Free vibration of cantilever beam FREE VIBRATION OF CANTILEVER BEAM PROCEDURE

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Elisabeth Mosley
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FREE VIBRATION OF CANTILEVER BEAM PROCEDURE AIM Determine the damped natural frequency, logarithmic decrement and damping ratio of a given system from the free

critical damping of the system and undamped natural frequency of the system NOTE: TO CARRY ON THE EXPERIMENT, LabVIEW RUNTIME ENGINE IS REQUIRED.

1 FREE VIBRATION OF CANTILEVER BEAM PROCEDURE AIM Determine the damped natural frequency, logarithmic decrement and damping ratio of a given system from the free vibration response Calculate the mass of the system actively participating in dynamics Determine the equivalent viscous damping present in the system Calculate critical damping of the system and undamped natural frequency of the system NOTE: TO CARRY ON THE EXPERIMENT, LabVIEW RUNTIME ENGINE IS REQUIRED. DOWNLOAD IT FROM HERE and install. PROCEDURE: Fig 1: (a) Schematic of the experimental setup; (b) Equivalent engineering model; (c) Lumped parameter system 1. Click on the NEXT button

The OFFLINE experiment, however, allows the user to work with the saved set of data (Saving of the data and the results is

2 2. A new tab is opened, which gives the user the option of switching on between the ONLINE mode and the OFFLINE mode. ONLINE mode gives users the option to conduct the experiment. The OFFLINE experiment, however, allows the user to work with the saved set of data (Saving of the data and the results is explained further). 3. See to it that the option is toggled to ONLINE mode to conduct the experiment. Once the ONLINE mode is switched on, press the START (#3a) button and proceed further by clicking on the NEXT (#3b) button.

ONLINE and OFFLINE Modes: For the USER to conduct an experiment, he/she must be connected to the SOLVE lab servers at NITK Surathkal. For this, the USER must be in the ONLINE mode.

3 ONLINE and OFFLINE Modes: For the USER to conduct an experiment, he/she must be connected to the SOLVE lab servers at NITK Surathkal. For this, the USER must be in the ONLINE mode. The user will be allowed to save the results of the online experiments and use the same for further analysis in OFFLINE mode. If the OFFLINE mode is switched ON, then the user will NOT be connected to the servers. However he/she can relook at the results in the form of graphs and other calculated values. For this to happen, the user MUST have a Saved Data of the same experiment. More details of saving the data is provided in the subsequent stages (#8) 4. Ensure that the CONTROL mode is highlighted. A detailed description of the CONTROL and the VIEW mode is as given below 5. See to it that the CONNECTED indicator is highlighted. This gives the confirmation that the user is now connected to the server and can perform the experiment by clicking the NEXT (#5a) button. CONTROL MODE: This mode allows the USER to perform the experiment. Users in this mode can actually perform the experiment for a specified time as indicated. It has to be noted that ONLY ONE user is allowed to be in the CONTROL mode at any instant. VIEW MODE: Users in this mode can view the experiment which is being conducted by the CONTROL MODE user who is having the privilege to perform the experiment. The VIEW mode users, can still capture the graph and data which is obtained by the CONTROL MODE user.

4 6. Now, the user is required to switch ON the electromagnet to induce an initial displacement. 7. Once the user clicks the switch on button, a pop up opens which indicates the user to wait until the data is acquired

5 8. Once the data is acquired, the screen looks like the image shown below. Trigger the electromagnet and wait for the graph to be plotted. If the user is satisfied with the quality of the data acquired, he/she can stop acquiring the data by clicking on the STOP acquisition button. Else if the graph is not as per the requirement, the user can retrigger the electromagnet. This can be done for three times in succession for a fixed duration of 120 seconds. Trigger the electromagnet BEFORE pressing the Stop Acquisition button. Else re-triggering cannot be done. NOTE: The time available for each of the users for a particular experiment is given in the slot Time left for Data Acquisition. o The maximum number of trials available for each user is three o Each user will be logged out in either of the following two cases: If the number of trials exceeds three If the Time Left counts down to zero SAVE DATA (#8a): This option allows the user to SAVE the acquired data for further analysis. Users can relook into the graphs as well as the numerical values obtained by conducting the experiment. To use the data, the user needs to exit the file and choose the OFFLINE mode. When prompted for the saved file, the same can be uploaded. 9. Proceed to the next step by clicking on the NEXT button.

