Nonlinear coupled transverse and axial vibration of a compliant structure: Free and forced

A compliant tower in the ocean environment is modeled as a beam undergoing coupled transverse and axial motion. The beam is supported by a torsional spring and has a point mass at the other end. It is assumed that the strains are small but the rotation is moderate compared to the strain so that the equations of motion for the axial and transverse motion are nonlinearly coupled. The nonlinear coupled equations of motion are derived here using Hamilton's principle. The forced responses due to random waves are observed here. The responses are obtained numerically using the finite difference approach.