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Model order reduction for design, analysis and control of nonlinear vibratory systems

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Model order reduction for design, analysis and control of nonlinear vibratory systems/ edited by Cyril Touzé, Attilio Frangi.
other author:	Touzé, Cyril.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	ix, 298 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Dimension reduction (Statistics) -
Online resource:	https://doi.org/10.1007/978-3-031-67499-0
ISBN:	9783031674990

Model order reduction for design, analysis and control of nonlinear vibratory systems
Model order reduction for design, analysis and control of nonlinear vibratory systems[electronic resource] /edited by Cyril Touzé, Attilio Frangi. - Cham :Springer Nature Switzerland :2025. - ix, 298 p. :ill. (some col.), digital ;24 cm. - CISM International Centre for Mechanical Sciences, Courses and lectures,v. 6142309-3706 ;. - Courses and lectures ;no. 505..

Modelling, Reductionism and the Implications for Digital Twins -- Nonlinear normal modes as invariant manifolds for model order reduction -- The Direct Parametrization of Invariant Manifolds applied to model order reduction of microstructures -- Understanding, computing and identifying the nonlinear dynamics of elastic and piezoelectric structures thanks to nonlinear modes.

The book presents reduction methods that are using tools from dynamical systems theory in order to provide accurate models for nonlinear dynamical solutions occurring in mechanical systems featuring either smooth or non smooth nonlinearities. The cornerstone of the chapters is the use of methods defined in the framework of the invariant manifold theory for nonlinear systems, which allows definitions of efficient methods generating the most parsimonious nonlinear models having minimal dimension, and reproducing the dynamics of the full system under generic assumptions. Emphasis is put on the development of direct computational methods for finite element structures. Once the reduced order model obtained, numerical and analytical methods are detailed in order to get a complete picture of the dynamical solutions of the system in terms of stability and bifurcation. Applications from the MEMS and aerospace industry are covered and analyzed. Geometric nonlinearity, friction nonlinearity and contacts in jointed structures, detection and use of internal resonance, electromechanical and piezoelectric coupling with passive control, parametric driving are surveyed as key applications. The connection to digital twins is reviewed in a general manner, opening the door to the efficient use of invariant manifold theory for nonlinear analysis, design and control of engineering structures.

ISBN: 9783031674990

Standard No.: 10.1007/978-3-031-67499-0doiSubjects--Topical Terms:

882203
Dimension reduction (Statistics)

LC Class. No.: TA347.D5

Dewey Class. No.: 621.015308

Model order reduction for design, analysis and control of nonlinear vibratory systems
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520 $a The book presents reduction methods that are using tools from dynamical systems theory in order to provide accurate models for nonlinear dynamical solutions occurring in mechanical systems featuring either smooth or non smooth nonlinearities. The cornerstone of the chapters is the use of methods defined in the framework of the invariant manifold theory for nonlinear systems, which allows definitions of efficient methods generating the most parsimonious nonlinear models having minimal dimension, and reproducing the dynamics of the full system under generic assumptions. Emphasis is put on the development of direct computational methods for finite element structures. Once the reduced order model obtained, numerical and analytical methods are detailed in order to get a complete picture of the dynamical solutions of the system in terms of stability and bifurcation. Applications from the MEMS and aerospace industry are covered and analyzed. Geometric nonlinearity, friction nonlinearity and contacts in jointed structures, detection and use of internal resonance, electromechanical and piezoelectric coupling with passive control, parametric driving are surveyed as key applications. The connection to digital twins is reviewed in a general manner, opening the door to the efficient use of invariant manifold theory for nonlinear analysis, design and control of engineering structures.
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