370
8 Free Vibration Analysis of Continuous Systems
A(x) = A 0
x
L
and I (x) = I 0
x
L
Determine the fundamental frequency of the beam.
8.23 Determine the effect of rotary inertia on a freely vibrating uniform cantilever
beam.
8.24 For a simply supported beam, determine the natural frequencies by considering it to be uniform. Consider the bending and shearing deformation and
not rotary inertia.
8.25 Determine an approximate frequency of rectangular membrane supported
along all edges by Rayleigh’s method with
W (x, y) = C 1 x y(x − a)(y − b)
References
1. H. Benaroya, Mechanical Vibration, Prentice-Hall, New Jersey, 1998.
2. J. B. Achenbach, Wave Propagation in Elastic Solids, North-Holland Publishing Co.,
Amsterdam, 1973.
3. M. S. Triantafyllou, Linear dynamics of cables and chains, Shock and Vibration Digest, V.16,
March 1984, pp. 9–17.
4. N. Y. Oleer, General solution to the equation of vibrating membrane, Journal of Sound and
Vibration, V.6, 1967, pp. 365–374.
5. J. Mazumdar, A review of approximate methods for determining the vibrational modes of
membranes, Shock and Vibration Digest, V.14, Feb. 1982, pp. 11–17.
8 Free Vibration Analysis of Continuous Systems
A(x) = A 0
x
L
and I (x) = I 0
x
L
Determine the fundamental frequency of the beam.
8.23 Determine the effect of rotary inertia on a freely vibrating uniform cantilever
beam.
8.24 For a simply supported beam, determine the natural frequencies by considering it to be uniform. Consider the bending and shearing deformation and
not rotary inertia.
8.25 Determine an approximate frequency of rectangular membrane supported
along all edges by Rayleigh’s method with
W (x, y) = C 1 x y(x − a)(y − b)
References
1. H. Benaroya, Mechanical Vibration, Prentice-Hall, New Jersey, 1998.
2. J. B. Achenbach, Wave Propagation in Elastic Solids, North-Holland Publishing Co.,
Amsterdam, 1973.
3. M. S. Triantafyllou, Linear dynamics of cables and chains, Shock and Vibration Digest, V.16,
March 1984, pp. 9–17.
4. N. Y. Oleer, General solution to the equation of vibrating membrane, Journal of Sound and
Vibration, V.6, 1967, pp. 365–374.
5. J. Mazumdar, A review of approximate methods for determining the vibrational modes of
membranes, Shock and Vibration Digest, V.14, Feb. 1982, pp. 11–17.