Free Vibration of Cantilever Beam with Lumped Mass at Free End


Good agreement of the theoretically calculated natural frequency with the experimental one is found. The present theoretical calculation is based on the cantilever beam end conditions (i.e., one end is fixed end). However, in actual practice it may not be always the case because of flexibility in support that may affect the natural frequency and the variation of free vibration response of cantilever beam with respect to time to an initial disturbance may be observed.


2.12 Precautions during the experiment and analysis

1.  Fixed end condition of the cantilever beam could be ensured by properly gripping one end of the beam as shown in Fig. 2.6.

2.  The beam should be given initial disturbance such that the first mode (Fig. 2.1(b)) is excited, i.e., a small deflection of the free end of the beam.

3.  Care should be taken that the cables of accelerometer should not affect the beam motion.

4.  Initial displacement of the beam should be small so that linearity assumption holds true.

5.  By considering all the precautions and by using the procedure step by step with proper coordination with the subsystem, measuring instruments, data acquisition system and vibration measuring software, the results can be improved.

7.  To minimize error in the result, user is suggested to use sensors and other measuring instruments with high sensitivity and minimize the noise in measuring data.

It is also suggested to user to repeat the experiment several times to confirm the consistency of results.

2.13  References

1.  Meirovitch, L, 1967, Analytical methods in vibration , Ccollier-MacMillan Ltd., London.

2.  Thomson, W.T., 2007, Theory of vibration with application , Kindersley Publishing, Inc., London.

3.  Rao, J. S, and Gupta, K., Introductory Course on Theory and Practice of Mechanical Vibrations , New Age International, New Delhi.

4.  S.Timoshenko, D.H. Young, 1961, Strength of Material , Stanford University, California.