmetry SolveThree nodal diameters

Modal Cyclic Symmetry SolveFour nodal diameters

Modal Cyclic Symmetry SolveZero nodal diameters (axisymmetric mode)

Modal Cyclic Symmetry SolveWhy is the harmonic index range important?For each harmonic index ANSYS will extract a specified number of modes.The user controls the range of harmonic indices for each of which modes are extracted. Minimum harmonic index number is 0 ( breathing mode).Maximum harmonic index value is (NSECTOR/2) for even number of sectors or ( NSECTOR-1)/2 for odd number number of sectors.Usually, the first few modes are extracted for the whole range of harmonic indices to cover all the low frequency modes.

Modal Cyclic Symmetry SolveThe relationship between the harmonic index k and nodal diameter d for a model consisting of N sectors is:The following table shows how the harmonic index, nodal diameter and number of sectors relate to one another:

Modal Cyclic SymmetryReview Results over 360Model the basic sectorIdentify cyclic symmetry planesApply BCsSpecify analysis type & optionsSpecify cyclic options and solve using ANSYS SOLVE command

Review results over 360Use the General Postprocessor (POST1).Four main steps:List frequencies.Issue /CYCEXPAND,,ON commandRead in results for the desired mode.Plot and animate the mode shape.

Modal Cyclic Symmetry Review ResultsList frequencies:General Postproc > Read Results > By PickEach harmonic index is stored as a separate load step.Harmonic index 0, modes 1-5Harmonic index 1, modes 1-5Harmonic index 2, modes 1-5Harmonic index 3, modes 1-5Harmonic index 4, modes 1-5

Modal Cyclic Symmetry Review ResultsType the command /CYCEXPAND,,ON. ( General Postproc > Cyclic Analysis > Cyc Expansion )All displays will now be graphically expanded to a full 360 image.

Read in results for the desired mode, using the SET command or By Load StepHarmonic index. LSTEP=1 means harmonic index 0 in this case.Mode number

Modal Cyclic Symmetry Review ResultsAnimate the mode shapePlotCtrls > Animate > Mode Shape...Harmonic Index 0

Modal Cyclic Symmetry Review ResultsHarmonic Index 1

Modal Cyclic Symmetry Review ResultsHarmonic Index 2

Modal Cyclic Symmetry Review ResultsHarmonic Index 3

Modal Cyclic Symmetry Review ResultsHarmonic Index 4

Modal Cyclic Symmetry Review ResultsCompare cyclic symmetry and full solutions:Frequencies match well.Notice that the lower modes are the first few modes for each harmonic index.538 elements and 1790 active DOF vs. 2690 elements and 17900 active DOF.The symmetry model requires less than half the CP time for solution.Results file size: 1.34 MB vs. 4.16 MB.36 Symmetry ModelFull 360 Model

Modal Cyclic SymmetryD. WorkshopIn this workshop, you will model one tooth of the spiral bevel gear shown to determine its natural frequencies.See your Dynamics Workshop supplement for details.Modal Cyclic Symmetry Workshop - Spiral Bevel Gear, Page W-67.

E. Large Deflection Modal AnalysisWhat is large deflection modal analysis?Modal analysis of a structure that has undergone significant geometry change due to loads.Some applications includeWhen pressure or spin load is applied to a relatively thin turbine blade, it tends to untwist the airfoil affecting natural frequency.Undersea pipeline installations where contact with seabed causes change in frequencies.Membranes under pressure load.

Large Deflection Modal AnalysisWhat is the difference between large deflection modal analysis and prestressed modal analysis?Prestressed modal assumes that stresses will affect the natural frequencies but deflections are small; that is the geometry has not changed.Large deflection modal assumes that the geometry is changing significantly due to deformation and that this updated geometry (in addition to the stress) will change the natural frequencies and mode shapes.Contact and large deflection

Large Deflection Modal Analysis ProcedureFive main steps:Build the modelRun static analysis with large deflection effects turned onUpdate geometry to the deformed geometryPerform modal analysis using partial solve proceduresReview resultsBuild the Model:Same considerations as a normal modal analysis.Remember to specify density with proper units.

