Hybrid Numerical Integration Scheme for Highly Oscillatory Dynamical Systems

Persistent Link:
http://hdl.handle.net/10150/306771
Title:
Hybrid Numerical Integration Scheme for Highly Oscillatory Dynamical Systems
Author:
Gil, Gibin
Issue Date:
2013
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Computational efficiency of solving the dynamics of highly oscillatory systems is an important issue due to the requirement of small step size of explicit numerical integration algorithms. A system is considered to be highly oscillatory if it contains a fast solution that varies regularly about a slow solution. As for multibody systems, stiff force elements and contacts between bodies can make a system highly oscillatory. Standard explicit numerical integration methods should take a very small step size to satisfy the absolute stability condition for all eigenvalues of the system and the computational cost is dictated by the fast solution. In this research, a new hybrid integration scheme is proposed, in which the local linearization method is combined with a conventional integration method such as the fourth-order Runge-Kutta. In this approach, the system is partitioned into fast and slow subsystems. Then, the two subsystems are transformed into a reduced and a boundary-layer system using the singular perturbation theory. The reduced system is solved by the fourth-order Runge-Kutta method while the boundary-layer system is solved by the local linearization method. This new hybrid scheme can handle the coupling between the fast and the slow subsystems efficiently. Unlike other multi-rate or multi-method schemes, extrapolation or interpolation process is not required to deal with the coupling between subsystems. Most of the coupling effect can be accounted for by the reduced (or quasi-steady-state) system while the minor transient effect is taken into consideration by averaging. In this research, the absolute stability region for this hybrid scheme is derived and it is shown that the absolute stability region is almost independent of the fast variables. Thus, the selection of the step size is not dictated by the fast solution when a highly oscillatory system is solved, in turn, the computational efficiency can be improved. The advantage of the proposed hybrid scheme is validated through several dynamic simulations of a vehicle system including a flexible tire model. The results reveal that the hybrid scheme can reduce the computation time of the vehicle dynamic simulation significantly while attaining comparable accuracy.
Type:
text; Electronic Dissertation
Keywords:
Multibody system dynamics; Numerical integration; Singular perturbation; Mechanical Engineering; Dynamical systems
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mechanical Engineering
Degree Grantor:
University of Arizona
Advisor:
Nikravesh, Parviz E.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleHybrid Numerical Integration Scheme for Highly Oscillatory Dynamical Systemsen_US
dc.creatorGil, Gibinen_US
dc.contributor.authorGil, Gibinen_US
dc.date.issued2013-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractComputational efficiency of solving the dynamics of highly oscillatory systems is an important issue due to the requirement of small step size of explicit numerical integration algorithms. A system is considered to be highly oscillatory if it contains a fast solution that varies regularly about a slow solution. As for multibody systems, stiff force elements and contacts between bodies can make a system highly oscillatory. Standard explicit numerical integration methods should take a very small step size to satisfy the absolute stability condition for all eigenvalues of the system and the computational cost is dictated by the fast solution. In this research, a new hybrid integration scheme is proposed, in which the local linearization method is combined with a conventional integration method such as the fourth-order Runge-Kutta. In this approach, the system is partitioned into fast and slow subsystems. Then, the two subsystems are transformed into a reduced and a boundary-layer system using the singular perturbation theory. The reduced system is solved by the fourth-order Runge-Kutta method while the boundary-layer system is solved by the local linearization method. This new hybrid scheme can handle the coupling between the fast and the slow subsystems efficiently. Unlike other multi-rate or multi-method schemes, extrapolation or interpolation process is not required to deal with the coupling between subsystems. Most of the coupling effect can be accounted for by the reduced (or quasi-steady-state) system while the minor transient effect is taken into consideration by averaging. In this research, the absolute stability region for this hybrid scheme is derived and it is shown that the absolute stability region is almost independent of the fast variables. Thus, the selection of the step size is not dictated by the fast solution when a highly oscillatory system is solved, in turn, the computational efficiency can be improved. The advantage of the proposed hybrid scheme is validated through several dynamic simulations of a vehicle system including a flexible tire model. The results reveal that the hybrid scheme can reduce the computation time of the vehicle dynamic simulation significantly while attaining comparable accuracy.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectMultibody system dynamicsen_US
dc.subjectNumerical integrationen_US
dc.subjectSingular perturbationen_US
dc.subjectMechanical Engineeringen_US
dc.subjectDynamical systemsen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMechanical Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorNikravesh, Parviz E.en_US
dc.contributor.committeememberNikravesh, Parviz E.en_US
dc.contributor.committeememberArabyan, Araen_US
dc.contributor.committeememberSanfelice, Ricardo G.en_US
dc.contributor.committeememberStepanov, Mikhailen_US
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