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27 March 2012 Optimization of a passive piezoelectric damper for a viscously damped main system
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Structural vibrations can be reduced by shunted piezoelectric elements. The passive piezoelectric damper considered here, consists of a piezoelectric element connected to a host structure and shunted by an inductor-resistor network. The paper gives an in depth analysis on the tuning of the inductor and resistor parameters of the electric network with regard to different optimization goals. The calculations are based on a 2-degree-of-freedom model of the host structure and the shunted piezoelectric element. Three optimization goals are studied: The objective of eigenvalue optimization is to get both pairs of eigenvalues to be equal. Then the damping ratio of the host structure is maximized, leading to a minimized decay time of the free vibration. In the H2 optimization the total vibration energy within the host system is minimized, leading to optimal results in case of a broad-band excitation. In the H optimization the objective is to minimize the maximum amplitude of the host structure over the whole frequency spectrum. Analytical solutions for these optimization goals are already known in the special case of a host structure without damping. In the more general case of a viscously damped host structure analytical solutions for the eigenvalue and H2 optimization goal are derived. In case of the H optimization goal an analytical solution cannot be found and perturbation theory is used to calculate an analytical approximation. The approximation is compared to the numerical solution in order to check its accuracy.
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Sebastian M. Schwarzendahl, Marcus Neubauer, and Jörg Wallaschek "Optimization of a passive piezoelectric damper for a viscously damped main system", Proc. SPIE 8341, Active and Passive Smart Structures and Integrated Systems 2012, 834107 (27 March 2012);

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