1、SECTION 11FREQUENCY RESPONSE ANALYSIS TABLE OF CONTENTSPageINTRODUCTION TO FREQUENCY RESPONSE ANALYSIS11-3DIRECT FREQUENCY RESPONSE 11-6DAMPING IN DIRECT FREQUENCY RESPONSE11-10CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATE11-12WORKSHOP 5 - DIRECT FREQUENCY RESPONSE OF A PLATE11-33EXCITATION DEFI

2、NITION 11-34THE RLOAD1 ENTRY11-37THE RLOAD2 ENTRY 11-41FREQUENCY RESPONSE CONSIDERATIONS11-46SOLUTION FREQUENCIES11-48 MENDATIONS11-88MODAL FREQUENCY RESPONSE11-90DAMPING IN MODAL FREQUENCY RESPONSE11-96MODE TRUNCATION IN FREQUENCY RESPONSE11-106MODAL VS DIRECT FREQUENCY RESPONSE11-110WORKSHOP 16 -

3、MODAL FREQUENCY RESPONSE OF A CAR11-111INTERPRETING FREQUENCY RESPONSE IN PATRAN11-112INTRODUCTION TO FREQUENCY RESPONSE ANALYSISFrequency response analysis is a method used to compute structural response to steady-state oscillatory excitation. Examples of oscillatory excitation include rotating mac

4、hinery, unbalanced tires, and helicopter blades. In frequency response analysis the excitation is explicitly defined in the frequency domain. All of the applied forces are known at each forcing frequency. Forces can be in the form of applied forces and/or enforced motions (displacements, velocities,

5、 or accelerations).INTRODUCTION TO FREQUENCY RESPONSE ANALYSIS (Cont.)Oscillatory loading is sinusoidal in nature.In its simplest case, this loading is defined as having an amplitude at a specific frequency. The steady-state oscillatory response occurs at the same frequency as the loading. The respo

6、nse may be shifted in time due to damping in the system. The shift in response is called a phase shift because the peak loading and peak response no longer occur at the same time. INTRODUCTION TO FREQUENCY RESPONSE ANALYSIS (Cont.)The important results obtained from a frequency response analysis usu

7、ally include the displacements, velocities, and accelerations of grid points as well as the forces and stresses of elements.The computed responses are complex numbers defined as magnitude and phase (with respect to the applied force) or as real and imaginary components, which are vector components o

8、f the response in the real/imaginary plane. DIRECT FREQUENCY RESPONSEIn the previous section on Transient Analysis two solution methods were described, Modal and Direct.The same two methods apply for Frequency Response Analysis.Look first at Direct Frequency ResponseDIRECT FREQUENCY RESPONSE (Cont.)

9、In direct frequency response analysis, structural response is computed at discrete excitation frequencies by solving a set of coupled matrix equations using complex algebra.Begin with the damped forced vibration equation of motion with harmonic excitation-w 2M + iw B+Ku(w )=P(w )The load in the abov

10、e equation is introduced as a complex vector, which is convenient for the mathematical solution of the problem.From a physical point of view, the load can be real or imaginary, or both. The same interpretation is used for response quantities.DIRECT FREQUENCY RESPONSE (Cont.)For harmonic motion (whic

11、h is the basis of a frequency response analysis), assume a harmonic solution of the form:u(w ) = f x(w ) eiw tWhere u(w ) is a complex displacement vector. Damping will be neglected temporarily, and u(w ) can be substituted into the vibration equation. Finally, the equation can be simplified by divi

12、ding out eiw t.-w 2 M f x(w ) + K f x(w ) = P(w)DIRECT FREQUENCY RESPONSE (Cont.)The equation of motion is solved by inserting the forcing frequency into the equation of motion. This expression represents a system of equations with complex coefficients if damping is included or the applied loads hav

13、e phase angles. The equations of motion at each input frequency are then solved in a manner similar to a statics problem using complex arithmetic.DAMPING IN DIRECT FREQUENCY RESPONSEDamping in direct frequency response is represented by the damping matrix and additions to the stiffness matrix.The da

14、mping matrix is comprised of several matricesB = B1 + B2where:B1 = damping elements (CVISC, CDAMPi, CBUSH) and B2GG.B2 = B2PP direct input matrix and transfer functions.DAMPING IN DIRECT FREQUENCY RESPONSE (Cont.)In frequency response, PARAM,G and GE on the MATi entry do not form a damping matrix. I

