Natural Frequencies Mode Shapes of a Cantilever Beam with Two Degrees of Freedom

1. Natural Frequencies & Mode Shapesof a Cantilever Beam with Two Degrees of Freedom

2. Objectives To determine the natural frequencies of a cantilever beam with two end masses To plot and animate the modes of vibration using Star Modal software

3. Equipment Needed FFT Analyzer Star Modal Software Beam with End mass C clamp Impact Hammer Accelerometer External power ICP Battery Power Unit Bees Wax Masking Tape

4. Equipment & Accessories

5. Using Multimeter

6. Beam Dimensions Measure the width, length and thickness of the beam Use the vernier calipers or the micrometer to measure the thickness Turn off the battery of the Calipers

7. Mass Measurements Weigh the mass of both the masses on the weighing scale(Make necessary assumptions regarding the mass of the beam and justify them in your report) Turn off the power after taking the measurement

8. Setting up the Beam with End Mass

9. Mounting the Accelerometer Use Bees Wax to attach the accelerometer to the Mass1, i.e, the outer mass Mounting direction indicated on the accelerometer by arrow Handle the Accelerometer with Care. It is Expensive Use Masking Tape to secure it to the beam when cables are attached. Note that the cable should not be taut after the set up

10. Connections1. Secure the beam with end mass using C-Clamp 2.Mount the Accelerometer to mass1 properly3.Connect the end of accelerometer to XDCR terminal of the ICP Battery 24.Connect the end of Impact Hammer to XDCR terminal of another ICP Battery15.Connect the Scope end of ICP Battery 1 to IN 1 terminal of the Analyzer card6.Connect the Scope end of ICP Battery 2 to IN 2 terminal of Analyzer card7. Connect the ICP Batteries to power source and setgain to unity initially Refer to Connections in Next slide

11. Connections

12. Starting Star Modal Software Click on the Shortcut to Star Icon to start the Star Modal Software A pop up screen will appear along with the main screen of the STAR modal software Click on Cancel, as we need to start a New Project, but not open an existing one

14. Creating a New Project Click on New Project A window appears Name the New Project and save it in the temp directory A new directory name will be created with the project name if the �Create New Directory� is checked.

15. Starting STAR Project ID is displayed Project Information may be entered for future references For determining the Mode shapes, the Test Setup is the default, Fixed Response The measurement units are in SI system The Driving point DOF indicates the direction of response, which is 1Z, where 1 indicates the point number in the given case.

16. Coordinates System Convention in STAR We need to define the coordinates for the given mesh The end with the end mass of the clamped beam is considered as origin (Point 1) X-axis is along the length of the beam, Z-axis(Response) is perpendicular to the width of the beam The beam has no mesh along the Y- axis, as the beam is designed as a Line element

17. Defining Geometry Click on Tables, Mesh Generator to get the window shown As we mesh the beam as a line element in the X direction for this experiment, check off the Activated option in the Y direction As we have two masses, we mesh the beam as two parts STAR designates the starting point as 1 by default

18. Defining Geometry Name the component Coordinate system used is �Rectangular� for the experiment Click Ok A confirmation message appears Click Ok Now click �Close� Clicking �Ok� may result in dual mesh or an error message

19. Assigning Coordinates Click Tables, Coordinates on the Menu Bar A default Coordinate table appears Click on Point 1, to define coordinates of Point 1 (0,0,0) in given case Point 2 has Coordinates (L1,0,0) whereL1 is the distance between two masses M1 and M2 Pont 3 has coordinates (L2,0,0) where L2 is the distance between mass M2 and the clamp end of the table

20. Saving Coordinates The assigned Coordinates may be saved by clicking on the File, Save or File,Save as options as shown for further reference

21. Setting Constraints The line element is fixed at the point 3 Hence give a value 1 to the Coefficient for Line 1 in the Z direction This constrains the Line element from any motion at the end, thus imposing the fixed end constraint

22. Saving Constraints The constraints applied may be saved either by the File, Save option or by File, Save as option for future references

23. Displaying Structure Click on Show Structure

24. Displaying the Structure Two windows pop up as shown The view control window enables to control the view direction,zoom etc. Close the View Control window Click, Animation and then Highlight

