Estimating the nonlinear resonant frequency of a single pile in nonlinear soil

Analytical expressions are determined for the nonlinear resonant frequency (or natural frequency) of the fundamental lateral mode of a pile. A pile with a floating toe, with and without pile cap is considered in this paper. The influence of a nonlinear soil spring model that varies with depth and a nonlinear damping model that is strain amplitude dependent is considered. A non-dimensional equation of motion for the system dynamics is derived from an energy based formulation. This equation is a Duffingʹs type nonlinear differential system that has nonlinear damping. Harmonic balance with numerical continuation is employed to determine the nonlinear resonance curves of the system. Comparison with some experimental results is made.