H2 Optimization of Tuned Mass Damper Inerter Attached to a Floating Platform Excited by Stochastic Load

Floating platform is an important bearing foundation for many offshore structures and generally subjected to the stochastic excitations from the ocean. A tuned mass damper inerter (TMDI) dynamic absorber is proposed to control the vibration of the platform for the steady operation of the superstructure. The TMDI system is a conventional tuned mass damper connected with a paralleled inerter device. The governing equations of motion of the TMDI-floating platform system are established to solve the transform function of the response. For the best performance of TMDI vibration control, the optimum parameters are designed based on the H2 optimization. The analytical optimum parameters are derived for the undamped structure using the extreme value theory. The numerical optimum parameters are obtained for the damped structure using numerical interior-point algorithm. The unified closed-form formulae for optimum parameters are proposed by the least square curve-fitting method considering both undamped and damped structure. Finally, the vibration control performance of the optimized TMDI is evaluated focus on the displacement response of floating platform subjected to the stochastic hydrodynamic loads. The time history analysis result shows that TMDI can significantly suppress the structural displacement response of the platform. Furthermore, the results illustrate that the relatively displacement of the mass block in TMDI is quite shorter than that of the conventional TMD. Therefore, the TMDI is more practical in engineering application for suppressing the vibration of the spar type floating platform.