S10-1 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation SECTION 10 TRANSIENT RESPONSE ANALYSIS

S10-2 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation

S10-3 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation INTRODUCTION TO TRANSIENT RESPONSE ANALYSIS n Compute a response to a time- varying input {P(t)}. n The excitation is explicitly defined in the time domain. All of the applied forces are known at each instant in time. n Computed response usually includes nodal displacements and accelerations, and element forces and stresses. n All responses are a function of time. n There are two categories of analysis u Direct u Modal n First look at the direct method

S10-4 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DIRECT TRANSIENT RESPONSE n The dynamic equation of motion is The response is solved at discrete times with a fixed time step, t. n Use central finite difference approximation for and at discrete times Disp u(t) unun u n-1 u n+1, the unknown time

S10-5 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DIRECT TRANSIENT RESPONSE (Cont.) n Use central finite difference to integrate u Average internal and applied force over three adjacent time points Time Average

S10-6 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DIRECT TRANSIENT RESPONSE (Cont.) n Numerical solution of dynamic equation u where u Write the solution equation as l This is similar to the linear static equation. Dynamic matrix Applied force For previous time points

S10-7 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DIRECT TRANSIENT RESPONSE (Cont.) n Solve this equation by decomposing [A 1 ]. n This is similar to the classical Newmark-Beta method, except u The internal forces (element forces) are averaged over 3 adjacent time points. This provides a nonsingular dynamic matrix, [A 1 ], for [M] and [B] equal to zero. u The applied force is averaged over 3 adjacent time points. n [M], [B], and [K] do not change with time. [A 1 ] needs to be decomposed only once if t is unchanged throughout the entire solution. If t is changed, [A 1 ] must be re-decomposed, which may be a computationally time consuming operation.

S10-8 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DIRECT TRANSIENT RESPONSE (Cont.) The results output time interval may be greater than the solution time interval (e.g., use solution t of second, and output (write) results every fifth solution time interval (output every second)).

S10-9 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DIRECT TRANSIENT RESPONSE (Cont.) n Some practical points to consider u Overall l It is often easier to think in milliseconds (ms); 0.001sec = 1ms. u Solution t l Keep t constant if possible. If t is changed, A 1 must be re-decomposed (which may be a time consuming operation). l The smaller the value of t, the more accurate the integration will be. l However, it may be time effective for a large model to decrease t at a time of critical interest (say under impulsive loading) and increase it later. Normally it will take a few runs to tune the model overall, and the effectiveness of this technique can be investigated. l The time step chosen should be sufficiently small to capture the highest frequency of interest in the response. For example, if this value is 100 Hz, each time period is 0.01s (10ms) so at the very least 5 steps to capture the response are needed, i.e.. t =0.002s (2ms). The preferred minimum number is 10 steps per period. l The accuracy of the load input is similarly dependent on the time step chosen, so a loading of 1000 Hz will need at least a t of s (0.2ms)

S10-10 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DIRECT TRANSIENT RESPONSE (Cont.) n Some practical points to consider (continued) u Results t l The results (output) time interval may be greater than the solution time interval. For example, if use a solution t of s (1ms), and output results every fifth time step, the output t is s (5ms). u Number of solution t -s l This controls the duration of the analysis. The duration should be sufficient to ensure the response has reached steady state and is decaying in a predictable manner. l For impacts and other short duration events, the time of loading will be on the order of 0.01ms to 10ms. The decay time will be dependent on the frequency content of the structure and amount of damping. If the overall time to be analyzed is 100ms and the highest frequency of interest is 200 Hz, we will need at least (0.1 sec * 200 cyc/sec) * 5 steps/cyc = 100 time steps of 1ms each. l The lowest significant frequency needs to be checked to ensure enough decay time has been allowed. Assume in the above case the lowest frequency is 10 Hz, then its time period is 100ms. The analysis needs to be extended to, say 300ms (300 time steps of 1ms), to ensure the capture of the long period motion. l For a seismic event the time can be 15s to 30s. If the highest frequency of interest is 40 Hz, at least (30*40)*5 = 6000 time steps will be needed.

