Free vibration analysis of beams on a Pasternak foundation using Legendre polynomials and Rayleigh-Ritz method.

A free vibration of Euler-Bernoulli and Timoshenko beams resting on a two-parameter elastic foundation of Pasternak type has been investigated. Rayleigh-Ritz method is employed to deduce the governing equation and the Legendre polynomials multiplied by a boundary function is used as admissible functions to define the displacement fields. Accuracy of the results is evaluated by comparing with those available in the literature. It is shown that the method has a good and rapid convergence regardless of the beam theory, boundary conditions and elastic foundation parameters. Natural frequencies of beams with different boundary conditions, elastic foundation parameters, and ratios of height-to-length are presented