25. Displaying the Structure A Highlight window appears with a Line Check the �Point Number� in Highlight option Check �All� in Highlight Points The beam is now shown as a Line element with the respective point numbers

26. Displaying the Structure Note that the constrained end i.e, Point 3 is shown with a box,while Point 1 and Point 2 are denoted by solid points If the structure is displayed correctly, the window may be closed

27. Starting the Analyzer Software Minimize the STAR Modal Software window, at this point of time Do not close it, Repeat..do not close STAR Click on the Signal Calc Analyzer icon to start the Signal Ace Analyzer

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31. Menu Bar

32. Sampling Parameters Settings

33. Measurement Parameters Settings Frames indicate the number of averages collected,when test starts Averages is the number of measurements desired to be taken,in given case it is five(5) Type indicates the weightage given to the averages collected. Refer Help contents for detailed explanation Set Type to Stable or Stable repeat for the given experiment

34.  Setting Averages, Type & Trigger  Trigger indicates the source which initiates collection of data Free Run option when selected causes the system to start data collection without waiting for any trigger Source indicates triggering from a given data source The Input option needs to be selected for the given test as the Impact Hammer acts as the Force Input

35. Sampling Parameters Settings FSpan indicates the frequency span or frequency range of interest of experiment Default value is 10000Hz FSpan Value to be set after calculating value from theory Lines indicate the resolution desired Higher resolution implies more data, large file size and longer time. Hence a compromise needs to be made.

36. Sampling Parameters In the given case, the frequency span has been set to a value of 312.5 Hz The resolution may be set to 800 Note that you can change the values by dragging the slider or by manual entry Ensure to press the Return key in case of Manual Entry The Overlap field may be ignored currently

40. Input Channel Settings Several Windows are available for measurement of various signals such as Hanning, Rectangle,Flat Top etc. Refer Help contents for more details Set Ch#1 window to Force as Hammer is connected to Channel 1 Set Ch#2 window to Response as Accelerometer is connected to Channel 2

42. In the given case, we trigger off Channel 1, as channel 1 is the HammerToo high a trigger level requires a large excitation leading to nonlinear vibration whereas Too Low a trigger level can cause triggering even without any impact

43. Input Channel Settings Click the Info tab on the Input Channel Settings It Displays the Current Point, Pt Inc(Point Increment) and the Channel Number In the given experiment, we excite the beam with the hammer at the first mass and then the second mass keeping the reference accelerometer at the first mass(Mass1) Hence we increment the Current point of Ch#1 by 1 and Current point of Ch#2 by zero, the force input being in �Z direction As per the notation in STAR, the first point is denoted by 1

44. Input Channel Settings The Info tab in the Input Channel settings remains inactive(gray) until you check the Point/Direction On,in the View,Run options. The active tab is shown in white as below The Cur Pt is incremented to 2, for Ch#1 after the five averages are taken

45. Saving the Test & using Layout Manager Save the test at this point of time by clicking on the File, Save Menu. Save the test in the Temp directory with some unique file name Click on Display => Layout Manager to get the screen shown above and Click on My Layout which may be renamed also Check options Preview,Run, Review, Auto Range and Click Ok. This enables to save and retrieve the existing settings and graphs to be displayed later even in case of some unexpected system/software crash/failure

47. Displaying Graphs Go to the Menu Bar Click on Display Click on New Graph, It displays the above screen

48. Graphs to be Displayed Display the Live X1 and Window Shape W1 graph as described earlier Live Signals with windows super posed represent the actual signal as in an oscilloscope The graph title can be changed in the same state by unchecking the Default title option

49. Graphs to be Displayed Display the Live X2 and Window 2 Graph The live time history signals with the windows superposed are used to select the appropriate window parameters and also check for any double impact or hits during the experiment

50. Setting Graph Attributes Set the necessary Graph attributes Set the necessary Axis attributes Tile the Windows Horizontally for better display For further details refer to the Help conents on Graph Attributes

51. Graphs to be Displayed Display the C 1,2 graph from the C x,y Coherence function of the base signals in the Signal Selector. The coherence should be as close to 1 as possible. Too low a coherence indicates error in measurement Display the G1,1 graph from the G x,x Average Auto Power Spectrum function. It may be noted that the fall in the Magnitude should not be more than 20 to 30dB in the frequency range of interest Also display the H1,2 graph in case it has been deleted. The peaks in H1,2 correspond to the natural frequencies of the system Use the �Tile Windows Horizontally� function from the �Window� option from the main menu bar to display all the graphs in an orderly fashion Save the test once again.