S10-11 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE

S10-12 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Problem Description u Using the direct method, determine the transient response of the flat rectangular plate, created in Workshop 1, subject to time-varying excitation. u This example structure is excited by 1 psi pressure load over the total surface of the plate varying at 250 Hz for a duration of seconds. u In addition, a 50 lb force of 250 Hz is applied at a corner of the tip for the same duration. u Use structural damping of g = 0.06 and convert this damping to equivalent viscous damping at 250 Hz. u Carry out the analysis for 0.04 seconds. u The structure and its constraint boundary conditions are imported into Patran CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-13 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Problem Description (cont.) u Below is a finite element representation of the flat plate. It also describes the loads and boundary constraints. CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-14 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n First consider the loading definitions and how to set these up in Patran u Both Pressure Loading vs. Time and Point Load vs. Time are set up via Non-Spatial fields in Patran u The variation of each through time is conveniently defined using a PCL function as both inputs are sine functions u The PCL functions are: sind(250*360*t) -sind(250*360*t) i.e. 180 degrees out of phase to correct the fact that pressure acts in the opposite sense to the force. where: t is the PCL global variable for Time sind is the PCL sine function in degrees CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-15 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Create a Non Spatial field for the pressure load. a. Fields: Create / Non Spatial / Tabular Input. b. Enter pressure for the Field Name. c. Select Time (t) as the Active Independent Variable. d. Click Input Data. e. Click Map Function to Table. f. Insert the parameters shown in the menu. g. Click Apply. h. Click OK on the table. i. Click Apply. f a b c d i g h e CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-16 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Create a Non Spatial field for the force load. a. Enter force for the Field Name. b. Select Time (t) as the Active Independent Variable. c. Click Input Data. d. Click Map Function to Table. e. Insert the parameters showed in the menu. f. Click Apply. g. Click OK on the table. h. Click Apply. a b c h e h f g CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-17 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation a.To verify the plot of the field use Fields/Show and pick the Field name Note that f =250Hz gives T =.004s So duration of.008s yields 2 cycles b.The point symbols have been added for clarity using XYPlot/Modify/Curve/O ptions c.The accuracy of the input signal is not high, the number of points should be increased CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-18 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Set up a Load Case which is defined as Time – Dependent and make it current u Initially only the constraint boundary conditions to this Load Case can be allocated. u However, the presence of a current Load Case which is Time- Dependent allows us to create Time-Dependent Loading B.C.s for the two loads CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-19 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Create a Time Dependent load case. a. Load Cases: Create. b. Enter direct_transient for the Load Case Name. c. Select Time Dependent as the Load Case Type. d. Click Assign/Prioritize Loads/ BCs. e. Click on the Displ_constraint in the Select Individual Loads/BCS field. f. Click OK. g. Click Apply. e f a b c d g CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-20 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation d e n Create the time dependent Force load. a. Loads/BCs: Create / Force / Nodal. b. Enter 50lb for the New Set Name. c. Click on the Input Data button. d. Enter for Force, and select Force for the Time/Freq. Dependent Field. e. Click OK. f. Click on Select Application Region. g. Change the Geometry Filter to FEM. h. Select the bottom right corner node for the application region. i. Click Add, and click OK. j. Click Apply. a b c f j g h i i CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-21 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation e f a b c d g j h i i n Create the time dependent Pressure load. a. Loads/BCs: Create / Pressure / Element Uniform. b. Enter pressure for the New Set Name. c. Change the Target Element Type to 2D. d. Click on the Input Data button. e. Enter -1 for Top Surf Pressure, and select Pressure for the Time/Freq. Dependent Field. f. Click OK. g. Click on Select Application Region. h. Select all the elements for the application region. i. Click Add, and click OK. j. Click Apply. CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-22 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Select the solution type as a Transient 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 we convert this to mass density) u Overall Structural damping Coefficient of 