15、nstead, they form the following complex stiffness matrix: K = (1 + iG)K + iSGEKEwhere:K = global stiffness matrixG = overall structural damping coefficient (PARAM,G)KE= element stiffness matrixGE= element structural damping coefficient (GE on the MATi entry)When the above parameters and/or coefficie

16、nts are specified, they are automatically incorporated into the stiffness matrix and therefore into the equation of motion for the solution.All of the forms of damping can be used in the same analysis, and their effects are added together.In frequency response analysis, it is not necessary to assume

17、 an equivalent viscous form for structural damping since the solution is complex. Therefore, a complex stiffness matrix is allowed.CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATECASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATEProblem DescriptionUsing the Direct Method, determine the frequency res

18、ponse of the flat rectangular plate created in Workshop 1a. This example structure is excited by a unit load at a corner of the tip. Use a frequency step of 20 Hz between a range of 20 and 1000 Hz. Use structural damping of g = 0.06.Below is a finite element representation of the flat plate. It also

19、 contains the loads and boundary constraints.CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATEFirst consider the loading definitions and how to set these up in PatranThe Point Load vs. Frequency is set up via a Non-Spatial field in PatranThe variation of Load vs. Frequency is conveniently defined us

20、ing a tabular function rather than a PCL function, as input is simply a constant functionCASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATECreate a Non Spatial field for the force load.Fields: Create / Non Spatial / Tabular Input.Enter frequency_dependent_load for the Field Name.Select Frequency (f)

21、as the Active Independent Variable.Click Input Data.Enter the values showed in the table.Click OK.Click Apply.1234567CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATEInspect the field using an X-Y plot.Fields: ShowSelect the field from the list. Click Input Data.Click Apply.123CASE STUDY - DIRECT FR

22、EQUENCY RESPONSE OF A PLATE1234567Create a Time Dependent load case.Load Cases: CreateEnter direct_freq_response for the Load Case Name.Select Time Dependent as the Load Case Type.Click Assign/Prioritize Loads/ BCs.Click on the Displ_constraint in the Select Individual Loads/BCS field.Click OK.Click

23、 Apply.CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATECreate the time dependent Force load. Loads/BCs: Create / Force / Nodal. Enter unit_load for the New Set Name.Click on the Input Data button.Enter for Force, and select frequency_dependent_load for the Time/Freq. Dependent Field.Click OK.12345C

24、ASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATECreate the time dependent Force load (cont.)Click on Select Application Region.Change the Geometry Filter to FEM.Select the bottom right corner node for the application region.Click Add, and click OK.Click Apply.12345CASE STUDY - DIRECT FREQUENCY RESPO

25、NSE OF A PLATEConcerning Load CasesMSC.Patran automatically puts newly created loads in the Current Load Case.When the Time/Frequency Dependent load case was created, the Make Current checkbox automatically set the Active Load Case, and the newly created load is automatically added to this Load Case

26、.Users should always try to keep track of which Load Case is set as the Active Load Case.CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATESelect the solution type as a Frequency Response Analysis and define the overall parametersAnalysis Method is DirectLumped Mass MethodParam,wtmass is .00259 (weig

27、ht density is used in the model and converted to mass density)Overall Structural damping Coefficient of 0.06 is used (as this is a direct method, there are no cost implications of using the Structural method of damping)CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATEaaaSubmit the model for analysis

28、 Analysis: Analyze / Entire Model / Full Run (cont.)Click on the Solution Type button.The Solution Type is Frequency Response.The Formulation is Direct.2431CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATEaaaSubmit the model for analysis (cont.)Click on the Solution Parameters button to set the over

29、all parameters for the Analysis.Param,wtmass is .00259 (weight density is used in the model and converted to mass density)Overall Structural Damping Coefficient of 0.06 is used (as this is a direct method, there are no cost implications of using the Structural method of damping)231CASE STUDY - DIREC

30、T FREQUENCY RESPONSE OF A PLATECreate a Subcase and setup parameters for itSelect the Load Case previously definedDefine the Frequencies, for which we want to calculate a response for, as 20 Hz to 1000 Hz with 49 even incrementsSince a direct method is being used, an adaptive technique to calculate

31、the ideal response frequencies cannot be used.(more on this later in the section)How is this frequency range acquired?The problem specification required a frequency range of 20 Hz to 1000 Hz in increments of 20 HzThe first frequency is defined as 20 Hz on the input formThe last frequency is defined

32、as 1000 HzAn increment of 49 defines 20 Hz stepsCASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATESubmit the model for analysis (cont.) Click on Subcases. Select direct_freq_response from the Available Subcases field. 21CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATE2134567Submit the model for anal

