NON-LINEAR DYNAMICS OF AN ARTICULATED TOWER IN THE OCEAN

Abstract

This paper presents studies on the response of an articulated tower in the ocean subjected to deterministic and random wave loading. The tower is modeled as an upright rigid pendulum with a concentrated mass at the top, having one angular-degree-of-freedom (planar motion) about a hinge with Coulomb friction, and viscous structural damping. In the derivation of the differential equation of motion, non-linear terms due to geometric (large angle) and fluid forces (drag and inertia) are included. The wave loading is derived using a modified Morison's equation to include current velocity, in which the velocity and acceleration of the fluid are determined along the instantaneous position of the tower, causing the equation of motion to be highly non-linear. Furthermore, since the differential equation's coefficients are time dependent (periodic), parametric instability can occur depending on the system parameters such as wave height and frequency, buoyancy, and drag coefficient. The non-linear differential equation is then solved numerically using `ACSL' software. The response of the tower to deterministic wave loading is investigated and a stability analysis is performed (harmonic, subharmonic and superharmonic resonance). To solve the equation for random loading, the Pierson-Moskowitz power spectrum, describing the wave height, is first transformed into an approximate time history using Borgman's method with slight modification. The equation of motion is then solved as buoyancy, initial conditions, wave height and frequency, and current velocity and direction, is investigated.