Free and Forced Vibration Analyses of Tapered Piles under Axial Harmonic Loads

Abstract

In this study, the free and forced vibration analyses of tapered piles subjected to axial harmonic loads were carried out. The first part of the paper presents the free vibration analysis of the tapered piles using an energy-based Rayleigh–Ritz method. The undamped natural frequency of the soil–pile system was obtained, and the results were validated using two analytical methods and a field test result reported in the literature. In the second part of the paper, the forced vibration analysis of tapered piles under vertical vibrations is carried out. Employing the Euler–Lagrange equation and calculus of variations, the governing differential equation for tapered piles under axial harmonic loading was obtained. A Taylor series expansion-based numerical technique called the differential transform method was used to solve the obtained differential equation. The numerical results were validated using reported full-scale forced vibration tests of cylindrical piles. The effects of the end fixities, slenderness ratio, the taper angle, and the degree of anisotropy on the response characteristics of tapered piles were discussed.