Naslov
Optimal damping for vibrating systems using dimension reduction

Autori
Tomljanović, Zoran

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Prirodoslovno-matematički fakultet, Matematički odsjek

Mjesto
Zagreb

Datum
31.05

Godina
2011

Stranica
134

Mentor
Truhar, Ninoslav ; Benner, Peter ; Drmač, Zlatko

Ključne riječi
vibrating system; damping optimization; Lyapunov equation; energy minimization; dimension reduction; error bound

Sažetak
This thesis considers optimization of damping in mechanical vibrating systems. When one has to find optimal positions together with corresponding viscosities of dampers in a mechanical vibrating system based on energy minimization, then numerous Lyapunov equations have to be solved. Thus, we have introduced different approaches which significantly accelerate the optimization procedure. First part considers the case when all undamped eigenfrequencies have to be damped and propose a dimension reduction technique which calculates approximation of the solution of the corresponding Lyapunov equation. We derive an error bound for this approximation which is then used in the process of viscosities optimization. The case of damping a selected part of undamped eigenfrequencies is also investigated in thesis. In this case we have derived an algorithm for the approximation of the trace of the Lyapunov equation and the corresponding error bound which uses the structure of the system. Then, viscosities are optimized using this error bound. Furthermore, we propose several approaches which accelerate optimization of dampers' positions. First, we propose two heuristics ; i.e. the "Multigrid-like" and the "Discrete to continuous" optimization approach. We present an algorithm that determines the area which contains the optimal dampers' positions (for specially structured systems). In thesis we have also investigated a case study for a very structured system. The main properties are that internal damping is zero and that undamped eigenfrequencies come in close pairs. Numerical experiments confirm the ability of introduces approximation techniques to significantly accelerate the optimization process.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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