S14-1 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation SECTION 14 RANDOM ANALYSIS

S14-2 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation

S14-3 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CLASSIFICATION OF DYNAMIC ENVIRONMENTS n So far in this course we have dealt with Deterministic Loading Types – using either Transient Response or Frequency Response. n We now look at Random Loading – and the subset, which is the Stationary, Ergodic type. n What does this mean? Examples appear on the next slides. Random Stationary Nonstationary Ergodic Deterministic Periodic Transient Simple Harmonic Shock Spectra

S14-4 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation EXAMPLES OF RANDOM DYNAMIC ENVIRONMENT n Stationary Random u The mean is constant and the nature of the signal remains the same. n Non-stationary Random u The mean may vary and the nature of the signal changes. In this example there are bursts of loading, and the characteristics of each burst are different. u It is possible to break up a non-stationary response like this into several near stationary responses.

S14-5 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation ERGODIC RANDOM DATA n Ergodic Random u A sample can be taken out of any signal, or across a signal and it will be representative of the event u This example could be aircraft turbulence across 4 flights in similar conditions with similar aircraft

S14-6 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation RANDOM RESPONSE ANALYSIS n Random vibration is vibration that can be described only in a statistical sense. Its instantaneous magnitude at any time is not known; rather, the probability of its magnitude exceeding a certain value is given. n Examples include earthquake ground motion, ocean wave heights and frequencies, wind pressure fluctuations on aircraft and tall buildings, and acoustic excitation due to rocket and jet engine noise. n MSC.Nastran performs random response analysis as postprocessing to frequency response. u Inputs include the output from a frequency response analysis as well as user-supplied loading conditions in the form of Power Spectral Densities and Cross Spectral Densities. u Outputs are response Power Spectral Densities, Autocorrelation Functions, Number of Zero crossings per unit time, and the RMS values of response.

S14-7 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation RANDOM RESPONSE ANALYSIS (Cont.) n The Input Data required was described as u Output from a Frequency Response Analysis u User Defined PSD (Power Spectral Density) n Output from Frequency Response Analysis? u It is necessary to know the relationship between an arbitrary unit loading input and the response at a point u This in essence is a Transfer or Gain Function u The Frequency Response at a point is used to assess how the structure would respond in a deterministic manner u The effect of the randomness of the loading input on the response is applied via a PSD n User Defined PSD? u This is a way of defining the nature of the random signal amplitude and its frequency content u Fuller details on the next slides

S14-8 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation WHAT IS A PSD ? n Imagine having a random loading which needs to be investigated u Assume the mean is zero u Define the loading as acceleration in g +g 0.0 -g Time n Square the signal to get a non-zero mean Time g2g2 Mean square value

S14-9 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation WHAT IS A PSD ? (Cont.) n It can be shown statistically that the Square Root of the Mean Square Value (RMS) is: Equal to the standard deviation of a Normal distribution One standard deviation or the RMS value of the signal is the value that has a 68.3% chance of occurring 3 gives a probability of 99.73% chance of occurring n There is now a measure of the mean amplitude of the signal as its RMS n How is the signal further characterized? u Apply a filter to the original signal to eliminate all frequencies above say f 1 u Square the signal and find the Mean Square Time g2g2 Mean square value below f 1

S14-10 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation WHAT IS A PSD ? (Cont.) Time g2g2 Mean square value below f 3 n Continue to apply a reducing upper limit on f u As each frequency range is cut off, the Mean Square value will be decreasing g2g2 Mean square value below f 4 g2g2 Mean square value below f 5

S14-11 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation WHAT IS A PSD ? (Cont.) Frequency n It is now possible to plot the variation of Mean Square with f i g2g2 Mean square value Total Mean square value......f 5 f 4 f 3 f 2 f 1 n This type of plot is called the Cumulative Mean Square (CMS) plot, or if the root terms are taken then it is the CRMS plot u It shows the frequency content of the random signal u In this case, for example, the MS value jumps considerably between f 3 and f 2 decreasing frequency content

S14-12 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation WHAT IS A PSD ? (Cont.) Frequency Hz n Now take the gradient of the Mean Square plot g 2 /Hz......f 5 f 4 f 3 f 2 f 1 n This type of plot is called the Power Spectral Density (PSD) u It shows the frequency content of the random signal, more directly than the CMRS u Again the g 2 /Hz value jumps considerably between f 3 and f 2 u The square root of the area under the curve is the RMS

