Modal Analysis

Modal AnalysisModal/Harmonic Analysis Using ANSYSANSYS TutorialgUsed to determine the natural frequencies andmode shapes of a continuous structureSlides to accompany lectures inVibro-Acoustic Design in Mechanical Systems 2012 by D. W. HerrinDepartment of Mechanical EngineeringUniversity of KentuckyLexington, KY 40506-0503Tel: 859-218-0609dherrin@engr.uky.eduDept. of Mechanical EngineeringUniversity of KentuckyReview of Multi DOF SystemsModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSx1F1[M ]{u } [C]{u } [K ]{u} {F}x2K2M1F2K3M2gC1C2C3Expressed in matrix form asg[M ]{u } [C]{u } [K ]{u} {F}Dept. of Mechanical EngineeringUniversity of Kentuckygggg3ME 510/499 VibroAcoustic DesignThe mass, damping and stiffness matrices areconstant with timeThe unknown nodal displacements vary withtimeDept. of Mechanical EngineeringUniversity of Kentucky4ME 510/499 VibroAcoustic DesignModal AnalysisModal AnalysisModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSA continuous structure has an infinite number ofdegrees of freedomgThe finite element method approximates thereal structure with a finite number of DOFsN mode shapes can be found for a FEM havingN DOFsgModal Analysisü ME 510/499 VibroAcoustic DesignReview of Multi DOF SystemsK1g2Process for determining the N natural frequencies andmode shapesDept. of Mechanical EngineeringUniversity of Kentucky5ME 510/499 VibroAcoustic DesignGiven “suitable” initial conditions, the structurewill vibrateü at one of its natural frequenciesü the shape of the vibration will be a scalarmultiple of a mode shapeGiven “arbitrary” initial conditions, the resultingvibration will be aü Superposition of mode shapesDept. of Mechanical EngineeringUniversity of Kentucky6ME 510/499 VibroAcoustic Design1

ggModal AnalysisMode Shape of a Thin Plate (240 Hz)Modal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSDetermines the vibration characteristics (naturalfrequencies and mode shapes) of a structuralcomponentsNatural frequencies and mode shapes are astarting point for a transient or harmonicanalysisü If using the mode superposition methodDept. of Mechanical EngineeringUniversity of KentuckyME 510/499 VibroAcoustic Design7Dept. of Mechanical EngineeringUniversity of KentuckyMode Extraction MethodsSubspacegBlock LanczosgPowerDynamicsgReducedgUnsymmetricgDamped and QR damped (Include damping)Modal/Harmonic Analysis Using ANSYSggDept. of Mechanical EngineeringUniversity of KentuckyME 510/499 VibroAcoustic Design9ME 510/499 VibroAcoustic DesignSteps in Modal AnalysisModal/Harmonic Analysis Using ANSYSg8gBuild the modelü Same as for static analysisü Use top-down or bottom-up techniquesApply loads and obtain solutionü Only valid loads are zero-value displacementconstraintsü Other loads can be specified but are ignoredExpand the modes and review resultsDept. of Mechanical EngineeringUniversity of Kentucky10ME 510/499 VibroAcoustic DesignIn-Class ExerciseIn-Class ExerciseModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSE 30E6 psib 43 inh 5 in2 lb s ρ 8.031E 4 3 in in gggSet element type to BEAM188Set the appropriate material constants andsection propertiesCreate Keypoints at the start and end of thebeam and a Line between them360 inchesDept. of Mechanical EngineeringUniversity of Kentucky11ME 510/499 VibroAcoustic DesignDept. of Mechanical EngineeringUniversity of Kentucky12ME 510/499 VibroAcoustic Design2

Create Three KeypointsCreate Lines Between KeypointsModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSPreprocessor Modeling - Create Keypoints InActive CSg Enter the following values for keypoint 1 Enter the following values for keypoint 2 NPT 1, x 0, y 0 z 0 Apply Preprocessor Modeling - Create Lines Straight Lineg Select KP 1 and 2 in graphics window NPT 2, x 180, y 0 z 0 Apply Select KP 2 and 3 in graphics windowEnter the following values for keypoint 3 Okay NPT 3, x 360, y 0 z 0 Apply Okay Dept. of Mechanical EngineeringUniversity of KentuckyME 510/499 VibroAcoustic DesignMesh the Lines to Create ElementsMesh the Line and Apply B.C.sModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSPreprocessor Meshing - Size Controls Lines All Lines ggDept. of Mechanical EngineeringUniversity of KentuckyME 510/499 VibroAcoustic Design Size 5 Okay Fix the Keypoint at the right end of the beamgPreprocessor Meshing - Mesh Lines Pick All Okay Dept. of Mechanical EngineeringUniversity of KentuckyggME 510/499 VibroAcoustic DesignDept. of Mechanical EngineeringUniversity of Kentucky16ME 510/499 VibroAcoustic DesignSet Solution OptionsSet Solution OptionsModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSChange the analysis type to Modalü Solution Analysis Type New Analysisü Modal Set the analysis optionsü Solution Analysis Optionsü Extract 10 mode OK ü Enter 1500 for the ending frequencyDept. of Mechanical EngineeringUniversity of Kentucky17ME 510/499 VibroAcoustic DesigngAt this point, you have told ANSYS to find aparticular quantity of modes and to look within aparticular frequency range. If ANSYS finds thatquantity before it finishes the frequency range,it will stop the search. If ANSYS does not findthat quantity before finishing the frequencyrange, then it will stop the search.Dept. of Mechanical EngineeringUniversity of Kentucky18ME 510/499 VibroAcoustic Design3

