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1、Modal Analysis,Module 2,July 22,2004Inventory#0021102-2,Module 2Modal Analysis,A.Define modal analysis and its purpose.B.Discuss associated concepts,terminology,and mode extraction methods.C.Learn how to do a modal analysis in ANSYS.D.Work on one or two modal analysis exercises.,July 22,2004Inventor
2、y#0021102-3,Modal AnalysisA.Definition&Purpose,What is modal analysis?A technique used to determine a structures vibration characteristics:Natural frequenciesMode shapesMode participation factors(how much a given mode participates in a given direction)Most fundamental of all the dynamic analysis typ
3、es.,July 22,2004Inventory#0021102-4,Modal Analysis Definition&Purpose,Benefits of modal analysisAllows the design to avoid resonant vibrations or to vibrate at a specified frequency(speakers,for example).Gives engineers an idea of how the design will respond to different types of dynamic loads.Helps
4、 in calculating solution controls(time steps,etc.)for other dynamic analyses.Recommendation:Because a structures vibration characteristics determine how it responds to any type of dynamic load,always perform a modal analysis first before trying any other dynamic analysis.,July 22,2004Inventory#00211
5、02-5,General equation of motion:Assume free vibrations and ignore damping:Assume harmonic motion(i.e.)The roots of this equation are i2,the eigenvalues,where i ranges from 1 to number of DOF.Corresponding vectors are ui,the eigenvectors.,Modal AnalysisB.Terminology&Concepts,July 22,2004Inventory#002
6、1102-6,Modal Analysis Terminology&Concepts,The square roots of the eigenvalues are wi,the structures natural circular frequencies(radians/sec).Natural frequencies fi are then calculated as fi=wi/2p(cycles/sec).It is the natural frequencies fi that are input by the user and output by ANSYS.The eigenv
7、ectors ui represent the mode shapes-the shape assumed by the structure when vibrating at frequency fi.,July 22,2004Inventory#0021102-7,Modal Analysis Terminology&Concepts(cont.),Mode Extraction is the term used to describe the calculation of eigenvalues and eigenvectors.Mode Expansion has a dual mea
8、ning.For the reduced method,mode expansion means calculating the full mode shapes from the reduced mode shapes.For all other methods,mode expansion simply means writing mode shapes to the results file.,July 22,2004Inventory#0021102-8,Modal Analysis-Terminology&ConceptsMode Extraction Methods,Several
9、 mode extraction methods are available in ANSYS:Block Lanczos(default)SubspacePowerDynamicsReducedUnsymmetricDamped(full)QR DampedWhich method you choose depends primarily on the model size(relative to your computer resources)and the particular application.,July 22,2004Inventory#0021102-9,Modal Anal
10、ysis-Terminology&Concepts Mode Extraction Methods-Block Lanczos,The Block Lanczos method is recommended for most applications.Efficient extraction of large number of modes(40+)in most modelsTypically used in complex models with mixture of solids/shells/beams etc.Efficient extraction of modes in a fr
11、equency range Handles rigid-body modes well,July 22,2004Inventory#0021102-10,Modal Analysis-Terminology&Concepts Mode Extraction Methods-Subspace,When extracting a small number of modes(40)in similar size models,the subspace method can be more suitable.Requires relatively less memory but large disks
12、paceMay have convergence problems when rigid body modes are present.Not recommended when constraint equations are present.Generally superseded by Block Lanczos,July 22,2004Inventory#0021102-11,Modal Analysis-Terminology&Concepts Mode Extraction Methods-PowerDynamics,For large(100K+DOF)models and a s
13、mall number of modes(20),use the PowerDynamics method.It can be significantly faster than Block Lanczos or Subspace,but:Requires large amount of memory.May not converge with poorly shaped elements or an ill-conditioned matrix.May miss modes(No Sturm sequence check)Recommended only as a last resort f
14、or large models.,July 22,2004Inventory#0021102-12,Modal Analysis-Terminology&Concepts Mode Extraction Methods-Reduced,For models in which lumping mass does not create a local oscillation,typically beams and spars,use the Reduced method.Memory and disk requirements are low.In general fastest eigen so
15、lverEmploys matrix reduction,a technique to reduce the size of K and M by selecting a subset of DOF called master DOF.Reduction of K is exact but M loses some accuracyAccuracy of M depends on number and location of master DOF.Generally not recommended due to Expertise required in picking master DOFE
