awb120_dynamics_04_spectrum

1、Chapter 4:Response SpectrumANSYS MechanicalDynamicsANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-1July 2009Inventory #002666Response Spectrum AnalysisTraining ManualTopics covered: Definition and purpose Overview of Workbench capabilities ProcedureANSYS, Inc. Proprietary 2009 ANSYS,

2、 Inc. All rights reserved.4-2July 2009Inventory #002666Response Spectrum AnalysisDescription & PurposeTraining ManualA response-spectrum analysis calculates the maximum response of a structure to a transient loading.It is performed as a fast alternative of approximating a full transient solution.The

3、 maximum response is computed as scale factor times the mode shape.These maximum responses are then combined to give a total response of the structure.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-3July 2009Inventory #002666Response Spectrum AnalysisTypes of AnalysesTraining ManualT

4、ypes of Response Spectrum analysis: Single-point response spectrum A single response spectrum excites all specified points in the model. Multi-point response spectrumDifferent response spectra excite different points in the model.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-4July 2

5、009Inventory #002666Response Spectrum AnalysisCommon UsesTraining ManualCommonly used in the analysis of:Nuclear power plant buildings and components, for seismic loadingAirborne Electronic equipment for shock loadingCommercial buildings in earthquake zonesANSYS, Inc. Proprietary 2009 ANSYS, Inc. Al

6、l rights reserved.4-5July 2009Inventory #002666Response Spectrum AnalysisTerminology & ConceptsTraining Manual Instead of simulating the response of a structure to a full time history, we could figure out how each mode would respond to the time history, then combine the responses together. In other

7、words, the response of each mode of a structure is similar to a 1-DOF oscillator, just scaled by some amount. If we know the natural frequencies and mode shapes of a structure, we can simply determine what the displacement would be for a 1-DOF oscillator, if it were subjected to the same transient l

8、oading, and scale the response by the appropriate amount. If there is more than one load, each will have its own spectrum.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-6July 2009Inventory #002666Response Spectrum AnalysisAssumptions & RestrictionsTraining Manual The structure is lin

9、ear (i.e. constant stiffness and mass). For single-point response spectrum analysis, the structure is excited by a spectrum of known direction and frequency components, acting uniformly on all support points. For multi-point response spectrum analysis, the structure may be excited by different input

10、 spectra at different support points.Up to 20 different simultaneous input spectra are allowed.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-7July 2009Inventory #002666TheoryParticipation FactorsTraining ManualA modal analysis must first be completed to determine the natural frequen

11、cies, mode shapes, and participation factors for each mode. This procedure was covered in Chapter 2: Modal Analysis.()- wM +Kf=20iif g=TMDiiANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-8July 2009Inventory #002666modefrequencymode shapeparticipation factor1w1f1g12w2f2g23w3f3g3Theory

12、Spectrum ValuesTraining ManualFor each natural frequency, the spectrum value can be determined by a simple look-up from the response-spectrum table. When values are needed between input frequencies, log-log interpolation is done in the space as defined.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All ri

13、ghts reserved.4-9July 2009Inventory #002666modefrequencymode shapespectrum valueparticipation factor1w1f1S1g12w2f2S2g23w3f3S3g3TheoryMode CoefficientsTraining ManualThe mode coefficients can be determined from the participation factors, depending on the type of spectrum input.displaceme ntvelocityac

14、celerati on= Sig= SigA= S giiAAwwiiiii2iiRecall: participation factors measure the amount of mass moving in each direction for a unit displacement.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-10July 2009Inventory #002666modefrequencymode shapespectrum valueparticipation factormode

15、coefficient1w1f1S1g1A12w2f2S2g2A23w3f3S3g3A3TheoryResponseTraining ManualThe response (displacement, velocity or acceleration) for each mode can then be computed from the frequency, mode coefficient, and mode shape.RiRiAi fiwi Ai fi=for displaceme nt response for veloci ty responsefor accelerati on

16、responseRwA f2iiiiIf there is more than one significant mode, the response for each mode must be combined using some method.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-11July 2009Inventory #002666modefrequencymode shapespectrum valueparticipation factormode coefficientresponse1w1f

17、1S1g1A1R12w2f2S2g2A2R23w3f3S3g3A3R3TheoryMode CombinationTraining Manual In general, mode combinations take the form:12NNR= eijRi Rji=1j =1where R is the total modal response and RiRj is the entrywise product (a.k.a. Hadamard or Schur product) of modes i and j. The modal correlation coefficients, ei

18、j, are uniquely defined, depending on the method chosen for evaluating the correlation coefficient.eij= 1for completely correlated modes i and for partially correlated modes i andfor uncorrelat ed correlated modes i andjj0 eij 1eij= 0j The methods for mode combination are SRSS, CQC, and ROSE.ANSYS,

19、Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-12July 2009Inventory #002666TheoryMode CombinationTraining Manual The SRSS method is generally more conservative than the other methods. assumes that all maximum modal values are uncorrelatedeijeij= 1.0= 0.0for i = jfor i j for a structures wit

20、h coupled modes, this assumption overestimates the responses overall The CQC and the ROSE methods providing a means of evaluating modal correlation for the response spectrum analysis.accounting for mode coupling makes the response estimate from these methods more realistic and closer to the exact ti

21、me history solutionSRSSCQCROSE111222 2NNNNN= =e R= eijRi Rj i=1 j =1RRRkRRiijiji=1i=1 j =1ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-13July 2009Inventory #002666Procedure:Response SpectrumANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-14July 2009Inventory #002666R

22、esponse SpectrumProcedureTraining Manual Drop a Modal (ANSYS) system into the project schematic.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-15July 2009Inventory #002666Response SpectrumProcedureTraining Manual Drop a Response Spectrum system onto the Solution cell of the Modal sys

23、tem.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-16July 2009Inventory #002666Response SpectrumProcedureTraining ManualCreate new geometry, or link to existing geometry.Edit the Model cell to bring up the Mechanical application.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights res

24、erved.4-17July 2009Inventory #002666Response SpectrumPreprocessingTraining ManualVerify materials, connections, and mesh settings.This was covered in Workbench Mechanical Intro.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-18July 2009Inventory #002666Response SpectrumPreprocessingTr

25、aining ManualAdd supports to the model.Displacement constrains must have a magnitude of zero.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-19July 2009Inventory #002666Response SpectrumSolution SettingsTraining ManualChoose the number of modes to extract.If needed, upper and lower bo

26、unds on frequency may be specified to extract the modes within a specified range.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-20July 2009Inventory #002666Response SpectrumPostprocessingTraining ManualReview the modal results before proceeding.ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.4-21July 2009Inventory #002666Response SpectrumPreprocessingTraining Manual Insert an Acceleration, Velocity, or Direction response spectrum. Set the Boundary Condition, Spectrum (Tabular) D