S11-1 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SECTION 11 FREQUENCY RESPONSE ANALYSIS

S11-2 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation

S11-3 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTRODUCTION TO FREQUENCY RESPONSE ANALYSIS n Frequency response analysis is a method used to compute structural response to steady-state oscillatory excitation. u Examples of oscillatory excitation include rotating machinery, unbalanced tires, and helicopter blades. n In frequency response analysis the excitation is explicitly defined in the frequency domain. u All of the applied forces are known at each forcing frequency. u Forces can be in the form of applied forces and/or enforced motions (displacements, velocities, or accelerations).

S11-4 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTRODUCTION TO FREQUENCY RESPONSE ANALYSIS (Cont.) n Oscillatory loading is sinusoidal in nature. u In its simplest case, this loading is defined as having an amplitude at a specific frequency. u The steady-state oscillatory response occurs at the same frequency as the loading. l The response 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.

S11-5 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTRODUCTION TO FREQUENCY RESPONSE ANALYSIS (Cont.) n The important results obtained from a frequency response analysis usually include the displacements, velocities, and accelerations of grid points as well as the forces and stresses of elements. n 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 of the response in the real/imaginary plane.

S11-6 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DIRECT FREQUENCY RESPONSE n In the previous section on transient analysis two solution methods were described, direct and modal. n The same two methods apply for frequency response analysis. u Look first at direct frequency response

S11-7 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Dynamic equation of motion n Apply two different loadings Multiply the equation for sin t loading by i ( ), and add it to the previous equation n Find a solution of the form DIRECT FREQUENCY RESPONSE (Cont.)

S11-8 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Resulting equation for steady-state amplitude n Write this equation as u It has the form of the equation for linear static analysis. This equation is solved for the steady-state response amplitude, {u( i )}, for a set of excitation frequencies, i. Finding the solution involves determining the inverse of the complex matrix [K( i )] for each excitation frequency. DIRECT FREQUENCY RESPONSE (Cont.) ~

S11-9 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE

S11-10 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Problem Description u Using the Direct Method, determine the frequency response 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 = u Below is a finite element representation of the flat plate. It also contains the loads and boundary constraints. CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-11 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n First consider the loading definitions and how to set these up in Patran u The Point Load vs. Frequency is set up via a Non-Spatial field in Patran u The variation of Load vs. Frequency is conveniently defined using a tabular function rather than a PCL function, as input is simply a constant function CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-12 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Create a Non Spatial field for the force load. 1.Fields: Create / Non Spatial / Tabular Input. 2. Enter frequency_dependent_load for the Field Name. 3. Select Frequency (f) as the Active Independent Variable. 4. Click Input Data. 5. Enter the values showed in the table. 6. Click OK. 7. Click Apply CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-13 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Inspect the field using an X-Y plot. 1.Fields: Show 2. Select the field from the list. Click Input Data. 3. Click Apply CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-14 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Create a Time Dependent load case. 1. Load Cases: Create 2. Enter direct_freq_response for the Load Case Name. 3. Select Time Dependent as the Load Case Type. 4. Click Assign/Prioritize Loads/ BCs. 5. Click on the Displ_constraint in the Select Individual Loads/BCS field. 6. Click OK. 7. Click Apply. CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-15 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Create the time dependent Force load. 1.Loads/BCs: Create / Force / Nodal. 2. Enter unit_load for the New Set Name. 3. Click on the Input Data button. 4. Enter for Force, and select frequency_dependent _load for the Time/Freq. Dependent Field. 5. Click OK CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-16 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Create the time dependent Force load (cont.) 1. Click on Select Application Region. 2. Change the Geometry Filter to FEM. 3. Select the bottom right corner node for the application region. 4. Click Add, and click OK. 5. Click Apply CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-17 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Concerning Load Cases u MSC.Patran automatically puts newly created loads in the Current Load Case. l 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. u 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 SIMPLE PLATE (Cont.)

S11-18 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Select the solution type as Frequency Response Analysis and define the overall parameters u Analysis method is direct u Lumped mass method u PARAM,WTMASS is (weight density is used in the model and converted to mass density) u 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 SIMPLE PLATE (Cont.)

S11-19 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Submit the model for analysis 1.Analysis: Analyze / Entire Model / Full Run (cont.) 2. Click on the Solution Type … button. 3. The Solution Type is Frequency Response. 4. The Formulation is Direct CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-20 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n aaa n Submit the model for analysis (cont.) 1. Click on the Solution Parameters button to set the overall parameters for the Analysis. 2.PARAM,WTMASS is (weight density is used in the model and converted to mass density) 3. 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 SIMPLE PLATE (Cont.)

