Multiple scales analyses of the dynamics of weakly nonlinear mechanical systemsSource: Applied Mechanics Reviews:;2003:;volume( 056 ):;issue: 005::page 455DOI: 10.1115/1.1581884Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This review article starts by addressing the mathematical principles of the perturbation method of multiple scales in the context of mechanical systems which are defined by weakly nonlinear ordinary differential equations. At this stage the paper investigates some different forms of typical nonlinearities which are frequently encountered in machine and structural dynamics. This leads to conclusions relating to the relevance and scope of this popular and versatile method, its strengths, its adaptability and potential for different variant forms, and also its weaknesses. Key examples from the literature are used to develop and consolidate these themes. In addition to this the paper examines the role of term-ordering, the integration of the so-called small (ie, perturbation) parameter within system constants, nondimensionalization and time-scaling, series truncation, inclusion and exclusion of higher order nonlinearities, and typical problems in the handling of secular terms. This general discussion is then applied to models of the dynamics of space tethers given that these systems are nonlinear and necessarily highly susceptible to modelling accuracy, thus offering a rigorous and testing applications case-study area for the multiple scales method. The paper concludes with comments on the use of variants of the multiple scales method, and also on the constraints that the method can bring to expectations of modelling accuracy. This review article contains 134 references.
keyword(s): Resonance , Dynamics (Mechanics) , Motion , Equations of motion , Vibration , Equations , Damping , Bifurcation AND Stability ,
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contributor author | MP Cartmell | |
contributor author | SW Ziegler | |
contributor author | R Khanin | |
contributor author | DIM Forehand | |
date accessioned | 2017-05-09T00:09:11Z | |
date available | 2017-05-09T00:09:11Z | |
date copyright | September, 2003 | |
date issued | 2003 | |
identifier issn | 0003-6900 | |
identifier other | AMREAD-25832#455_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/127763 | |
description abstract | This review article starts by addressing the mathematical principles of the perturbation method of multiple scales in the context of mechanical systems which are defined by weakly nonlinear ordinary differential equations. At this stage the paper investigates some different forms of typical nonlinearities which are frequently encountered in machine and structural dynamics. This leads to conclusions relating to the relevance and scope of this popular and versatile method, its strengths, its adaptability and potential for different variant forms, and also its weaknesses. Key examples from the literature are used to develop and consolidate these themes. In addition to this the paper examines the role of term-ordering, the integration of the so-called small (ie, perturbation) parameter within system constants, nondimensionalization and time-scaling, series truncation, inclusion and exclusion of higher order nonlinearities, and typical problems in the handling of secular terms. This general discussion is then applied to models of the dynamics of space tethers given that these systems are nonlinear and necessarily highly susceptible to modelling accuracy, thus offering a rigorous and testing applications case-study area for the multiple scales method. The paper concludes with comments on the use of variants of the multiple scales method, and also on the constraints that the method can bring to expectations of modelling accuracy. This review article contains 134 references. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Multiple scales analyses of the dynamics of weakly nonlinear mechanical systems | |
type | Journal Paper | |
journal volume | 56 | |
journal issue | 5 | |
journal title | Applied Mechanics Reviews | |
identifier doi | 10.1115/1.1581884 | |
journal fristpage | 455 | |
journal lastpage | 492 | |
identifier eissn | 0003-6900 | |
keywords | Resonance | |
keywords | Dynamics (Mechanics) | |
keywords | Motion | |
keywords | Equations of motion | |
keywords | Vibration | |
keywords | Equations | |
keywords | Damping | |
keywords | Bifurcation AND Stability | |
tree | Applied Mechanics Reviews:;2003:;volume( 056 ):;issue: 005 | |
contenttype | Fulltext |