0.06 is used at a matching frequency of 250Hz (1570 rad/sec) CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-23 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Submit the model for analysis. a. Analysis: Analyze / Entire Model / Full Run. b. Click on Solution Type. c. Select Transient Response. d. Change the Formulation to Direct. e. Click on Solution Parameter. f. Enter for Wt- Mass Conversion. g. Enter 0.06 for Struct. Damping Coefficient and 1570 for W3, Damping Factor. h. Click OK. i. Click OK f g h c d e i a b CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-24 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Create a Subcase and setup parameters for it u Select the Load Case previously defined u Define the Time Steps via a Delta T of sec (0.4 ms) and number as 100 n How is sec for Delta T acquired? u From the Normal Modes previously ran, Mode 3 is 821 Hz. As a result it is expected that this is the highest mode that will be excited. u The Time Period for Mode 3 is 1/821 secs = 1.2e-3 (1.2 ms) resulting in the need to capture 3 points per cycle u The loading is input at 250 Hz, Time period is 1/250 = sec (4 ms) so 10 points per cycle will be captured. u There are 100 Time Steps so duration = 100* = 0.04 sec CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-25 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Submit the model for analysis (cont.). a. Click on Subcases. b. Select direct_transient from the Available Subcases field. c. Click on Subcase Parameters. d. Click on DEFINE TIME STEPS button. e. Change Delta-T to Click Enter. f. Click OK. g. Click OK. h. Click Apply. i. Click Cancel. a e f d g c b h i CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-26 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n The.bdf file fragment written out for the time step is shown: n The full definition of the time step entry is shown: n The Term NO1 controls the rate at which calculation times are carried forward to output times u NO1 = 1 or blank means full output, NO1 = 5 means output every 5th calculation point n The TSTEP bulk data SID is called out from Case Control TSTEP=SID TSTEPSIDN1DT1NO1 TSTEP CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-27 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n The Patran input point for this parameter is in Output Request n Use the Advanced Option and input Percentage Output CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-28 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Submit the model for analysis (cont.). a. Click on Subcase Select. b. Select direct_transient and unselect Default. c. Click OK. d. Click Apply. a d b c CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-29 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Attach the XDB result file. a. Analysis: Access Results / Attach XDB / Result Entities. b. Click on Select Results File. c. Select ws3.xdb. d. Click OK. e. Click Apply. a b e c d CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-30 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Create an Y-X graph of displacement results. a. Results: Create / Graph / Y vs X. b. Click on SC1:DIRECT_TRA NSIENT. c. Select Global Variable as the Filter Method. d. Click Filter. e. Click Apply. f. Click Close. a b c d e f CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-31 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation nCreate a X-Y graph of displacement results (cont.). a. Select Displacement, Translational for the Select Y Result field. b. Select Z Component as the Quantity. c. Click on the Target Entities icon. d. Change the Target Entity Selection to Nodes. e. Select the node opposite of the node where force is applied. f. Click Apply. b a c CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-32 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-33 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n To improve the clarity of the x-y plot a. Go to XY Plot main menu b. Select Modify/Axis c. Click on the Scale option d. Change the Assignment Method to Range e. Set the lower and upper values to f. Set the Tick Marks to 9. c d e f b CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-34 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n To improve the clarity of the x-y plot (cont.) a. Select Modify/Axis b. Click on the Labels option c. Change the Label Format to Fixed b c a CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-35 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n To improve the clarity of the x-y plot (cont.) a. Select Modify/Axis b. Click on the Grid Lines option c. Set the Display to Primary and Secondary checked b c a CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-36 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n To improve the clarity of the x-y plot (cont.) a. Repeat the same options with the Y axis a CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-37 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Based on the clearer graphical plot, the response of the structure can be checked after the loading has finished. (0.008 secs) n The time for 3 periods of oscillation is: n Time period, T: n Frequency: CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.) T Loaded Free 3T

