Free Vibration of a Cantilever Beam(Continuous System)

4.10 Discussions

Good agreement between the theoretically calculated natural frequency and the experimental one is found. The correction for the mass of the sensor will improve the correlation better. The present theoretical calculation is based on the assumption that one end of the cantilever beam is properly fixed. However, in actual practice it may not be always the case because of flexibility in support.


4.11 Precautions during Experimentations and Analyses

1.  Fixed end condition of the cantilever beam could be ensured by properly gripping one end of the beam.

2.  The beam should be given initial disturbance such that the first mode (Fig. 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.  The end of the beam should be fixed rigidly so that cantilever end condition prevails in experiment.


4.12 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.

5.  Wahab, MA, 2008, Dynamics and Vibration , John Wiley & Sons Ltd., Ghent University, UK.

6.  Tiwari, R., 2010, Analysis and Identification in Rotor -Bearing Systems (part II), Development under the Curriculum Development Scheme of Quality Improvement Programme at IIT Guwahati, AICTE.