16、fficient alternatives such as Block Lanczosreduced cost of hardware,July 22,2004Inventory#0021102-13,Modal Analysis-Terminology&Concepts Mode Extraction Methods-Unsymmetric,The unsymmetric method is used for acoustics(with structural coupling)and other such applications with unsymmetric K and M.Calc
17、ulates complex eigenvalues and eigenvectors:Real part is the natural frequency.Imaginary part indicates stability-negative means stable,positive means unstable.,July 22,2004Inventory#0021102-14,Modal Analysis-Terminology&Concepts Mode Extraction Methods-Damped,Damping is normally ignored in a modal
18、analysis,but if its effects are significant,the Damped method is used.Typical application is rotor dynamics,where gyroscopic damping effects are important.Two ANSYS elements,BEAM4 and PIPE16,allow gyroscopic effects to be specified in the form of real constant SPIN(rotational speed,radians/time).Cal
19、culates complex eigenvalues and eigenvectors:Imaginary part is the natural frequency.Real part indicates stability-negative means stable,positive means unstable.,July 22,2004Inventory#0021102-15,Modal Analysis-Terminology&Concepts Mode Extraction Methods-Q-R damped,A second mode extraction method th
20、at considers damping effects is the Q-R Damped method.Faster and more stable than the existing Damped SolverWorks with poorly conditioned models All forms of damping allowed including damper elements Combines the best features of the real eigensolution method(Block Lanczos)and the Complex Hessenberg
21、 method(QR Algorithm)Outputs complex eigenvalues(frequency and stability)and damping ratio of each modeSupports the use of a material dependent damping ratio MP,DMPR in a subsequent mode superposition harmonic analysis,July 22,2004Inventory#0021102-16,Modal Analysis-Terminology&Concepts Mode Extract
22、ion Methods-Q-R damped,MODOPT,QRDAMP,NMODE,July 22,2004Inventory#0021102-17,Modal Analysis-Terminology&Concepts Mode Extraction Methods-Q-R damped,Comparison Demonstrating the Superior Solution Performance of the QR Damped Mode Extraction Method,July 22,2004Inventory#0021102-18,Modal Analysis-Termin
23、ology&ConceptsSummary for symmetric,undamped solvers,July 22,2004Inventory#0021102-19,Modal AnalysisC.Procedure,Four main steps in a modal analysis:Build the modelChoose analysis type and optionsApply boundary conditions and solveReview results,July 22,2004Inventory#0021102-20,Modal Analysis Procedu
24、reBuild the Model,Remember density!Linear elements and materials only.Nonlinearities are ignored.See also Modeling Considerations in Module 1.,July 22,2004Inventory#0021102-21,Modal Analysis ProcedureChoose Analysis Type&Options,Build the modelChoose analysis type and optionsEnter Solution and choos
25、e modal analysis.Mode extraction options*Mode expansion options*Other options*Discussed next,July 22,2004Inventory#0021102-22,Modal Analysis Procedure Choose Analysis Type&Options,Mode extraction optionsMethod:Block Lanczos recommended for most applications.Number of modes:Must be specified(except R
26、educed method).Frequency range:Defaults to entire range,but can be limited to a desired range(FREQB to FREQE).Specification of a frequency range requires additional factorizations and it is typically faster to simply request a number of modes which will overlap the desired range.Normalization:Discus
27、sed next.,defaults to 1e8,July 22,2004Inventory#0021102-23,Modal Analysis Procedure Choose Analysis Type&Options,Normalization of mode shapes:Only the shape of the DOF solution has real meaning.It is therefore customary to normalize them for numerical efficiency or user convenience.Modes are normali
28、zed either to the mass matrix or to a unit matrix(unity).Normalization to mass matrix is the default,and is required for a spectrum analysis or if a subsequent mode superposition analysis is planned.Choose normalization to unity when you want to easily compare relative values of displacements throug
29、hout the structure.Modes normalized to unity cannot be used in subsequent mode superposition analyses(transient,harmonic,spectrum or random vibration),July 22,2004Inventory#0021102-24,Modal Analysis Procedure Choose Analysis Type&Options,Mode expansion:You need to expand mode shapes if you want to d
30、o any of the following:Have element stresses calculated.Do a subsequent spectrum or mode superposition analysis.,July 22,2004Inventory#0021102-25,Modal Analysis Procedure Choose Analysis Type&Options,Mode expansion(continued):Recommendation:Always expand as many modes as the number extracted.The cos
31、t of this is minimal.,July 22,2004Inventory#0021102-26,Modal Analysis Procedure Choose Analysis Type&Options,Other analysis options:Lumped mass matrixMainly used for slender beams and thin shells,or for wave propagation problems.Automatically chosen for PowerDynamics method.Pre-stress effectsFor Pre
