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Rectangular barrettes are used in place of circular piles for their improved geotechnical performance. In this paper, a new mathematical approach is proposed for predicting the natural frequency and mode shape of vertically loaded barrettes. Unlike previous studies of the problem, the approach allows the investigation of nonhomogeneity for side friction resistance as well as rectangular cross-section of piles. The differential governing equation and boundary conditions are derived for the lateral free vibration of the barrettes, and solutions are numerically obtained by means of the Runge–Kutta scheme in conjunction with the determinant search algorithm. The calculated natural frequencies are in good agreement with those reported in the literature. The free vibration response and the results of a parametric study of barrettes are presented in non-dimensional form. The proposed approach is considered to provide a viable tool for studying the free vibration of rectangular barrettes for practical applications.

Lateral free vibration of rectangular barrettes subjected to vertical loading