Large Deflection Modal AnalysisRun Static AnalysisBuild the model

Run Static analysis Choose analysis type & options: Be sure to activate both prestress and large deflection effects.Loading: Apply the static loads. Follow guidelines from Chapter 8 , Structural Analysis GuideSolveSolution > Unabridged Menu Solution > Analysis Type > Analysis Options

Large Deflection Modal AnalysisUpdate Geometry to deformed shapeBuild the modelRun static analysis with large deflection effectsUpdate geometryAdd displacements from static analysis to the original geometry.This creates the new geometry on which modal analysis will be carried out.

Large Deflection Modal AnalysisPerform modal analysisBuild the modelRun static analysis with large deflection effectsUpdate geometry to the deformed geometry

Perform modal analysis using partial solve proceduresStep 1. Analysis type and optionsStep 2. Triangularize the matrix ( PSOLVE,TRIANG)Step 3. Compute eigenvalues ( PSOLVE,EIGLANB)Step 4. Expand mode shapes ( PSOLVE,EIGEXP)

Large Deflection Modal Analysis Perform Modal AnalysisStep 1. Analysis type and optionsSet analysis type to ModalSelect mode extraction method ( Block Lanczos recommended)Select the number of modes to extract

Large Deflection Modal Analysis Perform Modal AnalysisStep 2. Triangularize the matrix (PSOLVE,TRIANG)Solution > Solve > Partial Solu

Large Deflection Modal Analysis Perform Modal AnalysisStep 3. Compute eigenvalues (PSOLVE,EIGLANB)

Large Deflection Modal Analysis Perform Modal AnalysisStep 4. Expand mode shapes This is done as a separate pass (issue FINISH and get back into Solution)Turn expansion key ON

Large Deflection Modal Analysis Perform modal analysisStep 4. Expand mode shapes (continued)Select how many modes to expand

Large Deflection Modal Analysis Perform modal analysisStep 4. Expand mode shapes (continued)Perform partial solution to expand modes

At this point the user will have a standard modal analysis results file.

Large Deflection Modal AnalysisReview resultsMode 4, Frequency= 585.631 HzMode 2, Frequency = 151.584 HzMode 6 , Frequency=881.08 Hz

Large Deflection Modal Analysis Review results Large deflection modal analysisThe mode shapes are based on deformed geometry.You should remember that nonlinearities are ignored and contact elements retain their initial status at the start of the modal analysis. For instance , only modes where the beams are in contact with each other will be extracted in the example used in this chapter.With contact elements sliding motion may be allowed depending on the value of coefficient of friction used.Use Rough Contact (keyopt(12)=1) to prevent sliding motion.

Typical commands:/PREP7ET,...MP,EX,...MP,DENS,

! Geometry

! Mesh

Typical commands:/SOLUANTYPE,STATIC! Static analysisPSTRES,ON! Activate Pre-stress effects

! Loading...

! SolutionSOLVE

! Results/POST1PLDISP,2PLNSOL,S,EQVFINISHTypical commands:/SOLUANTYPE,MODALMODOPT,MXPAND,PSTRES,ONSOLVE

Typical Commands/POST1SET,LISTSET,1,n! n is the mode numberPLDISP,2FINISHTypical commands:/PREP7ET,MP,EX,MP,DENS,

! GeometryCSYS,1

! Mesh

Typical commands:NSEL,! Select one symmetry planeCM,name,NODE! name is the component nameNSEL,ALL! Select all nodes

Typical commands:ALLSELCYCGENTypical commands:/SOLUANTYPE,MODALMODOPT,LANB,5,,, ,,,2! 5 modes, accurate Lagrange methodMXPAND,5

Typical commands:CYCSOL,0,4,10,ND0! Nodal diameters 0-4, 10 total sectors, component ND0FINISHTypical commands:/POST1SET,LIST

Typical commands:EXPAND,10! If a 36-degree sector was modeledSET,1,2! Nodal diameter 0, mode 2

Typical commands:ANMODE,10,0.05

Typical commands:/PREP7ET,...MP,EX,...MP,DENS,

! Geometry

! Mesh