S10-38 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n This matches exactly with the first bending frequency of the plate as found in Workshop 1a. Again this emphasizes the need to know the normal modes results when carrying out a Direct Transient Analysis. n To find the higher frequency content of the response a Fourier Analysis needs to be carried out. n The other expected frequency is the high torsional mode. This is left as an exercise for the student in Workshop 3, to use the corner grids of the plate to try to identify this. CASE STUDY: DIRECT TRANSIENT ANALYSIS OF A SIMPLE PLATE (Cont.)

S10-39 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation WORKSHOP 3 DIRECT TRANSIENT ANALYSIS n Please now carry out Workshop 3 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 Nastran or 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.

S10-40 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation WORKSHOP 3 DIRECT TRANSIENT ANALYSIS (Cont.) n Further Discussion of the Transient Analysis Loading u It has been described how to apply a PCL function to represent a loading defined as a function u A Tabular Input Method can be used to represent a loading defined via a general time history

S10-41 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TRANSIENT EXCITATION n Create a time dependent load case n Define a non-spatial field u Input the values in the spreadsheet

S10-42 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TRANSIENT EXCITATION (Cont.) n Define force as a function of time, using the field definition.

S10-43 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TRANSIENT EXCITATION (Cont.) n Further Discussion of the Transient Analysis Loading u If a Tabular Input Method is used to represent a loading, then the time history needs to be inserted manually. This is not convenient for a lot of data, therefore a shareware technique is used to read in ASCII external data u Note this application is not supported by MSC.Software, it is shown for convenience…. u In the case of a typical seismic input there is 1560 accn.vs. time records u The method used maps an external ASCII file directly into a field

S10-44 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TRANSIENT EXCITATION (Cont.) n Further Discussion of the Transient Analysis Loading Field created Ready for use in loading seismic input file

S10-45 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TRANSIENT EXCITATION ISSUES n Remember the 1/3 smearing of applied loads. This will smooth the force, decreasing its apparent frequency content. n Avoid specifying discontinuous forces. Having this type of force may cause different results on different computers. If using a certain value of N t causes a solution to be obtained at ABC, then MSC.Nastran will select the average force at B. However, due to numerical roundoff, N t on one computer may be at time A- and the force at A will be obtained. On another computer, N t may be at time C+ and the force at C will be obtained. The results from integration will differ depending on whether the force at N t is at A, at B, or at C.

S10-46 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation Smooth a discontinuous force over one t. TRANSIENT EXCITATION ISSUES (Cont.) Un-smoothed force Smoothed force

S10-47 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TRANSIENT EXCITATION ISSUES (Cont.) n When defining an input table, ensure that the data extrapolates correctly. The Nastran rule for any TABLE is to extrapolate the first 2 and the last 2 data points. Poorly defined data points can lead to bad extrapolation. Intention Possible Errors – Negative force at t=0 Possible Errors - Negative force at t >5E-3 5E-3

S10-48 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Note now Patran 2001 onwards will automatically add extra points in attempt to overcome this problem Patran action is to extend these points Extra TRANSIENT EXCITATION ISSUES (Cont.)

S10-49 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Explore the way the NASTRAN Transient Loading data is set up when translated by Patran n NASTRAN has two methods of defining the variation of load with time: u TLOAD1 entry which uses ordered time, load pairs in a table input – this is the method Patran uses u TLOAD2 analytical definition of loadings with time – this is not supported in Patran, but can be very useful as a direct text input method TRANSIENT EXCITATION ISSUES (Cont.)

S10-50 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD1 ENTRY

S10-51 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD1 ENTRY (Cont.)

S10-52 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD1 ENTRY (Cont.) TLOAD $ Dynamic Load Table : force TABLED1 1 * * * * * * * * * * * * ENDT n TLOAD1 SID 5 is linked to TABLED1 TID 1 n The table contains the Time vs. Force pairs which make up the time dependency

S10-53 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD1 ENTRY (Cont.) n TLOAD1 SID 5 is also linked to an LSEQ entry, with SID 1, via an EXCITEID value (DAREA that defines {A}) field id 6 n The TLOAD1 defines the TIME variation of loading n This LSEQ entry allows the defining of the spatial variation of loading by linking to the FORCE SID 3 entry 50. lbf force LSEQ $ Nodal Forces of Load Set : 50 lbf FORCE Vector in Z-directionCID 0 GRID 11 TLOAD

