A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control

Abstract

Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publicationCitation for published version (APA): Besselink, B., Lutowska, A., Tabak, U., Wouw, van de, N., Nijmeijer, H., Hochstenbach, M. E., ... Rixen, D. J. (2013). A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control. (CASA-report; Vol. 1327). Eindhoven: Technische Universiteit Eindhoven. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. AbstractIn this paper, popular model reduction techniques from the fields of structural dynamics, numerical mathematics and systems and control are reviewed and compared. The motivation for such a comparison stems from the fact the model reduction techniques in these fields have been developed fairly independently. In addition, the insight obtained by the comparison allows for making a motivated choice for a particular model reduction technique, on the basis of the desired objectives and properties of the model reduction problem. In particular, a detailed review is given on mode displacement techniques, moment matching methods and balanced truncation, whereas important extensions are outlined briefly. In addition, a qualitative comparison of these methods is presented, hereby focussing both on theoretical and computational aspects. Finally, the differences are illustrated on a quantitative level by means of application of the model reduction techniques to a common example.

A MAC based excitation frequency increasing method for structural topology optimization under harmonic excitations

“…It is noted that, the inverse of the stiffness matrix can be represented by using all eigenmodes [17]:…”

“…Besselink et al [17] made comparisons between MDM and MAM, he found that MAM outperformed the MDM in all cases. Hence, we adopt the MAM to calculate the displacement response.…”

Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications

“…For this reason, a combination of the harmonic balance method (HBM) [18,[23][24][25] which is based on a fundamental harmonic or multi-harmonic approximation of the nonlinear forces, together with model reduction techniques [26][27][28] has emerged as a widely used approach to solve vibration problems.…”

Método computacional para la aceleración de análisis paramétricos de modificaciones locales en estructuras complejas sometidas a cargas dinámicas

“…Como se describe en [Qu, 2004] [Besselink, 2013], los métodos de reducción más comunes se basan en el método de la superposición modal [Rayleigh, 1945], según el cual un número limitado de modos de vibración de la estructura puede representar el comportamiento dinámico de la estructura completa a cambio de una pérdida de precision [Liu et al , 2000] [Leontiev, n.d.] [ Li & Gunter, 1981]. Es muy común la implementación de mejoras y modi…caciones a este método [Farstad & Singh, 1996] como el método [Rixen, 2001] del aumento de la truncatura modal [Tham et al , 2009], el método del desplazamiento modal o el método de la aceleración modal [Rixen, 2009].…”