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1 Image Processing & Communications

1 2006

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Frequency optimization based on semi-analytical and "exact" numerical differentiation methods

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Bednarek T. , Sosnowski W.

Image Processing & Communications

2006

tom Vol. 11, no 1

7-17

In this paper exact sensitivity and optimization of free vibrating systems is considered. Finite element formulation of natural frequencies problem is presented. It is known that natural frequencies of free vibrations can be treated as eigenvalues of some generalized eigen-problem. Reduction of the eigenvalue system algorithm is shown. The sensitivity of eigenvalues with respect to design parameter is presented. The stiffened plate and double-disk rotor shaft system are taken as an example. The goal of optimization is to move natural frequencies as far as possible from resonance frequency. The sensitivities of objective function are calculated by three different methods: Finite Difference Method, semi-analytical method and "exact" Direct Differentiation Method. Results are compared.