S11-21 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Create a Subcase and setup parameters for it u Select the Load Case previously defined l Define the Frequencies, for which we want to calculate a response for, as 20 Hz to 1000 Hz with 49 even increments l Since a direct method is being used, an adaptive technique to calculate the ideal response frequencies cannot be used.(more on this later in the section) u How is this frequency range acquired? l The problem specification required a frequency range of 20 Hz to 1000 Hz in increments of 20 Hz l The first frequency is defined as 20 Hz on the input form l The last frequency is defined as 1000 Hz l An increment of 49 defines 20 Hz steps CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-22 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Submit the model for analysis (cont.) 1. Click on Subcases. 2. Select direct_freq_response from the Available Subcases field. 2 1 CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-23 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Submit the model for analysis (cont.) 1. Click on Subcase Parameters. 2. Click on DEFINE FREQUENCIES… button. 3. Enter the data according to the table. 4. Click OK. 5. Click OK. 6. Click Apply. 7. Click Cancel. CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-24 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Submit the model for analysis (cont.) 1. Click on Subcase Select. 2. Select direct_freq_response and unselect Default. 3. Click OK. 4. Click Apply CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-25 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Attach the XDB result file. 1.Analysis: Access Results / Attach XDB / Result Entities. 2. Click on Select Result File. 3. Select ws5.xdb. 4. Click OK. 5. Click Apply CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-26 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Create a X-Y graph of displacement results. 1.Results: Create / Graph / Y vs X. 2. Click on SC1:DIRECT_FREQ_ RESPONSE. 3. Select Global Variable as the Filter Method. 4. Click Filter. 5. Click Apply. 6. Click Close CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-27 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Create a X-Y graph of displacement results. 1. Select Displacement, Translational for the Select Y Result field 2. Select Z Component as the Quantity. 3. Click on the Target Entities icon. 4. Change the Target Entity selection to Nodes. 5. Select the node where the force is applied. 6. Click Apply CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-28 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Create a X-Y graph of displacement results (cont.) 1. Click on Display Attribute. 2. Change Y Axis Scale from Linear to Log. 3. Click on Plot Option. 4. Change the Complex No. as to Magnitude. 5. Click Apply CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-29 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation Clearly it is visible that the true peaks have been missed because a standard spread of response points. This is a very important point in Frequency Response analysis and we will discuss how to improve the results later. CASE STUDY: DIRECT FREQUENCY RESPONSE OF A SIMPLE PLATE (Cont.)

S11-30 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Please now carry out Workshop 5 in the Workshop Section to allow you to set up this model and carry out the analysis. n The workshop will take you through step by step if you are unfamiliar with MSC.Nastran or MSC.Patran. n If you have some experience, then try to set up the analysis without referring to the step by step guide. n Please feel free to ask your tutor for help. WORKSHOP 5 - DIRECT FREQUENCY RESPONSE OF A PLATE

S11-31 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation EXCITATION DEFINITION n Define force as a function of frequency. n Several methods in MSC.Nastran: u RLOAD1 (defines frequency-dependent load in real and imaginary forms) u RLOAD2 (defines frequency-dependent load in magnitude and phase forms) n DLOAD Bulk Data entries are used to combine frequency-dependent forces. n RLOADi entries are selected by DLOAD Case Control commands. n The rules are the same as for creating transient loading.

S11-32 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation EXCITATION DEFINITION (Cont.) n Define force as a function of frequency. n Three entry options are possible in Patran and are translated to Nastran formats u Magnitude – Phase (degrees) – RLOAD2 u Magnitude – Phase (radians) – RLOAD2 u Real – Imaginary – RLOAD1

S11-33 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation EXCITATION DEFINITION (Cont.) n A Complex Scalar Field Type is chosen a.The options are chosen via the Complex Data Format b.Here choose mag/phase in degrees a b

S11-34 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation THE RLOAD1 ENTRY n Defines a frequency dynamic load of the form: { P( f ) } = { A } [C (f) + i D (f) ] e i{ - 2 f } for use in frequency response analysis. Example: RLOAD1SIDEXCITEIDDELAYDPHASETCTDTYPE RLOAD1531

S11-35 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation THE RLOAD1 ENTRY (Cont.) n Field Contents: u SID: Set identification number. (Integer > 0) u 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. (Integer > 0) DPHASE: Identification number of the DPHASE entry set that defines. (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) u TYPE: Defines the type of dynamic excitation.

S11-36 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation THE RLOAD1 ENTRY (Cont.) n Remarks: u 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,, C( f ) or D(f) will both be zero. Either TC or TD may be blank or zero, but not both. u RLOAD1 excitations may be combined with 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. u SID must be unique for all RLOAD1, RLOAD2, TLOAD1, TLOAD2, and ACSRCE (Acoustic Source Specification) entries. u The type of the dynamic excitation is specified by TYPE (field 8) according to the following table: TypeType of Dynamic Excitation 0, L, LO, LOA, or LOADApplied load (force or moment) (Default) 1, D, DI, DIS, DISPEnforced displacement using SPC/SPCD data 2, V, VE, VEL, or VELOEnforced velocity using SPC/SPCD data 3, A, AC, ACC, or ACCEEnforced acceleration using SPC/SPCD data

S11-37 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation THE RLOAD1 ENTRY (Cont.) n Remarks (cont.) u TYPE (field 8) also determines the manner in which EXCITEID (field 3) is used by the program as described below: l Excitation specified by TYPE is applied load n There is no LOADSET request in Case Control u EXCITEID may also reference DAREA, static and thermal load set entries. n There is a LOADSET request in Case Control n The 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. l Excitation specified by TYPE is enforced motion n There is no LOADSET request in Case Control EXCITEID will reference SPCD entries. u EXCITEID will reference SPCD entries. n There is a LOADSET request in Case Control u The program will reference SPCD entries specified by the LID field in the selected LSEQ entries corresponding to the EXCITEID.