Set Solution OptionsPostprocessingModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSgggSolve the load setü ANSYS generates a substep result for eachnatural frequency and mode shapeDept. of Mechanical EngineeringUniversity of KentuckyList results summary19ME 510/499 VibroAcoustic DesigngGeneral Postproc List Results ResultsSummaryRead results for a substepü General Postproc Read Results First Setü Plot deformed geometryü General Postproc Read Results Next Setü Plot deformed geometryDept. of Mechanical EngineeringUniversity of Kentucky20ME 510/499 VibroAcoustic DesignHarmonic Response AnalysisHarmonic Response AnalysisModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSSolves the time-dependent equations of motionfor linear structures undergoing steady-statevibrationgAnalyses can generate plots of displacementamplitudes at given points in the structure as afunction of forcing frequencygAll loads and displacements vary sinusoidally atthe same frequencygFi F sin(ωt φ1 )Fj F sin(ωt φ2 )Dept. of Mechanical EngineeringUniversity of Kentucky21ME 510/499 VibroAcoustic DesignDept. of Mechanical EngineeringUniversity of KentuckyForced ResponseForced ResponseModal/Harmonic Analysis Using ANSYSApply a 1.0 N load at the left end of the beamgNew Analysis HarmonicgSet the Analysis OptionsgSolution Load Step Opts – Time Frequency Freq and SubstepsSet the solution method to “Mode Superposition”Set the DOF printout format to “Amplitude andphase” OK Set the number of modes to 10 OK Dept. of Mechanical EngineeringUniversity of Kentucky23Set the frequency substepsü ü ü ME 510/499 VibroAcoustic DesignModal/Harmonic Analysis Using ANSYSgü 22ME 510/499 VibroAcoustic DesignSet the Harmonic Frequency Range tobetween 0 and 50 Hzü ü Set the number of substeps to 100ü Set to SteppedDept. of Mechanical EngineeringUniversity of Kentucky24ME 510/499 VibroAcoustic Design4

gForced ResponseExpansion PassModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSFinishSolution Analysis Type Expansion Pass Set the dampingSolution Load Step Opts – Time Frequency Dampingü ü gSet the Constant Damping Ratio to 0.01Solve the modelDept. of Mechanical EngineeringUniversity of KentuckyDept. of Mechanical EngineeringUniversity of KentuckyME 510/499 VibroAcoustic Design25ME 510/499 VibroAcoustic DesignForced ResponseExpansion Pass SetupModal/Harmonic Analysis Using ANSYSSolution Load Step Opts Expansion Pass Single Expand Range of Solu’s10026Modal/Harmonic Analysis Using ANSYSgEnter time history postprocessor Define Variables Important – if yes the files are huge50Define NewVariablesGraphVariablesList Variables andprint out to fileSolution Solve Current LSDept. of Mechanical EngineeringUniversity of Kentucky2728ME 510/499 VibroAcoustic DesignCreate NodesAdd Vertical Truss MemberModal/Harmonic Analysis Using ANSYSModal/Harmonic Analysis Using ANSYSPreprocessor Modeling - Create Nodes In ActiveCSg Dept. of Mechanical EngineeringUniversity of KentuckyME 510/499 VibroAcoustic DesigngEnter the following values for Node 1 NPT 1, x 180, y -10 z 0 Apply gPreprocessor Element type Add/Edit/Delete Add Okay Select Link 180 Close Preprocessor Real Constants Add/Edit/Delete Add Okay to select type 1 Enter the values Okay A 10 in2Dept. of Mechanical EngineeringUniversity of KentuckyME 510/499 VibroAcoustic DesignDept. of Mechanical EngineeringUniversity of Kentucky30ME 510/499 VibroAcoustic Design5

Set Element AttributesModal/Harmonic Analysis Using ANSYSgModeling Create Elements Elem Attributes Select appropriate material properties and real constant tablePreprocessor Modeling - Create Elements Auto-Numbered-ThruNodesg Select appropriate nodes and applyDept. of Mechanical EngineeringUniversity of Kentucky31ME 510/499 VibroAcoustic Design6

Modal/Harmonic Analysis Using ANSYS ME 510/499 Vibro-Acoustic Design Dept. of Mechanical Engineering University of Kentucky Modal Analysis g Determines the vibration characteristics (natura l frequencies and mode shapes) of a structural components g Natural frequencies and mode shapes are a starting point for a transient or harmonic analysis !