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The Euler-Bernoulli uniform beam considered in this paper consist of n portions and carry (n + 1) particles, two of which are at the beam ends. For the classical beam eigen-value technique developed here, n co-ordinate systems are chosen with origins at the particle locations. The mode shape of the jth portion of the beam is expressed in the form Y j (X j ) = AU j (X j ) + BV j (X j ) in which U j (X j ) and V j (X j ) are 'modiÿed' mode shape functions applicable to that portion but the constants A and B are common to all the portions. From the boundary conditions at the right end, the frequency equation was expressed in closed form as a second-order determinant equated to zero. Schemes are presented to compute the four elements of the determinant (from a recurrence relationship) and to evaluate the roots of the frequency equation. Computational di culties were not encountered in the implementation of the schemes. The ÿrst three natural frequency parameters of 16 combinations of the classical boundary conditions are tabulated for beams with three and up to nine portions for selected particle location and mass parameters. Frequency parameters of beams with one and up to 500 equi-sp

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Author

S. Naguleswaran

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0020-7403)

Published

2002

Language

EN

Field

Engineering (Physical Sciences)