Free vibrations of tapered piles embedded partially in elastic foundations

The numerical methods for calculating the natural frequencies and the mode shapes of the tapered piles embedded partially in the elastic foundations are developed. The ordinary differential equation governing the free vibrations of such piles are derived, in which the effect of axial load is considered. The Runge-Kutta method and the determinant search method combined with the Regula-Falsi method are used for integrating the differential equation and determining the eigenvalues(natural frequencies), respectively.