**44**, 3-4, pp. 375-388, 1996

### A study of the Numerical Convergence of Rayleigh-Ritz Method for the Free Vibrations of Cantilever Beam of Variable Cross-Section with Tip Mass

A numerical study on the convergence properties of the Rayleigh-Ritz method is presented, for the dynamic analysis of beams with continuously varying cross-section. The beam is assumed to be slender, the Euler-Bernoulli hypotheses are accepted, and some particular cases are considered, for which a closed-form solution is available in terms of Bessel functions. The comparisons between exact and approximate results can give some hint about the usefulness of the approximate method in more complex situations, for which the exact solution is not attainable.

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