S11-38 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation THE RLOAD2 ENTRY n Defines a frequency dynamic load of the form: { P( f ) } = { A } *B (f) e i{ f + 2 f } for use in frequency response analysis. Example: RLOAD2SIDEXCITEIDDELAYDPHASETBTPTYPE RLOAD2537

S11-39 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation THE RLOAD2 ENTRY (Cont.) n Field Contents: u SID: Set identification number. (Integer > 0) u 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. (Integer > 0) DPHASE: Identification number of the DPHASE entry set that defines in degrees. (Integer > 0) TB: Set identification number of the TABLEDi entry that gives B( f ). (Integer > 0) TP: Set identification number of the TABLEDi entry that gives ( f ). (Integer > 0) u TYPE: Defines the type of dynamic excitation.

S11-40 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation THE RLOAD2 ENTRY (Cont.) n Remarks: u 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, θ, or ( f ) will be zero. u RLOAD2 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. u SID must be unique for all RLOAD1, RLOAD2, TLOAD1, TLOAD2, and ACSRCE entries. u The type of the dynamic excitation is specified by TYPE (field 8) according to the following table: TypeType of Dynamic Excitation 0, L, LO, LOA, or LOADApplied load (force or moment) (Default) 1, D, DI, DIS, DISPEnforced displacement using SPC/SPCD data 2, V, VE, VEL, or VELOEnforced velocity using SPC/SPCD data 3, A, AC, ACC, or ACCEEnforced acceleration using SPC/SPCD data

S11-41 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation THE RLOAD2 ENTRY (Cont.) n Remarks (cont.): u TYPE (field 8) also determines the manner in which EXCITEID (field 3) is used by the program as described below: l Excitation specified by TYPE is applied load n There is no LOADSET request in Case Control u EXCITEID may also reference DAREA, static and thermal load set entries. n There is a LOADSET request in Case Control u The 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. l Excitation specified by TYPE is enforced motion u There is no LOADSET request in Case Control n EXCITEID will reference SPCD entries. n There is a LOADSET request in Case Control u The program will reference SPCD entries specified by the LID field in the selected LSEQ entries corresponding to the EXCITEID. u Alternatively for NAS2004, the LSEQ entry can be ignored as in the example on the next page. l The DLOAD in Case Control calls the DLOAD in the Bulk Data Section. l The DLOAD in Bulk Data calls the RLOAD1 card l The RLOAD1 card calls the FORCE and TABLED1 cards.

S11-42 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation THE RLOADi ENTRY (Cont.) SUBCASE 1 $ Subcase name : direct_freq_response SUBTITLE=direct_freq_response FREQUENCY = 1 SPC = 2 DLOAD = 2 DISPLACEMENT(SORT1,REAL)=ALL SPCFORCES(SORT1,REAL)=ALL $ Direct Text Input for this Subcase BEGIN BULK RLOAD DLOAD $ Nodal Forces of Load Set : unit_load FORCE $ Referenced Dynamic Load Tables $ Dynamic Load Table : frequency_depend_load TABLED ENDT Nastran 2004 Usage

S11-43 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation FREQUENCY RESPONSE CONSIDERATIONS n Exciting an undamped (or modal damped) system at 0.0 Hz gives the same results as a static analysis. Therefore, if the maximum excitation frequency is much less than the lowest resonant frequency of the system, a static analysis is sufficient. n Very lightly-damped structures exhibit large dynamic responses for excitation frequencies near resonant frequencies. A small change in the model (or running it on another computer) may give large changes in such response.

S11-44 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation FREQUENCY RESPONSE CONSIDERATIONS (Cont.) Use a fine-enough frequency step size ( f ) to adequately predict peak response. Use at least 5 points per half-power bandwidth, f 1 to f 2. For maximum efficiency, use an uneven frequency step size. Use smaller f in regions of resonant frequencies and larger f in regions removed from resonant frequencies.

S11-45 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES n Select frequency step size. u The FREQ entry is for the specification of a set of discrete excitation frequencies, e.g. f 1, f 2, f 3, …. The FREQ1 entry is for the specification of the first frequency (f 1 ) in the set of discrete excitation frequencies, frequency increment ( f), and the number of frequency increments (N f). u The FREQ2 entry is for the specification of the first and last frequency (f 1 and f 2 ) in the set of discrete excitation frequencies, and the number of logarithmic frequency intervals. u The FREQ3 entry is for the specification of excitation frequencies for modal, not direct, frequency response analyses. Specify the lower and upper bound for the frequency domain that contains the modal frequencies of interest (f 1 and f 2 ). Specify the number of excitation frequencies between two adjacent modal frequencies, and if the frequencies are to be created using linear or log interpolation. Specify any bias/clustering of the excitation frequencies at the two ends of the frequency domain.

