In a recent and comprehensive Letter to the Editor [1] approximate explicit formulae have been derived by El-Mously for the fundamental natural frequency for vibration of Timoshenko beams mounted on Pasternak foundation.
It is the purpose of this note to mention other previous works in which the application of the Pasternak foundation model is the important subject of an engineering "eld of great interest.
Probably because of the di$culties in the estimation of the value of the soil parameters, as pointed out by Franciosi and Masi [2], and because of the complexities of the model, closed-form solutions are available only for the simplest cases and the free vibration frequencies must be numerically calculated even for simply supported beams [3]. Therefore, due to the importance of this class of studies, it is very useful to obtain data from di!erent experimental tests in order to improve and validate theoretical models.
Wang and Stephens [4] showed the e!ect of rotatory inertia and shear deformation on the natural frequencies of a beam for various boundary conditions. This work was extended by Maurizi and Rosales [5] to rotating elastically restrained ends. Wang and Gagnon [6] completed the investigation of reference [4] by presenting the vibration of continuous Timoshenko beams.
In 1988, Filipich and Rosales [7, 8] determined the fundamental frequencies of Timoshenko beams resting in a Winkler}Pasternak (W}P) medium. They proposed the use of the variant of Rayleigh's method which allows an optimization of the approximate modal functions through a non-integer exponential parameter, originally suggested by Lord Rayleigh [9] and su$ciently employed in various eigenvalues and "eld problems. In the two papers mentioned the practical application of this technique yields very good results for hinged}hinged and clamped}clamped beams of uniform and variable cross section.
Subsequently, Yokoyama [10] developed a "nite element procedure analyzing the