By Farzad Ebrahimi

ISBN-10: 9533072091

ISBN-13: 9789533072098

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10] J-C. Hsu, H-Y. Lai, C-K. Chen, An innovative eigenvalue problem solver for free vibration of Timoshenko beams by using the Adomian Decomposition Method, Journal of Sound and Vibration 325 (2009) 451-470. [11] S. H. Ho, C. K. Chen, Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using Differential Transform, International Journal of Mechanical Sciences 48 (2006) 1323-1331. H. Register, A note on the vibrations of generally restrained, end-loaded beams, Journal of Sound and Vibration 172 (4) (1994) 561_571.

1 Free vibration analysis for a free-free beam with a single step The free vibration of the free-free beam studied in Koplow et al. (2006) is restudied using the CEM and the results are compared with those in Koplow et al. Figure 2 shows the geometry of the beam under study. 7 GPa . In the CEM when 350 numbers of c-dofs are used, the first three natural frequencies are converged. 7Hz, respectively. The calculated natural frequencies from the CEM are very close to the experimental values in Koplow et al.

Balasubramanian and Subramanian (1985) investigated the performance of a four-degree-of-freedom per node element in the vibration analysis of a stepped cantilever. De Rosa (1994) studied the vibration of a stepped beam with elastic end supports. Recently, Koplow et al. (2006) presented closed form solutions for the dynamic response of Euler–Bernoulli beams with step changes in cross section. There are also some works on the vibration of beams with more than one step change in cross-section. Bapat and Bapat (1987) proposed the transfer matrix approach for beams with n-steps but provided no numerical results.

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