Vibration reduction of rotating frame structure based on quadratic performance index

Abstract

An efficient method based on quadratic performance index and Lyapunov's second method is developed for the vibration reduction optimization of frame structure rotating at a constant angular velocity. Four optimization formulations and algorithms are studied for both low and high angular velocity. These formulations consider both linear vs nonlinear dynamic models as well as direct integration and Lypunov method to evaluate performance index. Three numerical examples are presented to compare the effectiveness of the four algorithms. Numerical results show that all the four optimization methods can reduce vibration at low rotating speed and find very similar optimal designs. However, at high rotating speed, dynamic model of rotating structure must consider nonlinear axial strain in order to obtain correct dynamic response. Since the Lyapunov's second method is not applicable for the nonlinear model and the NFTI (nonlinear dynamic model with nonlinear axial strain and time integration) method is very inefficient, the present study develops a perturbation method, linearizes the nonlinear dynamic model and establishes the LNFLA(linearized dynamic model with nonlinear axial strain, the Lyapunov's second method). Numerical examples show the optimization method LNFLA provides an efficient numerical method for vibration reduction of rotating frame structure with both low and high rotating speed.