S11-46 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Select frequency step size. u The FREQ4 entry is for the specification of excitation frequencies for modal, not direct, frequency response analyses. Specify the lower and upper bound for the frequency domain that contains the modal frequencies of interest (f 1 and f 2 ). Specify the spread (distribution) of the of excitation frequencies around each natural frequency. Specify the number of excitation frequencies to be evenly spaced between each natural frequency spread. u The FREQ5 entry is for the specification of excitation frequencies for modal, not direct, frequency response analyses. Specify the lower and upper bound for the frequency domain that contains the modal frequencies of interest (f 1 and f 2 ). Specify the fractions of the natural frequencies. u The FREQ3, FREQ4, and FREQ5 entries are available only for the modal method, as they use the natural frequencies, calculated during a modal analysis, to determined the frequencies for which the response will be determined. These are called adaptive methods. SOLUTION FREQUENCIES (Cont.)

S11-47 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES (Cont.) n FREQi Bulk Data entries are selected by the FREQUENCY Case Control commands. n All FREQi Bulk Data entries with the same set ID are used. Therefore, FREQ, FREQ1, FREQ2, FREQ3, FREQ4, and FREQ5 entries may all be used in an analysis. n To avoid overlap of frequency response points PARAM,DFREQ,tol can be set by Direct Text Input in MSC.Patran. This will eliminate duplicate points within a range of tol. n If PARAM,DFREQ is used the placement of the solution frequency points may not follow what it would be for the adaptive methods, but this is probably a secondary consideration. FREQ1 points FREQ3 points A duplicate point is eliminated that is within tolerance band tolerance

S11-48 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES (Cont.) n In the following examples, look at each of the forms of FREQi entries in MSC.Nastran and MSC.Patran and discuss best usage and typical examples using the frequency response results of Workshop 5.

S11-49 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ n FREQ – for set of specified frequencies; non-adaptive

S11-50 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ (Cont.) n FREQ – for set of specified frequencies; non- adaptive u There exists 5 arbitrary input points. One MSC.Patran spreadsheet entry per value, which makes it labor intensive.

S11-51 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ (Cont.) n The resulting FREQ entry from the MSC.Patran menu is shown below FREQSIDF1F2F3F4F5-etc.- FREQ

S11-52 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ1 n FREQ1 – linear domain; non-adaptive n This method gives a constant increment across a frequency domain n By itself it will miss data around the natural frequencies, as seen in the case study n It is best used as an overall sieve or background spread, in conjunction with adaptive methods

S11-53 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ1 (Cont.) n FREQ1 – using first freq. and freq. increment; non- adaptive

S11-54 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ1 (Cont.) n FREQ1 – define the frequencies at which a solution will be calculated. u Note the even distribution across range with no allowance for peaks. u However, this is a useful method to capture the overall trend.

S11-55 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ1 (Cont.) n The resulting FREQ1 entry from the MSC.Patran menu is shown below. n MSC.Patran input u Start Freq., End Freq., No. Incr. n MSC.Nastran input u First frequency (F1), Frequency increment (DF), Number of frequency increments (NDF) n DF is calculated by MSC.Patran using DF = (End Freq. - Start Freq.)/No. Incr FREQ1SIDF1DFNDF FREQ

S11-56 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ2 n FREQ2 – logarithmic domain; non-adaptive n This method gives a logarithmic increment across a domain n By itself it will miss data around the natural frequencies n It is best used in cases where the overall need is to bias data towards lower frequencies, in conjunction with other methods.

S11-57 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ2 (Cont.) n FREQ2 – using first and last freq. and log intervals

S11-58 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ2 (Cont.) n FREQ2 – define the frequencies at which a solution will be calculated using logarithmic increments u A logarithmic spread is defined, which will be biased towards the starting frequency and coarsen towards the end frequency. This method ignores the natural frequencies in a modal frequency response analysis. u Effect of NF choice is not intuitive

S11-59 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ2 (Cont.) n The resulting FREQ2 entry from the MSC.Patran menu is shown below FREQ2SIDF1F2NF FREQ

S11-60 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 n FREQ3 – spread (distribute) solution frequencies between adjacent natural frequencies for modal frequency response solutions n Linear or logarithmic domain; adaptive n Consider the following Linear Spread, Cluster Factor1.0, even spread 0.25, center bias 4.0, end bias Logarithmic Spread, Cluster Factor1.0 same as Linear 0.25, center bias 4.0, end bias

S11-61 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n FREQ3 – use lower and upper bound for modal freq. domain and number of freq.s within each sub- domain.