S10-54 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD1 ENTRY (Cont.) n Look at the same idea schematically n Defines static loads that are being applied dynamically. n The LSEQ Bulk Data entry is selected by the LOADSET Case Control command. n Contains an EXCITEID entry to identify the loadset for use with the TLOADi entries. n Relationship to other input: DLOAD TLOAD Static Load Dynamic Temporal Case Control Bulk Data EXCITEID Link Spatial LOADSET LSEQ

S10-55 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation LOAD SET COMBINATION – DLOAD n The applied load {P c } is constructed from a combination of component load sets {P k } u where l S = overall scale factor l S k = scale factor for k-th load set l {P k } = load vector for k-th load set, with corresponding SID of TLOAD entry n TLOAD1s and TLOAD2s must have unique SIDs. n Use the DLOAD entry to combine TLOADs. n The DLOAD Bulk Data entry is selected by DLOAD Case Control command. n Put it all together in the example on the next page DLOADSIDSS1S1 P1P1 S2S2 P2P2 -etc-

S10-56 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation LOAD SET COMBINATION – DLOAD (Cont.) DLOAD TLOAD LSEQ TLOAD LSEQ FORCE PLOAD THRU 40 TABLED1 2 * * * ENDT TABLED1 1 * * * * * ENDT In the Case Control section have DLOAD = 2 LOADSET = 1

S10-57 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD2 ENTRY n The TLOAD2 follows exactly the same pattern as the TLOAD1 in linking to other data entries n It is not supported by Patran but is straightforward to edit a dummy TLOAD1 entry into this form n It permits direct entry of sine, cosine type functions and can be useful when the loading specification calls for this type of input n Examples of its usage are: u A shock acceleration input of form half sine pulse at 10Hz, amplitude 15g applied from 0.0 to.05 secs u A continuous sinusoidal loading of 250 Hz, amplitude 3 lbf applied from 0 to 40 secs

S10-58 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD2 ENTRY (Cont.) n For defining excitation in the form of where

S10-59 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD2 ENTRY (Cont.)

S10-60 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD2 ENTRY (Cont.)

S10-61 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation TLOAD2 ENTRY (Cont.)

S10-62 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation INITIAL CONDITIONS n May impose initial displacement and/or velocity in direct or modal transient response via the TIC Bulk Data entry. n Be careful, DOFs that do not have initial conditions (IC) specified, MSC.Nastran sets their ICs to zero. n Initial conditions may be specified only for a-set DOFs. n The IC Case Control command is used to select the TIC Bulk Data entry.

S10-63 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation INITIAL CONDITIONS (Cont.) n Initial conditions are used to determine the values of {u -1 }, {P 0 }, and {P -1 } used in calculating {u 1 }. The acceleration for all nodes is set as zero for ({u -1 }={0} and {u 0 }={0}). n The load specified by the user at t = 0 is replaced by.

S10-64 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation INITIAL CONDITIONS (Cont.) n The recommended practice for any type of dynamic excitation is to use at least one time step of zero excitation prior to applying the dynamic force.

S10-65 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation INITIAL CONDITIONS (Cont.) n Initial displacements TICSIDGCU0U0 V0V0 TIC $ Initial Displacements of Load Set: initial displacements TIC1110

S10-66 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation INITIAL CONDITIONS (Cont.) n Initial velocities TICSIDGCU0U0 V0V0 TIC $ Initial Velocities of Load Set: initial velocity TIC

S10-67 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING FOR DIRECT TRANSIENT RESPONSE ANALYSIS n There are several sources of damping that can be modeled for direct transient response analysis in MSC.Nastran 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

S10-68 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING FOR DIRECT TRANSIENT RESPONSE ANALYSIS (Cont.) n Viscous damping form of equation of motion n Structural damping form of equation of motion u This equation cannot be solved by the direct transient method, because of the complex term n Solve these two equations for harmonic excitation and response u Viscous damping u Structural damping

