Nonlinear dynamics of heave motion of the sandglass-type floating body with piecewise-nonlinear, time-varying stiffness

In this paper, the dynamic behaviors and stability of the nonlinear heave response of the sandglass-type Floating Production, Storage, and Offloading unit (FPSO) under harmonic wave excitation force are studied. With consideration of the special shape characteristics, the heave restoring stiffness is modeled as a piecewise-nonlinear, time-varying (PNTV) function. The incremental harmonic balance (IHB) method in conjunction with the incremental arc-length method are employed to perform an elaborate investigation on its dynamic behaviors. Floquet theory is applied to determine the stability of the periodic solutions. The accuracy of the approach is verified through a comparison with the results of direct numerical integration using 4th-order Runge-Kutta method. Then, hardening-type nonlinearity of the heave motion is proved by parametric studies concerning the effects of damping ratio, wave excitation force, wave elevation and its phase difference with the wave excitation force on the nonlinear response. Based on this, a more reasonable approach considering frequency-dependent characteristic and memory effect of the hydrodynamic forces are established by the modification of traditional IHB method. The validity of the improvement is demonstrated by the widely used hybrid time-domain numerical simulation method in engineering application. Finally, by comparing the motion responses of two floating bodies with the corresponding linear heave RAO, the results show that even though the hardening-type nonlinearity can lead to the occurrence of unexpected severe heave motion, the wave-free characteristic of the heave motion for this type of floating body can suppress the development of the hardening-type nonlinearity and thus the established wave-free guideline is reasonable. Nevertheless, the frequency of the maximum RAO can exceed the wave-free frequency in the case of strong nonlinearity. Consequently, the nonlinearity of the heave motion should be fully considered and introduced in the existing design criteria.