32、-stressed modal analysis(discussed later).Full dampingUsed only if Damped mode extraction method is chosen.Damping ratio,alpha damping,and beta damping are allowed.BEAM4 and PIPE16 also allow gyroscopic damping.QR dampingAll types of damping are allowed.,July 22,2004Inventory#0021102-27,Modal Analys
33、is ProcedureApply BCs and Solve,Build the modelChoose analysis type and optionsApply boundary conditions and solveDisplacement constraints:Discussed next.External loads:Ignored since free vibrations are assumed.However,ANSYS creates a load vector which you can use in a subsequent mode superposition
34、analysis.Solve:Discussed next.,July 22,2004Inventory#0021102-28,Modal Analysis Procedure Apply BCs and Solve,Displacement constraints:Apply as necessary,to simulate actual fixity.Rigid body modes will be calculated in directions not constrained.Non-zero displacements are not allowed.,July 22,2004Inv
35、entory#0021102-29,Modal Analysis Procedure.Apply BCs and Solve,Displacement constraints(continued):Be careful with symmetrySymmetry BCs will only produce symmetrically shaped modes,so some modes can be missed.,Full Model,July 22,2004Inventory#0021102-30,Modal Analysis Procedure Apply BCs and Solve,D
36、isplacement constraints(continued):For the plate-with-hole model,the lowest non-zero mode for the full and the quarter-symmetry case is shown below.The 53-Hz mode was missed by the anti-symmetry case because ROTX is non-zero along the symmetry boundaries.,July 22,2004Inventory#0021102-31,Modal Analy
37、sis Procedure Apply BCs and Solve,Solve:Typically one load step.Multiple load steps can be used to study the effect of different displacement constraints(symmetry BC in one load step and anti-symmetry BC in another,for example).,July 22,2004Inventory#0021102-32,Modal Analysis ProcedureReview Results
38、,Build the modelChoose analysis type and optionsApply boundary conditions and solveReview results using POST1,the general postprocessorList natural frequenciesView mode shapesReview participation factorsReview modal stresses,July 22,2004Inventory#0021102-33,Modal Analysis Procedure Review Results,Li
39、sting natural frequencies:Choose“Read Results By Pick”in the General Postproc menu.Notice that each mode is stored in a separate substep.,July 22,2004Inventory#0021102-34,Modal Analysis Procedure Review Results,Viewing mode shapes:First read in results for the desired mode using First Set,Next Set,o
40、r By Load Step.Then plot the deformed shape:General Postproc Plot Results Deformed ShapeNotice that the graphics legend shows mode number(SUB=)and the frequency(FREQ=).,July 22,2004Inventory#0021102-35,Modal Analysis Procedure Review Results,Viewing mode shapes(continued):You can also animate the mo
41、de shape:Utility Menu PlotCtrls Animate Mode Shape.,July 22,2004Inventory#0021102-36,Modal Analysis Procedure Review Results,Participation Factors:Calculated for each mode in global translation and rotation directionsHigh value in a direction indicates that the mode will be excited by forces in that
42、 directionValues are relative based on a unit displacement spectrumThe final participation factor value(ROTZ)can be retrieved into a parameter using*GET command.A spectrum analysis with a specified direction(SED,0,1,0)could be used to obtain other valuesAlso printed out(to the output file)is the eff
43、ective mass.Ideally the sum of the effective masses in each direction should equal total mass of structureEffective Mass=(participation factor)2,July 22,2004Inventory#0021102-37,Modal Analysis Procedure Review Results,Modal stresses:Available if element stress calculation is activated when choosing
44、analysis options.Stress values have no real meaning,however these can be used to highlight hot spotsIf mode shapes are normalized to unity,you can compare stresses at different points for a given mode shape,July 22,2004Inventory#0021102-38,Modal Analysis Procedure Review Results,Mode shapes normaliz
45、ed to unity,July 22,2004Inventory#0021102-39,Modal AnalysisProcedure,Build the modelChoose analysis type and optionsApply boundary conditions and solveReview results,July 22,2004Inventory#0021102-40,D.Workshop-Modal Analysis,This workshop consists of two problems:1.Modal analysis of a plate with a h
46、ole A step-by-step description of how to do the analysis.You may choose to run this problem yourself,or your instructor may show it as a demonstration.Follow the instructions in your Dynamics Workshop supplement(WS2:Modal Analysis-Plate with a Hole,Page WS-17).2.Modal analysis of a model airplane wingThis is left as an exercise to you.Follow the instructions in your Dynamics Workshop supplement(WS3:Modal Analysis-Model Airplane Wing,Page WS-23).,
