Free Vibration of a Cantilever Beam(Continuous System)

4.6 Experimental procedure

1. Choose a beam of a particular material (steel, aluminum or copper), dimensions ( L , w , d ) and transducer (i.e., measuring device, e.g. strain gauge, accelerometer, laser vibrometer).

2.  Clamp one end of the beam as the cantilever beam support.

3.  Place an accelerometer (with magnetic base) at the free end of the cantilever beam , to measure the free vibration response (acceleration).

4.  Give an initial deflection to the cantilever beam and allow it to oscillate its own. To get the higher frequency it is suggested to give initial displacement at an arbitrary position apart from the free end of the beam (e.g. at the mid span).

5.  This could be done by bending the beam from its static equilibrium position by applying a small static force at the   free end of the beam and suddenly releasing it, so that the beam oscillates its own without any external force during the oscillation.

6.  The free oscillation could also be started by giving a small tap at the free end of the beam.

7.  Record the data obtained from the chosen transducer in the form of graph (variation of the vibration response with time).

8.  Repeat the procedure for 5 to 10 times to check the repeatability of the experimentation.

9.  Repeat the whole experiment for different material, dimensions, and measuring devices.

10.  Record the whole set of data in a data base.


4.7 Virtual experimentation

Virtual experimentation provides the interface, which gives facility to perform experiments virtually. It provides different options for material selection, instruments, and specimen dimensions. After making desired selection and running the program, it gives the result from a storage database for a particular configuration selected by the user. Fig. 4.12 shows an overall flowchart for a virtual laboratory in which several experiments can be performed through the internet by users remotely with the help of already stored measured data.


Fig. 4.12: Overview of measurement based virtual experiment


4.8 Steps in virtual experimentation and its programming

The virtual experiment program of forced vibration of single DOF cantilever beam is divided in many sections. The step by step description of program is as follows which also include the guideline to proceed in the virtual experiment…


1. Title Page - This is the first page of virtual experiment. It includes title of experiment and a photo of experimental setup with accelerometer. User starts the program by clicking the  RUN button given at the top of the page.


Fig 4.13: Title page displaying the name and photo of experimental setup


2. Introduction - This section contains aim of experiment, some important definitions related to the experiment. This page also includes the instructions and guidelines to perform the experiment with effectively and efficiently.


Fig 4.14: Introduction page describing the aim and some basic definitions


User has to follow all the instruction strictly for successful completion of the virtual experiment. Also please don’t try to go back to previous pages in between the program.


3. Entrance Test - This page offers an entry test to the user. This test is offered to ensure that user has adequate basic knowledge about the experiment. Total five objective types of questions are given, user has to select the right option among the given options. User can select only one option. To qualify the test, user has to give at least three right answers. After submitting the test, system evaluates the test and if user qualifies then automatically experiment will move to Input section. If user does not qualify the test then program will stuck at the same page. Therefore, it is suggested to the user to read the lab manual carefully.

If user qualify the test and page is not moving to input section then user is suggested to move to input page by using the tab button at the top of pages.


Fig 4.15: Pre-test to the users to perform the experiment


4. Input section - This section contains various input options for the experiment i.e. beam material, beam dimensions, transducer for measurement etc. User has to select proper input to proceed for the experiment. When user enters the input configuration, each parameter generates a specific number and form a set of numbers. Based on the input configuration, program takes the particular files which are related to that particular configuration from the database. For each experiment the database contains 10 set of files, which are chosen by program randomly. After entering the input, if user wants to change any parameter he has to stop the program and run it from initial step.


Fig 4.16: Choosing the different configurations to perform experiment i.e. input section


5. Questions - In between the virtual program, experiment offers some questions to the user to make the experiment more interactive. User should try to think about the answers of these questions with proper explanation. These questions are very basic and related to the experiment.


Fig 4.17: small questions related to experiment


6. Experiment  - In this section, user starts the experiment which implies a small initial disturbance in the system so that system starts vibrating freely. The data from the database files are read and plotted in a particular sequence. First the response-Time graph is plotted then FFT is plotted. The data from the file is taken as an array and it is plotted in the loop one-by–one by using a script code inside the loop. In case of actual experiment, user is suggested to give initial disturbance at the middle of the cantilever beam to vibrate the beam in second mode.


Fig 4.18: Response vs. time and FFT graphs for chosen configuration in input section


  7. Answers - The answers of the questions asked before the experiment are given in this page.


Fig 4.19: Answers for the questions asked in questions page


8. Theoretical calculations - The theoretical calculations are done based on the input configuration chosen by the user. Program decodes the input parameter and generates the related parameter like Young modulus, density and dimensions. By using these values the theoretical calculation is done with the help of formula node. Refer section 4.3 for the theoretical formulation and calculations.


Fig 4.20: Theoretical calculations of first and second natural frequencies


9. Experimental calculations - The experimental calculations are done by using the data taken from the files. A waveform peak detector is used to get the peak values and its locations. The damped natural frequencies can be obtained by observing the FFT plot. The peak locations of FFT plot shows the natural frequencies of the system. The undamped natural frequency can be calculated by using a formula node. Refer section 4.4 for the procedure for experimental calculation of the undamped natural frequencies.


Fig 4.21: Experimental calculations of first and second natural frequencies


10. Results The result page shows the comparison of theoretical and experimental results. Here user can perform the experiment again by same or different input configurations.


Fig 4.22: Comparison of theoretical and natural frequencies


11. Evaluation test - After completion of the experiment, program offers an evaluation test to judge the knowledge gained by the user. Here five optional questions are given, user has to select right option and submit the test.


Fig 4.23: A small test based on the experiments


12. Exercise - The exercise problems are given to the user to explore the knowledge about the basics of the experiment. User has to find out the answer of these questions. 


Fig 4.24: Exercises


13. Feedback - At the end of the program, it asks for the feedback about the different issues related with the program. User should submit a valuable and effective feedback for the program. These feedbacks are taken and used for further enhancement of the program.


Fig 4.24: Feedbacks from the users



4.9 Instructions for using Virtual program

1.  Read the given instruction carefully and Follow all strictly.

2.  Perform the experiment step-by-step

3.  All the inputs are taken by the user only at the INPUT page; don’t try to give any input in other pages.

4.  In case of any inconvenience in functioning of button "NEXT PAGE", use the tab at the top.

5.  If you find that the output data are not appropriate or in case of any inconvenience please stop the program and perform again.