6 10. By using the graph, the required parameters can be found. o First bring the cursors to the ORIGIN by typing the X and Y values as 0,0 in the (#10 a) slot provided o Now move the vertical and the horizontal axis to the peak value of the first curve as shown in (#10 b) (This is y 0. Note this value) o o o o Next the axes are now moved on to another peak amplitude (Say third peak) as shown in (#10 c) (This is y n. Note this value) and the values of X and Y are noted down as shown in (#10d), Amplitude values are in Y axis and Time on X. Now from the value of the logarithmic decrement, the value of Damping Ratio is found by using the formula provided in the table. From the graph, find the time period with the help of axis (Difference of time in consecutive x-axis) and then calculate the frequency. This frequency is the Damped natural frequency. Once the damped natural frequency is calculated, calculate the natural frequency from the formula table given below.

PARAMETERS TO BE CALCULATED FORMULA TO BE USED UNITS Logarithmic decrement Damping factor δ = 1 n ln (y 0 y n ) wherein y0 and yn are the amplitudes 1 ζ = 1 + ( 2π δ )2 Damped vibration time period τ

7 PARAMETERS TO BE CALCULATED FORMULA TO BE USED UNITS Logarithmic decrement Damping factor δ = 1 n ln (y 0 y n ) wherein y0 and yn are the amplitudes 1 ζ = 1 + ( 2π δ )2 Damped vibration time period τ d = t 1 t 0 Seconds Damped natural frequency f d = 1 τ d Hz Damped natural frequency ω d = 2πf d Rad/Sec Natural frequency of the system ω n = (1 ζ 2 ) Natural frequency Stiffness (Mass m is the total mass involving in the dynamics. It has to be calculated by summing the mass of beam as well as the sensor ) Critical damping f n = 2π ω n ω d k = ω n 2. m c c = 2 mk Rad/Sec Hz N/m Ns m Equivalent viscous Damping coefficient of the system c = ζc c Ns m

To obtain the results, various tools are available in the form of graph legends (Pan, Zoom, etc). The values are now to be entered in the CALCULATE section as shown in (#10e).

8 To obtain the results, various tools are available in the form of graph legends (Pan, Zoom, etc). The values are now to be entered in the CALCULATE section as shown in (#10e). Once this is done, click on the SUBMIT button. Note that the submit button is to be pressed ONLY when the user is sure of the answer. Once submitted the answers cannot be reverted. 11. The response message is seen once the data is SUBMITTED. Click YES to continue. 12. Upon successful submission of the answers, click NEXT button to proceed further.

Next the user has to calculate the values of the stiffness and the damping

9 13. The user is now able to compare the calculated values with the actual values as shown. 14. Click on the NEXT button to proceed further. Next the user has to calculate the values of the stiffness and the damping coefficient with the available values of the mass. The formula list is available in the table.

Once the answers are submitted, a pop-up window asks for the confirmation.

10 15. Once the values are calculated, the values are needed to be entered in the slots provided (#15a). Click SUBMIT (#15b) button to submit the answers for evaluation. 16. Once the answers are submitted, a pop-up window asks for the confirmation. Proceed further by clicking YES and to the next step by clicking on the NEXT button. This step marks the end of experiments on beam1.

11 17. The next set of experiments is done on the beam 2 with a damping tape. The same procedure is adopted for the damped set of conditions. A series of images of the same are as shown below:

13 18. The final results can be viewed from the tabular column as shown above. The data can be saved using the SAVE RESULT option. 19. Press EXIT button to exit from the experiment.

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