S14-13 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation WHAT IS A PSD ? (Cont.) Frequency Hz n A prime contractor will typically take many random input loadings and look at the response at a key point in a structure using a set of response PSDs g 2 /Hz n Enveloping this set will produce a Power Spectral Density (PSD) specification u The final envelope will depend on many factors u It will be a balance between safety and cost u Effect of notching is important Frequency Hz g 2 /Hz......f 5 f 4 f 3 f 2 f 1

S14-14 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation 1.0 Frequency 10.0 Frequency SUMMARIZING THE INPUT Frequency Output spectrum scales similarly… 5.8 Frequency Input spectrum scales like this… RR (PSD) Input RR (PSD) Output FR Input FR Output Frequency Response (FR) Random Response (RR)

S14-15 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation 1.0 Frequency 10.0 Frequency SUMMARIZING THE INPUT Frequency RR (PSD) Input RR (PSD) Output FR Input FR Output Frequency Response (FR) Random Response (RR)

S14-16 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation HOW ARE RANDOM RESULTS USED ? n RMS values u Square Root of the Area under XY curve if plotting PSD u Plot as contours for stress, etc. Multiplied by 3 to give 3 probability of exceedance u RMS gives mean stress for fatigue n PSD Plot u Shows response compared to input PSD u Important frequencies are seen n Number of positive crossings u A statistical calculation predicts how many zero crossings will occur per unit time of response u This is also known as apparent frequency and gives cycle count for fatigue n Cumulative RMS plot u Shows which frequencies contribute the most

S14-17 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation n Autocorrelation plots u Gives an indication of the degree of randomness of a response u The signal is multiplied by itself with different phase shifts u If a signal is non-random (sine function, square wave etc.) then a broad correlation is seen u If a signal is highly random then the autocorrelation output is very peaky HOW ARE RANDOM RESULTS USED ? (Cont.)

S14-18 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation MSC.RANDOM OVERVIEW n In this course, use MSC.Random as the tool to carry out Random Analysis n MSC.Random post processes on the back of u MSC.Nastran frequency response analysis or, u MSC.Nastran normal modes analysis n Interactive Random Analysis u Calculations done on the fly (w/o having to re-run MSC.Nastran) u RMS fringe plots u Specialized XY-Plotting

S14-19 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation MSC.RANDOM - FLOWCHART MSC.Patran bdf MSC.Nastran xdb MSC.Random psd

S14-20 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation MSC.RANDOM – FLOWCHART (Cont.) Step 1:.xdb (post,0) Harmonic Analysis (MSC.Nastran) Step 3: Step 2: Random Analysis (MSC.Random) XY Plots RMS Plots Random Input File.pat file (Binary) RMS Analysis

S14-21 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY n RANDOM VIBRATION ANALYSIS OF A SATELLITE u The purpose of this case study is to show the use of MSC.Random in performing a Random Vibration analysis. u A satellite structure model is to be excited by the launcher vehicle loading as a random acceleration loading. Both vertical and lateral loading are to be considered. u The response at a location of the satellite, where it is intended to mount a PCB, is to be determined. u First perform a modal frequency response analysis using the method shown previously. u Second, perform a random analysis using MSC.Random. The results from the frequency response analysis and a supplied input PSD are to be used. u Post process the results, at the model location of interest, using MSC.Random.

S14-22 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY n Case study steps 1. Import an MSC.Nastran Input file that contains the representation of the satellite model. The file name is satellite.bdf. 2. Create a frequency dependent field of amplitude 1.0, over the frequency domain 1.0 Hz to Hz, for the subsequent frequency response analyses. 3. Create two load cases, one named vertical acceleration and the other named lateral acceleration. 4. Apply an enforced unit acceleration motion at the bottom of the satellite model in the axial or in a lateral direction. Use the field created during Step Submit the model to MSC.Nastran twice to do a frequency response analysis for each of the two directions. 6. Create a frequency dependent field for the input PSD. 7. Open MSC.Random under MSC.Patran Tools: Random Analysis. 8. Select an.XDB results file from a frequency response analysis, and perform a random vibration analysis using MSC.Random. 9. Post process the results using MSC.Random to create acceleration versus frequency plots for various locations.

S14-23 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation The model is imported as usual. Create a non spatial field for the frequency response analyses. Enter frequency response for Field Name. Select Frequency (f) as the active independent variable. Click on Input Data button. Enter the values shown in the table. CASE STUDY

S14-24 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation Create a load case for the vertical acceleration enforced motion Enter vertical acceleration for Load Case Name. Change load case Type to Time Dependent. Click on Assign/Prioritize Loads/BCs button. Select Displ_spc1.3 from Select Individual Loads/BCs window. CASE STUDY

S14-25 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Create another load case, that for the lateral acceleration enforced motion Enter lateral acceleration for Load Case Name. Make it Time Dependent Select Displ_spc1.1 from Select Individual Loads/BCs window.