S10-69 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING FOR DIRECT TRANSIENT RESPONSE ANALYSIS (Cont.) n These two equations yield an equal solution if u or Thus, the structural damping can be represented by viscous damping by using a single value of the frequency, e.g. 3

S10-70 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Analytical conveniences used to model damping u Viscous damping force l n b = viscous damping coefficient l Equation of motion for SDOF system u Structural damping force l n where n g = structural damping coefficient l Equation of motion for SDOF system VISCOUS DAMPING VERSUS STRUCTURAL DAMPING, SDOF SYSTEM

S10-71 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Assume sinusoidal response u Then Viscous damping: Structural damping: VISCOUS DAMPING VERSUS STRUCTURAL DAMPING, SDOF (Cont.)

S10-72 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Both equations are identical if Therefore, if structural damping, g, is to be modeled using viscous damping, b, the equality holds at only one frequency, e.g. 3. n If u and VISCOUS DAMPING VERSUS STRUCTURAL DAMPING, SDOF (Cont.)

S10-73 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation u then = critical damping ratio (percent critical damping) l g = 1/Q = structural damping factor l Q = quality factor or magnification factor VISCOUS DAMPING VERSUS STRUCTURAL DAMPING, SDOF (Cont.)

S10-74 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation Viscous and structural damping are equivalent at frequency or. VISCOUS DAMPING VERSUS STR DAMPING (CONSTANT DISPLACEMENT)

S10-75 NAS122, Section 10, 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 transient response, the dynamic matrices are DAMPING FOR DIRECT TRANSIENT RESPONSE ANALYSIS (Cont.)

S10-76 NAS122, Section 10, 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).

S10-77 NAS122, Section 10, 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.

S10-78 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS n Direct Transient Response n Example 1 u Assume there is a structure where 2% overall structural damping needs to be applied and the first significant mode is at 73.4 Hz u The damping coefficient* is input as PARAM,G,0.04 u The frequency used to match structural and viscous damping is 73.4*(2*pi) = rad/sec u The frequency is input as PARAM,W3,461.9 u Warning Note: If W3 is not supplied, then the default is 0.0 rad/sec and this will cause the damping coefficient to be ignored and no damping will be input *Note: 2% damping needs to be multiplied by 2.0 to get 0.04 when using the PARAM,G entry. See the MSC.Nastran Quick Reference Guide for further information.

S10-79 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n If the amount of damping in the case study analysis is varied, the variation is visible in the response 6% 12% 18%

S10-80 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n Direct Transient Response n Example 2 u Assume there is a structure where 4% overall structural damping needs to be applied and the first significant mode is at 32.8 Hz u In addition there is a significant region made of Carbon Fiber Reinforced Plastic (CFRP) modeled using an equivalent orthotropic material, where the damping level needs to be at 10%. The significant mode in the CFRP is at 46.5 Hz u The damping terms are additive, therefore they are defined 4% overall and 6% in the CFRP elements u The overall damping coefficient is input as PARAM,G,0.08 u The CFRP damping coefficient is input on a MAT8 material card via the GE term set to 0.12 u The overall matching frequency is input as PARAM,W3,206.1 u The CFRP matching frequency is input as PARAM,W4,292.2

S10-81 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation 0.08 DAMPING IN DYNAMIC ANALYSIS (Cont.) n Direct Transient Response Data input via MSC.Patran 0.12

S10-82 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n Direct Transient Damping u A further example of the Case Study plate was run twice with total of 18% damping. l G set at 18% l G set at 12% and GE at 6% u The results are identical

S10-83 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n Direct Transient Damping 6% 12% 18% Note : Identical 18 % curves achieved by a) all G and W3 b) By 12 % G and W3, 6% GE and W4

S10-84 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n Direct Transient Damping n Checking Damping Results u The damping present in a transient analysis should be checked using the logarithmic decrement method for small damping u G=d/pi where d = ln (x1/x2) X1 and X2 are successive amplitudes n In the previous slide the values are u G1=.056 (red curve) u G2=.116 (blue curve) u G3=.174 (black curve) n Which match very well with input values

