Abstract
We consider a mathematical model of a linear vibrational system described by the second-order system of differential equations \(M\ddot{x} + D\dot{x} + Kx = 0\), where M, K and D are positive definite matrices, called mass, stiffness and damping, respectively. We are interested in finding an optimal damping matrix which will damp a certain part of the undamped eigenfrequencies. For this we use a minimization criterion which minimizes the average total energy of the system. This is equivalent to the minimization of the trace of the solution of a corresponding Lyapunov equation. In this paper we consider an algorithm for the efficient optimization of the damping positions based on dimension reduction techniques. Numerical results illustrate the efficiency of our approach.
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Benner, P., Tomljanović, Z., Truhar, N. (2011). Damping Optimization for Linear Vibrating Systems Using Dimension Reduction. In: Náprstek, J., Horáček, J., Okrouhlík, M., Marvalová, B., Verhulst, F., Sawicki, J. (eds) Vibration Problems ICOVP 2011. Springer Proceedings in Physics, vol 139. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2069-5_41
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DOI: https://doi.org/10.1007/978-94-007-2069-5_41
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