33、ysis (cont.) Click on Subcase Parameters.Click on DEFINE FREQUENCIES button.Enter the data according to the table.Click OK.Click OK.Click Apply.Click Cancel.CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATESubmit the model for analysis (cont.)Click on Subcase Select.Select direct_freq_response and u

34、nselect Default.Click OK.Click Apply.2134CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATEAttach the XDB result file. Analysis: Access Results / Attach XDB / Result Entities.Click on Select Result File.Select ws5.xdb.Click OK.Click Apply.21345CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATECreate a

35、 X-Y graph of displacement results.Results: Create / Graph / Y vs X.Click on SC1:DIRECT_FREQ_RESPONSE.Select Global Variable as the Filter Method.Click Filter.Click Apply.Click Close.213456CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATECreate a X-Y graph of displacement results.Select Displacement

36、, Translational for the Select Y Result fieldSelect Z Component as the Quantity.Click on the Target Entities icon.Change the Target Entity selection to Nodes.Select the node where the force is applied.Click Apply.213456CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATECreate a X-Y graph of displaceme

37、nt results (cont.)Click on Display Attribute.Change Y Axis Scale from Linear to Log.Click on Plot Option.Change the Complex No. as to Magnitude.Click Apply.21345CASE STUDY - DIRECT FREQUENCY RESPONSE OF A PLATEClearly it is visible that the true peaks have been missed because a standard spread of re

38、sponse points.This is a very important point in Frequency Response analysis and we will discuss how to improve the results later.Please now carry out Workshop 5 in the Workshop Section to allow you to set up this model and carry out the analysis.The workshop will take you through step by step if you

39、 are unfamiliar with MSC.Nastran or MSC.Patran.If you have some experience, then try to set up the analysis without referring to the step by step guide.Please feel free to ask your tutor for help.WORKSHOP 5 - DIRECT FREQUENCY RESPONSE OF A PLATEEXCITATION DEFINITIONDefine force as a function of freq

40、uency.Several methods in MSC.Nastran:RLOAD1 (defines frequency-dependent load in real and imaginary forms)RLOAD2 (defines frequency-dependent load in magnitude and phase forms)DLOAD Bulk Data entries are used to combine frequency-dependent forces.RLOADi entries are selected by DLOAD Case Control com

41、mands.The rules are the same as for creating transient loading.EXCITATION DEFINITION (Cont.)Define force as a function of frequency.Three entry options are possible in Patran and are translated to Nastran formatsMagnitude Phase (degrees) RLOAD2Magnitude Phase (radians) RLOAD2Real Imaginary RLOAD1EXC

42、ITATION DEFINITION (Cont.)A Complex Scalar Field Type is chosenThe options are chosen via the Complex Data FormatHere choose mag/phase in degrees abTHE RLOAD1 ENTRYDefines a frequency dynamic load of the form:P(f) = AC(f) + iD(f) eiq - 2pftfor use in frequency response analysis.Example:12345678910RL

43、OAD1SIDEXCITEIDDELAYDPHASETCTDTYPERLOAD1531THE RLOAD1 ENTRY (Cont.)Field Contents:SID: Set identification number. (Integer 0)EXCITEID: Identification number of the DAREA or SPCD entry set that defines A. (Integer 0)DELAY: Identification number of the DELAY entry set that defined t. (Integer 0)DPHASE

44、: Identification number of the DPHASE entry set that defines q. (Integer 0)TC: Set identification number of the TABLEDi entry that gives C(f). (Integer 0)TD: Set identification number of the TABLEDi entry that gives D(f). (Integer 0)TYPE: Defines the type of dynamic excitation.THE RLOAD1 ENTRY (Cont

45、.)Remarks:Dynamic excitation sets must be selected with the Case Control command DLOAD = SID.If any of DELAY, DPHASE, TC, or TD fields are blank or zero, the corresponding t, q, C(f) or D(f) will both be zero. Either TC or TD may be blank or zero, but not both.RLOAD1 excitations may be combined with

46、 RLOAD2 excitations only by specification on a DLOAD entry. That is, the SID on a RLOAD1 entry must not be the same as that on a RLOAD2 entry.SID must be unique for all RLOAD1, RLOAD2, TLOAD1, TLOAD2, and ACSRCE entries.The type of the dynamic excitation is specified by TYPE (field 8) according to t

47、he following table:TypeType of Dynamic Excitation0, L, LO, LOA, or LOADApplied load (force or moment) (Default)1, D, DI, DIS, DISPEnforced displacement using SPC/SPCD data2, V, VE, VEL, or VELOEnforced velocity using SPC/SPCD data3, A, AC, ACC, or ACCEEnforced acceleration using SPC/SPCD dataTHE RLO

