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Correlation of eigenmodal values and material parameters of a dynamical system using Neural Networks

Manos Andreas

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Summary

The eigenmodal values of a dynamical system are its eigenvalues and eigenvectors and show its way of response. They are described by mathematical relations, but the practical part of obtaining its solution is difficult and challenging, especially when it needs to be integrated with real time systems.In the current thesis, the relation between the eigenmodal values of a mechanical dynamical system and its parameters is approached, using Neural Networks. In particular, the change of its eigenvalues and eigenvectors is studied, when the elasticity modulus has different values at different spots on the construction. Analysis is applied to a rod model which is discretized by the finite element method. The results are depicted in the Octave’s programming environment.Firstly, the main components of a dynamical system are stated. Its main properties and the way of its analysis are mentioned. Furthermore, Neural Networks are presented as they are an essential tool for the study of the dynamical problem of the current thesis.Subsequently, the way of approaching of the subject of the thesis is analyzed. The processes that took place in the Octave’s environment and the changes in the data that the program used, are explained. Moreover, the eigenmodal values and the diagrams depicting the changes that occurred are presented.At the end, Neural Network’s results are assessed. The changes caused to the system are mentioned and corresponding conclusions are drawn.

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