Reduced-order multiple tuned mass damper optimization: A bounded real lemma for descriptor systems approach

This paper presents a novel technique for multiple tuned mass damper optimization based on the dissipativity inequalities for a class of descriptor systems. Under the assumptions of regularity, asymptotic stability and index one property of the descriptor system representing the structure with tuned mass dampers, optimization criterion is defined in terms of H∞H∞ norm of the system. In doing so, special structure of the system matrices is utilized to eliminate some of the optimization variables. To overcome its high computational cost and make it applicable for optimization of large-scale structures, a novel reduced-order optimization algorithm is proposed. Unlike the existing approaches, the presented optimization framework does not impose restrictions regarding regularity and constantness of the mass matrix, and consequently allows simultaneous optimization of mass, damping and stiffness matrices. Numerical examples which clearly illustrate the applicability and effectiveness of the proposed optimization procedure, as well as the comparison with other methods, are presented.

► An algorithm is derived from a bounded real lemma for descriptor systems.
► Simultaneous optimization of tuned mass damper mass, damping and stiffness matrices.
► Applicable for optimization of systems with singular mass matrix.
► Reduced-order algorithm for optimization of large-scale structures.