S10-85 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n Direct Transient Damping n Checking Damping Results u One of the common errors in defining structural damping is to calculate W3 or W4 wrongly (maybe by forgetting to input as rad/s and using Hz) n The influence of the error can be predicted graphically: Structural Damping, fs = iGku Equiv. Viscous Damping, fv = ibwu damping too high – non-conservative damping too low – conservative

S10-86 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n Transient Damping effect of errors in W3 W3=300 Hz Damping is too low W3=133 Hz W3=50 Hz Damping is too high

S10-87 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DAMPING IN DYNAMIC ANALYSIS (Cont.) n Direct Transient Damping n Checking Frequency Results u The Frequency content in a transient analysis should be checked by looking at the time period between clearly identifiable peaks where the influence of frequencies is obvious, after the loading input is complete u The Frequency content of the loading should be checked by looking at the response under the loading u In this case the dominant time period after loading is T = 7.71e-3 u Which equates to F= Hz (compared to Hz from a Normal Modes run) u This again emphasizes the need to know the natural frequencies even in a direct analysis

S10-88 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation WORKSHOP 17 DIRECT TRANSIENT ANALY OF CAR MODEL n Now please carry out Workshop 17 which analyzes the response of an automotive body when driven over a bump, using a Direct Transient Response Method. n Response is considered at the dashboard, drivers seat and roof positions. n The workshop will take you through step by step if you are unfamiliar with Nastran or 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.

S10-89 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRANSIENT RESPONSE n Now look at an alternative method of carrying out Transient Analysis, using Modal Coordinates n It has been witnessed that for very large models, with many time steps, the cost becomes high n One way to reduce the cost is to use the previously used principle. If relatively few Modal Coordinates are used to represent the Physical Coordinates and if careful about the damping terms, the problems to SDOF can be reduced significantly.

S10-90 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRAN RESP W/O DAMPING n Transform from modal to physical coordinates. n Ignore damping temporarily, [B] = [0]. n Substitute the transformation equation into the dynamic equation. Pre-multiply this equation by [ ] T.

S10-91 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation u where l is the modal mass matrix; it is diagonal l is the modal stiffness matrix; it is diagonal l is the modal force vector n Write the dynamic equation as a decoupled system u where k is the k-th modal coordinate k is the k-th modal frequency l N k is the k-th modal force MODAL TRAN RESP W/O DAMPING (Cont.)

S10-92 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Use the transformation from modal space to physical space, as before n Viscous damping (no structural damping) [ ] T [B][ ] is diagonal l where k is the k-th modal coordinate k is the k-th modal frequency k is the k-th modal damping ratio n N k is the k-th modal force MODAL TRAN RESP WITH DAMPING

S10-93 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation l Use Duhamels integral to solve for modal response as decoupled SDOF systems. n Duhamels integral MODAL TRAN RESP WITH DAMPING (Cont.) No initial conditions are allowed in MSC.Nastran for modal transient response for versions prior to MSC.Nastran V2004

S10-94 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation [ ] T [B][ ] is not diagonal l The modal coupled problem is solved using modal coordinates and utilizing direct transient response Newmark-Beta type numerical integration. n where MODAL TRAN RESP WITH DAMPING (Cont.)

S10-95 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Structural damping (no viscous damping, [B] =0) In the presence of either 1) explicit damping elements (CVISC, CDAMPi, CBUSH), or 2) structural damping ((g/ 3 ) [K], (1/ 4 ) g e [k e ), then u The damping term cannot be decoupled via orthogonalization u The modal transient equation must be solved using a time domain algorithm similar to the direct transient method, but in terms of modal coordinates u It is recommended to use the direct transient method if either of these types of damping terms are included MODAL TRAN RESP WITH DAMPING (Cont.)