S11-62 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n FREQ3 – define the frequencies at which a solution will be calculated using linear cluster u This is an adaptive method, so the normal modes are used to define a set of intervals over which the spread or cluster is used. u The default value of Lin. Cluster is 1.0, which gives an even spread between adjacent natural frequencies. u End points 20.0Hz and Hz are treated as ends of the first and last interval All Intervals are evenly spread

S11-63 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n The resulting FREQ3 entry from the MSC.Patran menu is shown below FREQ3SIDF1F2TYPENEFCLUSTER FREQ LINEAR10

S11-64 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n FREQ3 – define the frequencies at which a solution will be calculated using a linear cluster value of 0.25 u Setting Cluster/Spread less than 1.0 will bias the spread to the center of the interval. u A value of 0.25 is used. u The end points are treated as before. Bias to the center of the interval

S11-65 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n The resulting FREQ3 entry from the MSC.Patran menu is shown below FREQ3SIDF1F2TYPENEFCLUSTER FREQ LINEAR10.25

S11-66 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n FREQ3 – define the frequencies at which a solution will be calculated using a linear cluster value of 4.0 u Setting Cluster/Spread greater than 1.0 will bias the spread toward the ends of interval. u A value of 4.0 is used. u The end points are treated as before. Bias to the ends of the interval

S11-67 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n The resulting FREQ3 entry from the MSC.Patran menu is shown below FREQ3SIDF1F2TYPENEFCLUSTER FREQ LINEAR104.

S11-68 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n FREQ3 – define the frequencies at which a solution will be calculated using log cluster u When the Cluster/Spread is set to the default of 1.0, the result obtained is the same as that for Lin. Cluster.

S11-69 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n The resulting FREQ3 entry from the MSC.Patran menu is shown below FREQ3SIDF1F2TYPENEFCLUSTER FREQ LOG10

S11-70 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n FREQ3 – define the frequencies at which a solution will be calculated using a log cluster value of 0.25 u Compare this to a previous graph to see the difference between linear cluster and logarithmic cluster.

S11-71 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n The resulting FREQ3 entry from the MSC.Patran menu is shown below FREQ3SIDF1F2TYPENEFCLUSTER FREQ LOG10.25

S11-72 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n FREQ3 – define the frequencies at which a solution will be calculated using a log cluster value of 4.0 u Compare this to a previous graph to see the difference between linear cluster and logarithmic cluster.

S11-73 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ3 (Cont.) n The resulting FREQ3 entry from the MSC.Patran menu is shown below FREQ3SIDF1F2TYPENEFCLUSTER FREQ LOG104.

S11-74 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ4 n FREQ4 – spread (distribute) solution frequencies around each natural frequency for modal frequency response solutions n Also, specify the number of solution frequencies within the spread n Consider the following Linear Spread, Fractional Amount+/ (default) +/- 0.03

S11-75 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ4 (Cont.) n FREQ4 – use lower and upper bound for modal freq. domain and frequency spread for each natural frequency.

S11-76 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ4 (Cont.) n FREQ4 – (continued)

S11-77 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ4 (Cont.) n FREQ4 – (continued)

S11-78 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ4 (Cont.) n FREQ4 – define the frequencies at which a solution will be calculated using a spread about each natl freq. u Specify for each natural frequency a spread of solution frequency points using No. Incr. MSC.Nastrans NFM is equal to No. Incr. u The fractional amount of spread (Cluster/Spread) is left blank here. That produces the MSC.Nastran default of +/ of a natural frequency. This equates to the MSC.Nastran FSPD input Spread is over +/- 10% of each natural frequency

S11-79 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ4 (Cont.) n The resulting FREQ4 entry from the MSC.Patran menu is shown below FREQ4SIDF1F2FSPDNFM FREQ

S11-80 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ4 (Cont.) n FREQ4 – define the frequencies at which a solution will be calculated using a spread about each natural frequency u The fractional amount of spread (Cluster/Spread) is set as 0.03 here.

S11-81 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ4 (Cont.) n The resulting FREQ4 entry from the MSC.Patran menu is shown below FREQ4SIDF1F2FSPDNFM FREQ

S11-82 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ5 n FREQ5 – use lower and upper bound for modal freq. domain and fractions of each natural frequency.

S11-83 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ5 (Cont.) n FREQ5 – use lower and upper bound for modal freq. domain and fractions of each natural frequency (continued).

S11-84 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES, FREQ5 (Cont.) n FREQ5 – define the frequencies at which a solution will be calculated using fractions of the natural frequencies u Specify for each natural frequency a fractional spread about it. u All natural frequencies from the modal analysis will be assessed to see if their fractional values fall within the frequency response domain of F of F of F 3

S11-85 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation SOLUTION FREQUENCIES (Cont.) n The resulting FREQ5 entry from the MSC.Patran menu is shown below. u It is possible in MSC.Nastran to define all FRs in one entry. This is not supported by MSC.Patran FREQ FREQ FREQ5 FR1F2F1SIDFREQ

S11-86 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation RECOMMENDATIONS n Recommendations on FREQi entries u The range of FREQi cards available makes it confusing to the user u Some techniques are tedious to input in Patran u Some techniques are unpredictable u The following combinations are recommended, but not exhaustive: l For Modal Method n FREQ1 set to give the smallest Delta f practical across range of interest n FREQ4 Spread set to, damping level, and number to at least 9 to give 9 points even spread per half-power bandwidth n PARAM,DFREQ set to appropriate filter value l For Modal Method n FREQ1 set to give a relatively coarse Delta f across range of interest n FREQ3 Log Cluster set to 4, and number to as high as practically possible - will be affected if natural frequencies have wide variation in spacing n PARAM,DFREQ set to appropriate filter value