S14-26 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Create the lateral acceleration load Make lateral acceleration the current load case Enter lateral acceleration for New Set Name. Enter for Trans Accel and select frequency_response for Time/Freq. Dependence field. Select the nodes along the bottom edge of the exhaust cone.

S14-27 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Create the vertical acceleration load Make vertical acceleration the current load case Enter vertical acceleration for New Set Name. Enter for Trans Accel and select frequency_response for Time/Freq. Dependence field. Select the nodes along the bottom edge of the exhaust cone.

S14-28 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Submit the vertical acceleration load case for frequency response analysis Enter satellite_vertical_acc for the job name. Select FREQUENCY RESPONSE and Modal formulation. Change the Wt-Mass Conversion to Change the Number of Desired Roots to 20

S14-29 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Define up subcase Select vertical acceleration. Click on Subcase Parameters… Click on DEFINE FREQUENCIES. Enter the values shown in the table.

S14-30 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY a b c Select Crit. Damp. (CRIT) for Modal Damping Click on DEFINE MODAL DAMPING. Enter the values shown in the table.

S14-31 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Click on Output Requests Select Accelerations from the Select Result Type box

S14-32 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Click on Subcase Select Select vertical acceleration from the top box Unselect Default from the Subcase Selected box Run the analysis

S14-33 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY The results of the vertical acceleration enforced motion are shown for the grid of interest, Node 3326 The plot has been enhanced using XYPlot

S14-34 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Node 3326 The results for the vertical acceleration frequency response case are shown at 22.2Hz. The dominant motion is a vertical motion of the satellite, with most of the deflection taking place in the base support ring. The ring acts rather like a vibration isolator and filters out the vertical input. The vertical case is discounted now and no random analysis is done on this input.

S14-35 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Submit the horizontal acceleration load case for frequency response analysis Click on the satellite_vertical_acc in the Available Jobs box. This will allow Patran to use same setting for Solution Type as those used in the satellite_vertical_acc analysis. Change Job Name to satellite_lateral_acc. Repeat the same procedure as before, but choose the lateral acceleration subcase for this analysis job. Click on Subcase Select. Select lateral acceleration from Subcases For Solution Sequence box and unselect Default from Subcases Selected box.

S14-36 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY The results of the lateral acceleration are shown for the grid of interest, Node 3326 The plot has been enhanced using XYPlot

S14-37 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Node 3326 The results for the lateral acceleration frequency response case are shown at 22.2Hz. The dominant motion is a bending motion of the satellite, with large deflection in the base support ring.

S14-38 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Create a non spatial field for the MSC.Random analysis Enter psd for Field Name. Select Frequency (f) as Active Independent Variable. Click on Input Data button. Enter the values shown in the table. Use Fields: Show to check the data.

S14-39 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation PSD (g 2 /Hz) Freq. (Hz) Input PSD CASE STUDY Care must be taken with the input PSD format It is usually assumed that the definition is on a LOG- LOG scale. This assumption must be checked. Plotting the field using XY Plot requires both axes scales set to LOG. The MSC.Nastran PSD definition must be set to LOG input. Note carefully whether input is g or acceleration units.

S14-40 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY PSD (g 2 /Hz) Freq. (Hz) Input PSD To get an optimum plot for checking the PSD input: Set Y-axis to a LOG scale. Use semi-Auto method. Use lowest number; in this case This is -2 *log (the BASE power) Specify number of cycles; in this case.010 to.1, and.1 to 1 is two cycles. Do the same for the X-axis. Pick tick marks and Grid lines as required.

S14-41 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Open MSC.Random MSC.Patran Tools: Random Analysis. Change the Action from Freq. Response to RMS Analysis.

S14-42 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation n A random analysis (RMS Analysis) uses the results from a frequency response analysis. If a frequency response analysis has not been performed prior to doing a random analysis, select Freq. Response first. n If a frequency response analysis has not been done it is necessary to select the loading type u Base acceleration w/ large mass u Applied force(s) u Acoustic pressures CASE STUDY

S14-43 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation n Loading type for frequency response analysis from within MSC.Random u Base Input l Enforced acceleration at a single enforced (base) point n Use RBE2 where the single base point is the independent node and the other points, at the base of the model, are the dependent nodes n Use large mass method, where the large mass is at the single base point. The large mass is ~ 1e6 * total mass of the structure. n Directions selected CASE STUDY

S14-44 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation n Loading type for frequency response analysis from within MSC.Random (continued) u Force Input or Acoustic input l Select pre-defined load case CASE STUDY

S14-45 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Setup the model for random analysis Choose RMS Analysis Click on Select XDB File. Select satellite_lateral_acc.xdb (the results from the previous frequency response analysis) Select Random Input. Change Random Input Method to Single Case. Click on the Excited Set field and select 1:LATERAL ACCELERATION from the Available Subcases box. Click on Input Field field and select psd.