S10-96 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation DATA RECOVERY MODAL TRANSIENT RESP n Recover physical response, e.g. {u}, as the summation of the modal response. u where {w} is a vector of internal forces [ ] w is a transformation matrix

S10-97 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRANSIENT RESPONSE n Modal Transient Response n How is the modal damping integrated into the analysis u Define damping vs. frequency pairs in a Nastran table called TABDMP1 u This forms a look-up table for the analysis, which then interpolates or extrapolates the table to find the value of damping bi at each modal frequency used in the analysis Note the extrapolation method in TABDMP1. Beware of extrapolating into –ve damping region in error TABDMP1IDTYPE F1G1F2G2F3G3-etc-ENDT g f (Hz)

S10-98 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRANSIENT RESPONSE (Cont.) n Modal Transient Response n Example 1 u Assume that there is a structure where a 2% overall structural damping via modal damping needs to be applied. u Input the damping via a TABDMP1 bulk data entry. The damping is flat across the frequency range for the structure, therefore only two damping vs. frequency pairs need to be defined. u The damping TYPE is G for structural damping u In addition the damping is called out in Case Control: SDAMPING = TABDMP199G ENDT

S10-99 NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRANSIENT RESPONSE (Cont.) n Modal Transient Response n Example 2 u Assume there is a structure where a 3% of a critical damping via modal damping needs to be applied u The damping TYPE is CRIT for a Critical structural damping definition (Damping definitions are further discussed on the next slide) u Damping is called out in Case Control as before: SDAMPING = TABDMP199CRIT ENDT

S NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRANSIENT RESPONSE (Cont.) n Modal Damping definitions n The method of defining modal damping can use one of three forms u StructuralG - the default u Percentage CriticalCRIT u Amplification factorQ n The relationships between these are: u CRIT = G/2Q = 1/G u Percentage Critical is the ratio between the damping value present, and the Critical damping Value. u The Critical damping Value is that which just avoids oscillatory motion

S NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRANSIENT RESPONSE (Cont.) n Modal Transient Damping n The use of Non-Modal damping, with or without Modal damping is permitted, but not recommended. u So it would be possible to have: l PARAM,G l PARAM,W3 l PARAM,W4 l GE on MATi card l CVISC or CDAMP elements l TABDMP1 called out by SDAMPING !!!!

S NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRANSIENT RESPONSE (Cont.) n Modal Transient Damping Patran permits entry of non-modal terms, but it is best avoided

S NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRANSIENT RESPONSE (Cont.) n Modal Transient Damping This is cheaper and more efficient for modal analysis Example: for 10% critical damping

S NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODE TRUNCATION n May not need all of computed modes. Often only the lowest few will suffice for dynamic response calculation. n PARAM,LFREQ gives the lower limit on the frequency range of retained modes. n PARAM,HFREQ gives the upper limit on the frequency range of retained modes. n PARAM,LMODES gives the number of the lowest modes to be retained. n Truncating high-frequency modes truncates high- frequency response. n Manual input is required for this in Patran via the Direct Text Input. u Example: PARAM, HFREQ, 100.0

S NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODE TRUNCATION (Cont.)

S NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation MODAL TRANSIENT VERSUS DIRECT TRANSIENT ModalDirect Small ModelX Large ModelX Few Time StepsX Many Time StepsX High Frequency Excitation X NonlineartiesX Initial ConditionsXX

S NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation n Now please carry out Workshop 4, which analyzes the response of a plate to a loading input, using the Modal Method. n The workshop will take you through step by step if you are unfamiliar with Nastran or 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 4 MODAL TRANSIENT ANALYSIS X Y Z psi over the total surface X Y Z

S NAS122, Section 10, August 2005 Copyright 2005 MSC.Software Corporation WORKSHOP 18 MODAL TRANSIENT ANALYSIS OF THE TOWER MODEL WITH SEISMIC INPUT n Now please carry out Workshop 18, which uses a modal transient response method to analyze the response of a tower structure, subject to a base motion input. n The base motion input is defined via an acceleration time history of a section of the El-Centro Earthquake. The time history is defined in an external data file. n The workshop will take you through step by step if you are unfamiliar with Nastran or 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.