S11-87 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation RECOMMENDATIONS (Cont.) n Recommendations on FREQ cards to use (cont.) u The following combinations are recommended, but not exhaustive: l For Direct Method n FREQ1 set to give the smallest Delta f practical across range of interest n FREQ set to all known natural frequencies and % of them to capture data in the half-power bandwidth n Repeated FREQ1s set to coarser Delta f, but choosing the frequency range of each to be between known natural frequency values. u Note: l The Direct Method does rely heavily on knowledge of the natural frequencies and will be compromised if a single FREQ1 entry alone is used. l A common mistake is to miscalculate the range of interest and use freq1 – and get a null result, or incomplete results

S11-88 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DAMPING FOR DIRECT FREQUENCY RESPONSE ANALYSIS n There are several sources of damping that can be modeled for direct frequency response analysis in MSC.Nastran. This is the same as for direct transient response analysis. u Viscous damping using l CVISC – viscous damper connection l CDAMPi – scalar damper connection l CBUSH – generalized spring/damper u Structural damping l Uniform/constant for entire model l Varies from element to element, but is constant for each element u Direct matrix input l B2GG l B2PP

S11-89 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Viscous damping form of equation of motion n Structural damping form of equation of motion DAMPING FOR DIRECT FREQUENCY RESPONSE ANALYSIS (Cont.)

S11-90 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n The general dynamic equation used in the direct methods is u where p = a derivative operator {u d } = the union of the analysis set {u a } and extra points {u e }. n For direct frequency response, the dynamic matrices are DAMPING FOR DIRECT FREQUENCY RESPONSE ANALYSIS (Cont.)

S11-91 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DYNAMIC MATRIX DEFINITIONS n is the reduced structural stiffness matrix plus the reduced direct input K2GG, (symmetric). n is the reduced direct input matrix K2PP plus the reduced transfer function input, (symmetric or unsymmetric). n is the reduced structural damping matrix obtained by summing the product of the stiffness matrix of each individual structural element, [k e ], and the elements damping factor, g e, (symmetric). n is the reduced viscous damping matrix plus the reduced direct input B2GG, (symmetric).

S11-92 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DYNAMIC MATRIX DEFINITIONS (Cont.) n is the reduced direct input matrix B2PP plus the reduced transfer function input, (symmetric or unsymmetric). n is the reduced mass matrix plus the reduced direct input M2GG, (symmetric). n is the reduced direct input matrix M2PP plus the reduced transfer function input, (symmetric or unsymmetric). g, 3, 4 are the constants specified by the user.

S11-93 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Modal frequency response analysis is an alternate approach to computing the frequency response of a structure using the direct method. u This method uses the normal modes of the structure to reduce the size of the model, uncouple the equations of motion (when modal damping or no damping is used), and make the numerical solution more efficient. u Since the normal modes are typically computed as part of the characterization of the structure, modal frequency response is a natural extension of a normal modes analysis. MODAL FREQUENCY RESPONSE

S11-94 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation MODAL FREQ RESP W/O DAMPING n Start with equation for steady-state complex forcing, ignoring damping n Use the transformation from modal space to physical space n The following equations are arrived at

S11-95 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Convert to modal coordinates and solve as a set of decoupled SDOF equations n Damping was ignored for this development, but will be included for the next development MODAL FREQ RESP W/O DAMPING (Cont.)

S11-96 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Viscous damping (no structural damping) n Use the transformation from modal space to physical space n The following equation is arrived at [ ] T [B][ is diagonal MODAL FREQ RESP WITH DAMPING

S11-97 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Convert to modal coordinates and solve as a set of decoupled SDOF equations n Much quicker to solve this equation than using the direct method MODAL FREQ RESP WITH DAMPING (Cont.)

S11-98 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation [ ] T [B][ is not diagonal l This equation is solved by MSC.Nastran using the direct method n Structural damping (no viscous damping, [B]=0) n Use the transformation from modal space to physical space n The following equations are arrived at MODAL FREQ RESP WITH DAMPING

S11-99 NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation u This is a set of decoupled equations. u However, in MSC.Nastran the structural damping problem is solved using the direct method because the stiffness matrix can involve both uniform and element/material structural damping. n Since the number of modes used in a solution is typically much less than the number of physical degrees-of-freedom, finding the solution of the coupled equation in terms of modal coordinates is less time consuming than using physical variables. MODAL FREQ RESP WITH DAMPING