S14-46 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation Select Random Input Method to be Single Case. Clicking on Excited Set field will bring up a list of Available Subcases. The frequency response analysis should be there. Clicking on Input Field field will give a list of all fields, and the PSD definition field should be there. The complex X input is the scale factor. Select Auto Spectral Density Set axes as appropriate; in this case the input is LOG – LOG. CASE STUDY

S14-47 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation Other Options: Select Random Input Method to be Existing RANDPS File This will allow the user to select a.inp file, defined for MSC.Random as a Nastran.bdf fragment with RANDPS data defined CASE STUDY

S14-48 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY a b Create XY Plots of the PSD Response: Change Action to XY Plots. Select Node 3326, which is where the PCB board will be located. Change the Res. Type to Accel. Set the Plot Scale to 1.0 Change Component to DOF 1. Change the Plot Type to PSDF.

S14-49 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Note: All labels, gridlines, and scales are set automatically. RMS is 5.774g So the safe g limit at 3*RMS is 17.32g The apparent frequency is 22.9 Hz, showing that Mode 1 dominates

S14-50 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Base input and full PSD plotted Base Input Full PSD Analysis only up to 50 Hz Overlay the base input and see the effect of the input PSD. From the previous work on modal analysis and effective mass of this structure, it is assumed 50 Hz is a valid cutoff (for the first 10 modes)

S14-51 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Another way to display some results is to use MSC.Patran Results and create an RMS fringe plot. The result case is accessed by the XDB attachment. The resulting RMS plot is an RMS acc magnitude plot. The graphical result of g RMS agrees.

S14-52 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY From the RMS fringe plot, it is visible that the panel local mode plays an important part in the RMS response. If there is a component located there, it will see the highest loading environment of 7.71 g RMS. To investigate further it is possible to do a PSD plot of this position (grid 3606) and see that the local mode does indeed play a major role with the first bending mode. Out of interest, a grid on the support skirt is investigated and it can be seen it has a low RMS value and the bending mode dominates.

S14-53 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY Based on this analysis, it is possible to provide a subcontractor with a PSD specification which is derived by enveloping the PSD response that was obtained. In the workshops which follow, the input PSD for the Printed Circuit Board is based on this type of analysis. The question could arise however about the effect of the original PSD input over the range greater than 50 Hz – could it have been significant? This is left to the student to investigate. Also note that an input PSD with a bias to the lower frequencies would be a far more damaging environment in our case.

S14-54 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation INPUT FORMAT

S14-55 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation INPUT FORMAT (Cont.)

S14-56 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation INPUT FORMAT (Cont.)

S14-57 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation INPUT FORMAT (Cont.)

S14-58 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation n Executive Control Section SOL(required) n Case Control Section RANDOM(selects Bulk Data RANDPS, RANDT entries and entries for frequency response, and must be above the subcases) n Bulk Data Section RANDPS(PSD specification) RANDT1(autocorrelation time lag entries for frequency response) INPUT FORMAT (Cont.)

S14-59 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation RANDOM ANALYSIS RECOMMENDATIONS n Most spectra are given as a log function. Use the log features on the TABRND1 entry if PSD is given in log scale. n Always generate the output PSD at the input location if possible. n Plot the output PSD. Do not use the summary output blindly. n Use several frequencies in the vicinity of each mode. For the modal method, a combination of FREQ1 (or FREQ2) and FREQ4 usually works best. n For low frequencies (

S14-60 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation WORKSHOP 9 - RANDOM ANALYSIS USING MSC.RANDOM n Please carry out Workshop 9 n This workshop uses MSC.Random to calculate the response of a simple plate structure n Please do not hesitate to ask your tutors advice.

S14-61 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation WORKSHOP 11 - RANDOM VIBRATION ANALYSIS OF A SATELLITE USING MSC.RANDOM n Please carry out Workshop 11 n This workshop uses MSC.Random to calculate the response of the satellite structure shown in the case study. n Please do not hesitate to ask your tutors advice.

S14-62 NAS122, Section 14, August 2005 Copyright 2005 MSC.Software Corporation