Abstract: An articulated tower platform is modeled as a flexible 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 and large deflection, nonlinearly coupled equations of motion and boundary conditions are derived. The fluid forces are modeled using a semi-empirical Morison equation under Airy wave theory and second-order Stokes wave theory. The nonlinear vibrations under two wave theories are analyzed through a finite difference approach and the Runge-Kutta method. The influences of nonlinearity of the second-order Stokes wave theory on the vibrations are studied, and the results of the nonlinear structures with accurate angles and with approximate angles and the linear structures are compared.