Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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.
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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.
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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.
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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 𝑦0 . Note this value)
o Next the axes are now moved on to another peak amplitude (Say third peak) as shown in
(#10 c) (This is 𝑦n. 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.
o Now from the value of the logarithmic decrement, the value of “Damping Ratio” is found by
using the formula provided in the table.
o 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”.
o Once the damped natural frequency is calculated, calculate the natural frequency from the
formula table given below.
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
PARAMETERS TO BE CALCULATED FORMULA TO BE USED UNITS
Logarithmic decrement
𝛿 =1
𝑛𝑙𝑛 (
𝑦0
𝑦n) wherein
y0 and yn are the amplitudes
Damping factor 𝜁 =
1
√1 + (2𝜋𝛿⁄ )
2
Damped vibration time period 𝜏𝑑 = 𝑡1 − 𝑡0 Seconds
Damped natural frequency 𝑓𝑑 = 1
𝜏𝑑
Hz
Damped natural frequency 𝜔𝑑 = 2𝜋𝑓𝑑 Rad/Sec
Natural frequency of the system 𝜔𝑛 =𝜔𝑑
√(1 − 𝜁2) Rad/Sec
Natural frequency 𝑓𝑛 = 2𝜋
𝜔𝑛
Hz
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 )
𝑘 = 𝜔𝑛2 . 𝑚
N/m
Critical damping 𝑐𝑐 = 2√𝑚𝑘
𝑁𝑠
𝑚
Equivalent viscous Damping coefficient of the system
𝑐 = 𝜁𝑐𝑐
𝑁𝑠
𝑚
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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.
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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.
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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.
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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:
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
Free vibration of cantilever beam RT Lab
SOLVE the virtual lab@ NITK Surathkal RT Lab Vibration Lab
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.