preview

The Optimization Problem Of Matlab Routines

Decent Essays

Relevant numerical techniques, which have been done with the help of MATLAB routines, are applied to solve the arising optimization problem and to find the optimum parameters of the TMD. For a given mass ratio, µ, one can assume different values of the frequency ratio, f, and for each frequency ratio assuming a range of damping factor ζ2 of the TMD and estimate the optimum parameters that minimize a certain desired output. Fig. 8 is an example of the numerical optimization conducted to estimate the optimal frequency ratio and damping factor of the TMD for two different mass ratios under wind loads modeled as white-noise. The optimization is based on the minimization of the displacement of the primary structure. In this numerical optimization, the responses of the primary structure are normalized, which means that the response obtained with the TMD when attached to the structure is divided by the corresponding response obtained without the TMD. The optimal values of the frequency ratio and the damping factor of the TMD are written on the subfigures. It is shown that a TMD with 1% mass ratio can provide a significant reduction in the displacement response of the primary structure. The reduction in the displacement depends very much on the tuning frequency and the damping ratio of the TMD. By increasing the mass ratio from 1% to 5%, the displacement response of the primary structure is reduced. However, the TMD with 5% mass ratio is more robust to the changes in the frequency

Get Access