NONLINEAR FREE VIBRATION OF A COMPLIANT STRUCTURE

A compliant structure in the ocean environment is modeled as a beam supported by a linear-elastic torsional spring at the base and with a point mass at the free end. Using the method of continuum mechanics and on the basis of small deformation, accurate angle and large deflection, nonlinearly coupled equations of motion and boundary conditions are derived. The fluid forces are modeled using a semi-empirical Morison equation. The free response in vacuum and the free response in still water without and with damping are analyzed through finite difference approach and Runge-Kutta method. The results of the nonlinear structures with both accurate angles and approximate angles and the linear structures are compared, respectively.