A simplified optimization strategy for nonlinear tuned mass damper in structural vibration control

Abstract

In this paper, a simplified optimization strategy for the nonlinear tuned mass damper (TMD) is presented, and the optimal parameter setting can be simply determined, by which the nonlinear TMD is effective over a wide frequency range. In the given numerical model, the nonlinear TMD is attached to the structure, which is represented by a single-degree-of-freedom system, and the environmental load is assumed to be the Gaussian white noise process. Governing differential equations of motion of the coupled structure-TMD system are derived, and the equivalent linearization method is introduced in the numerical calculation. The standard deviation of the structural displacement is adopted as the optimized objective function. Furthermore, it is pointed out that the response of the system can be controlled in a case of multiple probable steady-state processes caused by the nonlinearity of the stiffness element. Different from the linear TMD, the performance of the nonlinear TMD may be influenced by the excitation. Thus, the performance sensitivity of optimal nonlinear TMD is investigated with different excitation intensities and structural damping ratios. The results show that the sensitivity may limit the engineering applications of nonlinear TMD. © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.