Non-linear coupled transverse and axial vibration of a compliant structure, Part 2: forced vibration

Responses of a beam undergoing both axial and transverse vibration are studied when the beam is subjected to transverse forces. The beam is supported by a torsional spring at the base and has a point mass at the free end. This is a simplified model of a complaint offshore structure. It is assumed that the environmental forces are due to waves and current. The semi-empirical Morison equation is used to model the fluid forces. Waves in this case are assumed to be random and their heights follow the Pierson-Moskowitz spectrum. Borgman's method is used to obtain the wave height from the Pierson-Moskowitz spectrum, and the wave velocities and the accelerations are obtained from the wave height using the Airy linear wave theory. The wave velocities and accelerations are then used in the Morison equation to form the fluid forcing function. As a preliminary study, the harmonic force is used to model the fluid force. When the deterministic harmonic force at various frequencies is applied, subharmonic resonances of order 1/2 are observed. Parametric studies of random forcing are performed by varying current velocity and significant wave height.