Zoran Tomljanović

Optimal Damping of Selected Eigenfrequencies Using Dimension Reduction

We consider a mathematical model of a linear vibrational system described by the second-order differential equation

Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts

M \ddot{; ; ; ; x}; ; ; ; + D \dot{; ; ; ; x}; ; ; ; + Kx = 0

Damping optimization in mechanical systems with external force

, where

Optimization of material with modal damping

M

Damping optimization over the arbitrary time of the excited mechanical system

and

Optimal Direct Velocity Feedback

K

Damping Optimization for Linear Vibrating Systems Using Dimension Reduction

are positive definite matrices, representing mass and stiffness, respectively. The damping matrix

Optimizing a damped system-a case study

D

Damping optimization of parameter dependent mechanical systems by rational interpolation

is positive semidefinite. We are interested in finding an optimal damping matrix which will damp a certain (critical) part of the undamped eigenfrequencies. For this we use an optimization criterion based on minimization of the average total energy of the system. This is equivalent to the minimization of the trace of the solution of the corresponding Lyapunov equation

Dimension Reduction for Damping Optimization in Linear Vibrating Systems

A X+ X A^T =-GG^T