Modal derivatives based reduced-order modelling in parametrically driven structures and frequency dividers

Master thesis (2019)

Authors

J.L. van den Broek Mechanical Engineering

Contributors

F. Alijani Dynamics of Micro and Nano Systems - Mechanical, Maritime and Materials Engineering (supervisor 1)
P. Tiso ETH Zürich (supervisor 1)
G.J. Verbiest Dynamics of Micro and Nano Systems - Mechanical, Maritime and Materials Engineering (supervisor 2)
A.M. Aragon Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering (supervisor 2)
Faculty
Mechanical Engineering
Copyright: © 2019 Jaïr van den Broek
Reduced order model Parametric resonance Modal derivatives
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Published Date

27-11-2019

Language

English

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Faculty

Mechanical Engineering

Abstract

The application of Modal Derivatives (MDs) in conventional reduction methods is an effective method to capture geometric nonlinearities in Finite Element Models (FEMs). Reduction methods, in general, are used to effectively reduce the number of unknowns in FEMs for the sake of computational efficiency. We investigated the applicability of three MDs-based reduction methods in parametrically excited and parametric resonating structures, the focus lays on the steady-state responses. Benchmark in this project is a mechanical Frequency Divider (FD) that consists of cascading mechanical components, each of which is excited by the preceding one by means of parametric resonance. After full activation of the FD, a frequency division along the array of resonators is achieved with a factor 2^i at resonator i. The modularity of the FD makes it an excellent candidate for testing the application of component mode synthesis, where each substructure of the cascade is independently reduced and connected to other members via common interface.