Bridging the Gap Between Nonlinear Normal Modes and Modal Derivatives

Bridging the Gap Between Nonlinear Normal Modes and Modal Derivatives

Sombroek, C.S.M.

Tiso, P. (mentor)

Mechanical, Maritime and Materials Engineering

Precision and Microsystems Engineering

Engineering Mechanics

2015-11-02

Nonlinear Normal Modes (NNMs) have a clear conceptual relation to the classical linear normal modes (LNMs), yet they offer a solid theoretical framework for interpreting a wide class of non-linear dynamical phenomena with no linear counterpart. The main difficulty associating with NNMs is that the computation for real-size models is expensive, particularly for models with distributed nonlinearities e.g. those of geometric nature. The NNM computation involves repeated direct nonlinear time integration combined with a sensitivity analysis to determine the frequency-energy dependency for the modes of interest. In this thesis, NNMs are computed from reduced order models (ROMs) comprising LNMs and Modal Derivatives (MDs). The MDs have a direct relationship with the vibration modes (VMs), and can therefore be used as natural extension to LNMs to accurately represent the NNMs of interest. Two projection based reduction methods are used, one being the classical Galerkin projection reduction technique, the other is obtained from a quadratic coordinate transformation based on the Taylor series expansion. The NNMs computed from the ROMs are directly compared to those obtained from the full system analysis, which will highlight the importance of MDs in capturing essential nonlinear phenomena. The methodology is demonstrated on a doubly clamped beam, a shallow arch and a Roorda-frame.

Nonlinear Normal Modes
Modal Derivatives
Model-order reduction
Quadratic manifold

http://resolver.tudelft.nl/uuid:dc31561d-5fdc-47b4-bdcb-0957360bbed1

Student theses

master thesis

(c) 2015 Sombroek, C.S.M.