Ivana Kuzmanović

Optimization of material with modal damping

Abstract This paper considers optimal parameters for modal damping D = Mf 1 ( M - 1 K ; α 1 , … , α k ) + Kf 2 ( K - 1 M ; α 1 , … , α k ) in mechanical systems described by the equation M x ¨ + D x ˙ + Kx = 0 , where matrices M and K are mass and stiffness matrices, respectively. Different models of proportional and generalized proportional damping are considered and optimal parameters with respect to different optimization criteria related to the solution of the corresponding Lyapunov equation are given. Also, some specific example problems are compared with respect to the optimal and estimated parameters.

Damping optimization over the arbitrary time of the excited mechanical system

In this paper, we consider damping optimization in mechanical system excited by an external force. We use optimization criteria based on minimizing average energy amplitude and average displacement amplitude over the arbitrary time. As the main result we derive explicit formulas for objective functions. These formulas can be implemented efficiently and accelerate optimization process significantly, which is illustrated in a numerical example.

Sherman–Morrison–Woodbury formula for Sylvester and T-Sylvester equations with applications

In this paper, we present the Sherman–Morrison–Woodbury-type formula for the solution of the Sylvester equation of the form as well as for the solution of the T-Sylvester equation of the form where U 1, U 2, V 1, V 2 are low-rank matrices. Although the matrix version of this formula for the Sylvester equation has been used in several different applications (but not for the case of a T-Sylvester equation), we present a novel approach using a proper operator representation. This novel approach allows us to derive a matrix version of the Sherman–Morrison–Woodbury-type formula for the Sylvester equation as well as for the T-Sylvester equation which seems to be new. We also present algorithms for the efficient calculation of the solution of structured Sylvester and T-Sylvester equations by using these formulas and illustrate their application in several examples.