52. Setting up File Transfer to STAR Click on View, Signal Map The Following window pops up Click on the �+� sign to expand the tree

53. Setting up File Transfer to STAR Click on �+� sign of Allocated Signals

54. Setting up File Transfer to STAR Click on �+� sign of Base Signals to further expand the list of signals

55. Setting up File Transfer to STAR Left Click on �Export Targets� icon Now right click on the �Export targets� icon and a window pops up Check the SMS Star files and Click �Ok�,as the output files need to be exported to STAR for plotting mode shapes

56. Setting up File Transfer to STAR Left Click on �SMS Star Files � icon below Export Targets Now click on the �H x,y Transfer Function� icon in the �Allocated Signals�and drag the H 1,2 by keeping the left mouse button pressed and leave the button when it reaches the SMS Star Files(Exporting Transfer Function to STAR) Note that the SMS Star files icon has a �+� sign which on left click shows the H 1,2 icon below it

57. Setting Up File Transfer to STAR Right click on SMS Star Files icon A pop up window appears Leave the Run Folder option and Saves/Run options as �Overwrite�(Default) The Run Folder name is the name of the folder to which the Transfer Function files selected earlier will be transferred to Left Click on �Browse�

58. Setting Up File Transfer to STAR Select the Root Folder to be the same as the folder where STAR Project was saved initially This enables all the required files to be in one directory If the �Create a new folder� is Checked on, a New folder will be created in the Selected Directory The Signals will be saved with a name,as indicated in the �Saved Signals Name� box Click Ok

59. Completing File Transfer to STAR Click Ok to complete the File Transfer Process

60. Before You start the Test.. Click on View => Run Options to set the run options Each measurement taken is saved with a run number shown at the top of your screen Check all the options and click OK Check the Point/Direction ON Note that the Info Tab on the Input Channel Settings is activated Save the test again

61. Starting the Test After assuring the necessary connections, graphs and settings in the software, click on the Start button At the left bottom corner of the screen you can see an instruction saying �Waiting for Trigger� Observe that the Frames counter at the top will read �0� initially

62. Observe that Cur Pt on the Info tab is 1 for Ch#1 The system is waiting to be triggered

63. Running the Test Strike the Mass1 at the center gently and ensure that there is no double hit If the strike is clean, a sharp single spike can be observed in the Live X1,W1 window The ADC indicators will display green and the number of frames is incremented to 1 �Waiting for capture completion� and subsequently �Waiting for Trigger� instructions can be observed at the left bottom corner of the screen Repeat the above steps till number of averages/frames are equal to 5(for given expt.)

64. Oops..Some Problem!!!Things may not be smooth as we expect ADC indicators turn red indicating overrange Also observe the warning �Filters Settling� at the left bottom corner of the screen Allow the filters to settle down, try to change the values in the ADC indicators by clicking the adjust buttons shown and strike the mass again Still no improvement� Try to change the hammer tip and strike the beam with mass again after the filters settle Filters not settling i.e, ADC indicators still in red for a long time�

65. Over range Problem Sometime the Impact may be too high for the range set and it may take long for the filters to settle In the given case, stop the test by pressing the �Stop� button. End the test by clicking �End� Click �AutoR� button to get the ADC indicators back to normal Adjust/increase the range by clicking on the adjust arrows Check all other settings including �Run Options� Save the test and Click on �Start� to restart the experiment If the graphs displayed disappear at any point of time click on �My Layout� from the scroll down Display menu to retrieve your layout

66. No change in Frame Count?? The number of frames may not be incremented for any input you give. Check for all the connections and settings Check the �Trigger level�in the Channel Input parameters. Adjust it so that the trigger in not too high or too low Try to strike the mass again If there is no change, try increasing the gain by turning the knob on the ICP Battery Power unit,corresponding to the Hammer Repeat the process

67. Once the Mass is hit by the hammer and the signal is fine, an instruction saying �Waiting for capture completion� appears Once the signal is captured the software prompts for trigger, when the next hit should be made