48、AD1 ENTRY (Cont.)Remarks (cont.)TYPE (field 8) also determines the manner in which EXCITEID (field 3) is used by the program as described below:Excitation specified by TYPE is applied loadThere is no LOADSET request in Case ControlEXCITEID may also reference DAREA, static and thermal load set entrie

49、s.There is a LOADSET request in Case ControlThe program may also reference static and thermal load set entries specified by the LID or TID field in the selected LSEQ entries corresponding to the EXCITEID.Excitation specified by TYPE is enforced motionThere is no LOADSET request in Case Control EXCIT

50、EID will reference SPCD entries.EXCITEID will reference SPCD entries.There is a LOADSET request in Case ControlThe program will reference SPCD entries specified by the LID field in the selected LSEQ entries corresponding to the EXCITEID.THE RLOAD2 ENTRYDefines a frequency dynamic load of the form:P(

51、f) = A * B(f) e if(f) + q - 2pftfor use in frequency response analysis.Example:12345678910RLOAD2SIDEXCITEIDDELAYDPHASETBTPTYPERLOAD2537THE RLOAD2 ENTRY (Cont.)Field Contents:SID: Set identification number. (Integer 0)EXCITEID: Identification number of the DAREA or SPCD entry set that defines A. (Int

52、eger 0)DELAY: Identification number of the DELAY entry set that defined t. (Integer 0)DPHASE: Identification number of the DPHASE entry set that defines q in degrees. (Integer 0)TB: Set identification number of the TABLEDi entry that gives B(f). (Integer 0)TP: Set identification number of the TABLED

53、i entry that gives f(f). (Integer 0)TYPE: Defines the type of dynamic excitation.THE RLOAD2 ENTRY (Cont.)Remarks:Dynamic excitation sets must be selected with the Case Control command DLOAD = SID.If any of DELAY, DPHASE, or TP fields are blank or zero, the corresponding t, , or f(f) will be zero.RLO

54、AD2 excitations may be combined with RLOAD1 excitations only by specification on a DLOAD entry. That is, the SID on a RLOAD2 entry must not be the same as that on a RLOAD1 entry.SID must be unique for all RLOAD1, RLOAD2, TLOAD1, TLOAD2, and ACSRCE entries.The type of the dynamic excitation is specif

55、ied by TYPE (field 8) according to the following table:TypeType of Dynamic Excitation0, L, LO, LOA, or LOADApplied load (force or moment) (Default)1, D, DI, DIS, DISPEnforced displacement using SPC/SPCD data2, V, VE, VEL, or VELOEnforced velocity using SPC/SPCD data3, A, AC, ACC, or ACCEEnforced acc

56、eleration using SPC/SPCD dataTHE RLOAD2 CARD (Cont.)Remarks (cont.):TYPE (field 8) also determines the manner in which EXCITEID (field 3) is used by the program as described below:Excitation specified by TYPE is applied loadThere is no LOADSET request in Case ControlEXCITEID may also reference DAREA

57、, static and thermal load set entries.There is a LOADSET request in Case ControlThe program may also reference static and thermal load set entries specified by the LID or TID field in the selected LSEQ entries corresponding to the EXCITEID.Excitation specified by TYPE is enforced motionThere is no L

58、OADSET request in Case ControlEXCITEID will reference SPCD entries.There is a LOADSET request in Case ControlThe program will reference SPCD entries specified by the LID field in the selected LSEQ entries corresponding to the EXCITEID.Alternatively for NAS2004, the LSEQ entry can be ignored as in th

59、e example on the next page.The DLOAD in Case Control calls the DLOAD in the Bulk Data Section.The DLOAD in Bulk Data calls the RLOAD1 cardThe RLOAD1 card calls the FORCE and TABLED1 cards.THE RLOADi CARD (Cont.)SUBCASE 1$ Subcase name : direct_freq_response SUBTITLE=direct_freq_response FREQUENCY =

60、1 SPC = 2 DLOAD = 2 DISPLACEMENT(SORT1,REAL)=ALL SPCFORCES(SORT1,REAL)=ALL$ Direct Text Input for this SubcaseBEGIN BULKRLOAD1 4 3 1DLOAD 2 1. 1. 4 $ Nodal Forces of Load Set : unit_loadFORCE 3 11 0 1. 0. 0. 1.$ Referenced Dynamic Load Tables$ Dynamic Load Table : frequency_depend_loadTABLED1 1 20.