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation MODAL FREQUENCY RESPONSE (Cont.) n The modal form of the frequency response equation of motion is much faster to solve than that of the direct method, because it represents a sequence of uncoupled single degree-of-freedom systems. n Once the individual modal responses are computed, physical responses are recovered by summing the modal responses. n These responses are in complex form (magnitude/phase or real/imaginary) and are used to recover additional output quantities requested in the Case Control Section.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN MODAL FREQUENCY RESPONSE n The TABDMP1 Bulk Data entry defines the modal damping ratios. A table is created by the frequency/damping pairs specified on the TABDMP1 entry. MSC.Nastran refers to this table for the damping value to be used for a particular natural frequency. The TABDMP1 Bulk Data entry has a Table ID. A particular TABDMP1 table is activated by selecting the Table ID with the SDAMPING Case Control command.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN MODAL FREQUENCY RESPONSE (Cont.) n At resonance, the three types of damping are related by the following equations: Critical Amplification

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN MODAL FREQUENCY RESPONSE (Cont.) n Defines model damping as a tabular function of natural frequency. n Example: TABDMP1TIDTYPE f1g1f2g2f3g3-etc TABDMP ENDT

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN MODAL FREQUENCY RESPONSE (Cont.) n Field Contents u TID: Table identification number. u TYPE: Type of damping units: l G (default) l CRIT l Q f i : Frequency value (cycles per unit time). g i : Damping value in the units specified

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN MODAL FREQUENCY RESPONSE (Cont.) n Note that the subscript is for the i-th mode, and not the i-th excitation frequency. The values of f i and g i define pairs of frequencies and dampings. n Note that values in the TABDMP1 can be entered as one of the following: structural damping (default), critical damping, or quality (Amplification) factor. n The entered damping is converted to structural damping internally using

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN MODAL FREQUENCY RESPONSE (Cont.) n Straight-line interpolation is used for modal frequencies between consecutive values. Linear extrapolation is used at the ends of the table. ENDT ends the table input.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN MODAL FREQUENCY RESPONSE (Cont.) n For example, if modal damping is entered using the table shown and modes exist at 1.0, 2.5, 3.6, and 5.5 Hz, MSC.Nastran interpolates and extrapolates as shown below. Note that there is no table entry at 1.0 Hz; MSC.Nastran uses the first two table entries at 2.0 Hz and 3.0 Hz to extrapolate the value for 1.0 Hz. Entered f Computed F

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN MODAL FREQUENCY RESPONSE (Cont.) n Modal damping is processed as a complex stiffness when PARAM,KDAMP is entered as -1. The uncoupled equation of motion becomes - 2 m i i ( ) + (1 + iG( )) k i i ( ) = p i ( ) n The default for PARAM,KDAMP is 1, which processes modal damping as a damping matrix as shown in - 2 m i i ( ) + i b i i ( ) + k i i ( ) = p i ( ) n The decoupled solution procedure used in modal frequency response can be used only if either no damping is present or modal damping alone (via TABDMP1) is used. n Otherwise, the modal method uses the coupled solution method on the smaller modal coordinate matrices if nonmodal damping (i.e., CVISC, CDAMPi, GE on the MATi entry, or PARAM,G) is present.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation MODE TRUNCATION IN MODAL FREQUENCY RESPONSE ANALYSIS n It is possible that not all of the computed modes are required in the frequency response solution. u You need to retain, at a minimum, all the modes whose resonant frequencies lie within the range of forcing frequencies. l For example, if the frequency response analysis must be between 200 and 2000 Hz, all modes whose resonant frequencies are in this range should be retained. u This guideline is only a minimum requirement, however. For better accuracy, all modes up to at least two to three times the highest forcing frequency should be retained. l In the example where a structure is excited to between 200 and 2000 Hz, all modes from 0 to at least 4000 Hz should be retained.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation MODE TRUNCATION IN MODAL FREQUENCY RESPONSE ANALYSIS (Cont.) n The frequency range selected on the eigenvalue entry (EIGRL or EIGR) is one means to control the modes used in the modal frequency response solution. n Also, three parameters are available to limit the number of modes included in the solution. u PARAM,LFREQ gives the lower limit on the frequency range of retained modes u PARAM,HFREQ gives the upper limit on the frequency range of retained modes. u PARAM,LMODES gives the number of lowest modes to be retained. u These parameters can be used to include the proper set of modes. Note that the default is for all computed modes to be retained.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n In modal frequency response analysis, two options are available for recovering displacements and stresses: u the mode displacement method u the matrix method. n Both methods give the same answers, although with differences in cost. n The mode displacement method computes the total physical displacements for each excitation frequency from the modal displacements, and then computes element stresses from the total physical displacements. u The number of operations is proportional to the number of excitation frequencies. n The matrix method computes displacements per mode and element stresses per mode, and then computes physical displacements and element stresses as the summation of modal displacements and element stresses. u Costly operations are proportional to the number of modes. MODE TRUNCATION IN MODAL FREQUENCY RESPONSE ANALYSIS (Cont.)

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation n Since the number of modes is usually much less that the number of excitation frequencies, the matrix method is usually more efficient and is the default. n The mode displacement method can be selected by using PARAM,DDRMM,-1 in the Bulk Data. n The mode displacement method is required when frequency-frozen structural plots are requested, for example in plotting deformation or stress distribution in Patran. MODE TRUNCATION IN MODAL FREQUENCY RESPONSE ANALYSIS (Cont.)

