A momentum subspace method for the model-order reduction in nonlinear structural dynamics

Theory and experiments

Journal article (2020)

Authors

Kautuk Sinha Student
Niels K. Singh Student
Mostafa M. Abdalla Zewail City of Science and Technology
R. De Breuker Aerospace Structures & Computational Mechanics - Aerospace Engineering
F. Alijani Dynamics of Micro and Nano Systems - Mechanical, Maritime and Materials Engineering
Research Group
Aerospace Structures & Computational Mechanics (Aerospace Engineering) (TU Delft)
Copyright: © 2020 Kautuk Sinha, Niels K. Singh, Mostafa M. Abdalla, R. De Breuker, F. Alijani
DOI: https://doi.org/10.1016/j.ijnonlinmec.2019.103314
Finite element method Hamiltonian mechanics Model order reduction Nonlinear vibrations
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Published Date

2020

Language

English

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Faculty

Aerospace Engineering

Department

Aerospace Structures & Materials

Research Group

Aerospace Structures & Computational Mechanics

Abstract

The article proposes a method developed for model order reduction in a Finite Element (FE) framework that is capable of computing higher order stiffness tensors. In the method, a truncated third order asymptotic expansion is used for transformation of an FE model to a reduced system. The basis matrix in the formulation of the reduced-order model (ROM) is derived from linear mode shapes of the structure. The governing equations are derived using Hamilton's principle and the method is applied to geometrically nonlinear vibration problems to test its effectiveness. An initial validation of the numerical formulation is obtained by comparison of results from time domain nonlinear vibration analyses of a rectangular plate using Abaqus. Subsequently, a stiffened plate is modeled to test a more complex structure and a continuation algorithm is used in combination with the ROM to compute nonlinear frequency response curves. The validation of the stiffened plate has been performed through comparisons with the results of nonlinear vibration experiments. The experiments are conducted with Polytec Laser Doppler Vibrometer and PAK MK-II measurement systems for large amplitude vibrations to validate the nonlinear vibration analyses.