68. After the five averages for the first mass are over, an Auto Save message appears Click Ok Observe that now the Cur Pt of Ch#1 is incremented to 2 after you click �Yes�,indicating that you should now excite Mass2 Also observe the instruction �Waiting for Trigger�

69. Running the Test Now strike the Mass2 gently and ensure that there is no double hit Repeat the experiment as in the previous trial till the five averages are taken Hit the mass after completing stopping the vibrating mass Wait for the �Save Measurement Number 2� window to pop up Click �Yes�

70. Minimize Signal Calc and Open STAR Minimize the Signal Calc Software window Do not Close it Maximize the STAR Modal Software window now

71. Identify the Modes Click on the Identify Modes icon in the STAR software The Measurement and Curve Fit Panel windows pop up Click on File, Open in the Measurement window to retrieve the transferred files from Signal Calc to STAR

72. Identify the Modes Open the respective directory where the transferred file are saved with an extension �.frf� where frf stands for �Frequency Response Function�(Transfer Function referred to as above by STAR software) Select either of the .frf files and Click Ok

73. Curve Fitting Ignore any warning message Click �Yes� on the message The measurement window now shows a plot and gets renamed as �Frequency Response�

74. Curve Fitting Change the Units near the left side of the plot from �Real� to �Log Mag� by clicking on �Real� Check �Both Traces� The Frequency Response window now shows a plot with Log Mag on Y �axis and Frequency(Hz) along the X-axis

75. Curve Fitting The modes may be identified from the dominant peaks Bands have to be set for curve fitting the mode shapes in the frequency range of interest Set the cursors to fit the first peak in the band and Click on Set Change the Band number to 2 and set the cursors to fit the second peak Click on Set again Check the Fit Function and List results on

76. Curve Fitting Check the �Autofit� option Click �Fit� after the bands are set Autopreferences window is shown Since we have response only in the Z direction uncheck X,Y,R,T,P Mode shapes for all the points are desired, hence check �ALL� Click Ok

77. Curve Fit & List Results The Frequency response window now shows the Polynomial fitted curves A Frequency Results window pos up with the corresponding frequency and damping values Both the tables may be saved from the �File, Save or Save As� options The windows may be closed after saving the results

78. Plotting Modeshapes Animated plots of mode shapes may be obtained by clicking the �Show Structure� icon The mode shapes are depicted The animation may be adjusted as per requirements Mode shapes may also be varied by clicking the respective Mode number in the �View Control Panel� The mode shapes may be printed by Clicking on �Edit, Still/Copy/Print� option in the Show Structure Menu A frame wise animation can also be viewed by adjusting the Animation Controls Once the Mode Shapes have been printed and the Frequency Results are noted, Click on �Save Project�

79. Plotting Modeshapes Click on �Show Structure� A Frequency Domain animation window appears with a mode number and a corresponding animated mode shape The mode number can be changed by controls in the View Control panel Mode shapes may be printed by clicking on the Edit button

80. Plotting Modeshapes Click on �Show Structure� A Frequency Domain animation window appears with a mode number and a corresponding animated mode shape The mode number can be changed by controls in the View Control panel Mode shapes may be printed by clicking on the Edit button

81. What is Success in the Experiment You should be able to get the desired Mode shapes from STAR software The value of the first natural frequency from the Frequency results of STAR and H1,2 graph of Signal Calc must agree with the theoretical results The coherence should be as close to 1 as possible in the Signal Calc Software The magnitude of G 1,1 should not drop more than 20 to 30dB in the frequency range of interest in the Signal Calc Software The Live X1,W1 graphs should not indicate any double hits in the Signal Calc Software Identify the possible sources of error and include in the discussion

82. Last..but not the Least You are done with the experiment�but do your house keeping part. Close both the Software windows after saving the test results Remove all the connections Place the equipment in their respective boxes/holders Turn off the power supply to the ICP Battery power units and the Weighing scale Close the software and log off from the workstation

83. Reviewing Results Later To review the results at a later point of time, Open the Signal calc software Click on Test =>Review Select the test by browsing the corresponding directory and filename Open the run number desired to retrieve the results Note that generally the latest measurement will be saved with the maximum Run number and maximum Save number For reviewing results in STAR, Click on Star icon, open the respective Project name and Click on Tables, Results to view the results

84. End