Control efficiency optimization and Sobol’s sensitivity indices of MTMDs design parameters for buffeting and flutter vibrations in a cable stayed bridge

Abstract

This paper studies optimization of three design parameters (mass ratio, frequency ratio and damping ratio) of multiple tuned mass dampers MTMDs that are applied in a cable stayed bridge excited by a strong wind using minimax optimization technique. ABAQUS finite element program is utilized to run numerical simulations with the support of MATLAB codes and Fast Fourier Transform FFT technique. The optimum values of these three parameters are validated with two benchmarks from the literature, first with Wang and coauthors and then with Lin and coauthors. The validation procedure detected a good agreement between the results. Box-Behnken experimental method is dedicated to formulate the surrogate models to represent the control efficiency of the vertical and torsional vibrations. Sobol’s sensitivity indices are calculated for the design parameters in addition to their interaction orders. The optimization results revealed better performance of the MTMDs in controlling the vertical and the torsional vibrations for higher mode shapes. Furthermore, the calculated rational effects of each design parameter facilitate to increase the control efficiency of the MTMDs in conjunction with the support of the surrogate models.

Keywords

MTMDs / power spectral density / fast Fourier transform / minimax optimization technique / Sobol’s sensitivity indices / Box-Behnken method

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Acknowledgements

The author would like to thank Prof. Dr. Guido Morgenthal and Prof. Dr. Tom Lahmer, for their continuous support in providing guidance and consultancy relating to this research study at the faculty of civil engineering at Bauhaus Universitat Weimar, Germany.

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