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation MODAL VERSUS DIRECT FREQUENCY RESPONSE

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation WORKSHOP 16 – MODAL FREQUENCY RESPONSE OF A CAR MODEL n Please now carry out Workshop 16 in the Workshop Section. n A loading is applied to one engine mount across a frequency range. The response at different locations on the vehicle is calculated. n Use the results of the previous Workshop 13, which ran a normal modes analysis of this structure, to validate the frequency response curves. n The workshop will take you through step by step if you are unfamiliar with Nastran or Patran. If you have some experience, then try to set up the analysis without referring to the step by step guide. n Please feel free to ask your tutor for help.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN n In this example, use a square plate built in at one edge and investigate the stresses at the first natural frequency of Hz. Because of damping, a phase shift between the loading and any response exists. This is described via real/imaginary terms or magnitude/phase terms. real imag mag

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) n Request the MSC.Nastran results in the.f06 file to be in real/imaginary or magnitude/phase via Case Control requests. This is done in MSC.Patran under Advanced Output Requests as Rectangular or Polar.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) n Post-process the Nastran results in Patran by using create/fringe for a particular component stress. Now set up any of the real, imaginary, magnitude or phase terms as a stress plot by setting the mapping of the complex number stress result.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) Mapping to a Real Plot shows max x stresses at the top corner: Element 31 Node 43

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) To compare the Nastran F06 results, switch off Element averaging. This shows both edge grids on the element at peak x stress of 3.74E5

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) FREQUENCY = E+00 C O M P L E X S T R E S S E S I N Q U A D R I L A T E R A L E L E M E N T S ( Q U A D 4 ) (REAL/IMAGINARY) OPTION = BILIN ELEMENT FIBRE - STRESSES IN ELEMENT COORDINATE SYSTEM - ID GRID-ID DISTANCE NORMAL-X NORMAL-Y SHEAR-XY 0 31 CEN/ E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E+03 The Nastran F06 results for Hz at Element 31, Node 43, Real x stresses are shown and agree with Patran. Note the format for Real/Imaginary in the F06 file.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) Repeat the process with the Imaginary stress Plot.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) To compare with Nastran F06 results, switch off Element averaging.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) FREQUENCY = E+00 C O M P L E X S T R E S S E S I N Q U A D R I L A T E R A L E L E M E N T S ( Q U A D 4 ) (REAL/IMAGINARY) OPTION = BILIN ELEMENT FIBRE - STRESSES IN ELEMENT COORDINATE SYSTEM - ID GRID-ID DISTANCE NORMAL-X NORMAL-Y SHEAR-XY 0 31 CEN/ E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E E E+05 / E E+04 / E E+04 / E+03 The Nastran F06 results for Hz at Element 31, Node 43 imaginary are shown and agree with Patran.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) To check the Phase Plot, calculate the phase angle. For x stress at the grid point: = tan -1 (sig imag/sig real) = degrees Notice the phase distribution looks sensible for this frequency, with 180 degrees shift between quadrants.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) Switch off Element averaging to check the phase distribution. Node 43 stress is –5.93 degrees out of phase with loading.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) Same idea with the Magnitude Plot

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) To check the Magnitude Plot, calculate the magnitude for x stress at the grid point: Sig mag = (sig imag 2 +sig real 2 ) 1/2 = 3.760E5 psi This agrees with the Patran distribution.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation It allows us to input the angular position of the cycle and then plot the amplitude at that angle. In this case, use the phase angle between response and loading so the peak response can be captured at. Cycle through the response in this same way. INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) n All the mappings except angle have been looked at; what does that do? imag mag real mag angle imag mag

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) n In the first plot on the right, use angle = 0 degrees. The result for Node 43 x stress is 3.74e5 psi. This is the same as the previous real component plot, as real is the same as amplitude at 0 degrees. n In the next plot on the right, use angle = degrees. The result for Node 43 x stress is 3.76e5 psi. This is the same as the previous magnitude plot, as there exists a degrees lag before a peak is reached.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) angle amplitude peak n In the next plot on the right, use angle = degrees. The result for Node 43 x stress is 0.0 psi. This is because the amplitude is 0.0 at 90 degrees from the peak.

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation INTERPRETING FREQUENCY RESPONSE RESULTS IN MSC.PATRAN (Cont.) n Animation of a response at a frequency uses the same method as Angle. It cycles through 360 degrees, showing the amplitude as a function of angle. a.Ensure that Modal animation method is selected. b.If there is a phase lead or lag in the response, then this can be dealt with by setting this value into the Angle Offset box. This will allow the peak amplitude to be shown at zero angle (i.e. the first frame). c.It is recommended that 19 frames be used for a typical PC based Graphics card, so that the angle is in increments of 20 degrees in a cycle. n The animation option overrides whatever was previously set up, as the mapping complex to … is now not appropriate. a b c

S NAS122, Section 11, August 2005 Copyright 2005 MSC.Software Corporation