manlab

2. Descriptif manlab (en français)

Sami Karkar — 2011-06-29T08:44:31Z

Qu'est-ce que Manlab?

Manlab est un logiciel de continuation graphique et interactif destiné à tracer des diagrammes de bifurcation complexes. Il est basé sur la méthode de continuation ``MAN'' reposant sur des développements en séries d'ordre élevé. Manlab est implémenté en language orienté objet sous environnement (c)Matlab. Il est doté d'une interface graphique permettant le contrôle interactif de la continuation: calcul d'une portion de branche, choix d'une direction lors d'un point de bifurcation, changement de sens, ``visualisation utilisateur'' d'un point solution, choix puis effacement d'une portion de branche non désirée. Cet ensemble de fonction apporte une souplesse et une efficacité très appréciable lors de la continuation.

Developpements

Manlab est développé au Laboratoire de Mécanique et d'Acoustique (CNRS-UPR7051). La version 1.0 a été écrite en 2006 pendant la thèse de Remi Arquier (soutenue en 2007). La version 2.0 a été écrite en 2010 pendant la thèse de Sami Karkar (soutenance prévue fin 2011).

Les principaux contributeurs sont :
Rémy Arquier
Bruno Cochelin
Sami Karkar
Arnaud Lazarus
Olivier Thomas
Christophe Vergez.

Documentation

Sami Karkar — 2011-06-29T08:36:48Z

The available documentation consists in:
user guide (see the download section)
scientific papers (see the references section)

1. Description of the Manlab software

2011-06-29T08:30:00Z

What is ManLab?

It's a Matlab package for interactive continuation and bifurcation analysis of non linear systems of equations of the form R(U)=0, where R is a vector of n smooth equations and U a vector of n+1 unknowns.

Manlab provides stability and bifurcation analysis for equilibrium points (fixed points) of dynamical systems.

Manlab also provides algorithms for continuation, stability and bifurcation analysis of periodic orbits of a given dynamical system, using the Harmonic Balance Method.

The continuation principle in ManLab

The continuation is based on the MAN algorithm [1][2] which consists in expanding the unknown U as a formal power series of a path parameter. By using a high order approximation, an accurate and continuous description of the solution branches is obtained.

Linear stability analysis and Bifurcation analysis

The method of computation of the stability in ManLab is based on the computation of the Floquet exponents in the frequency domain with a Hill eigenvalue problem. Since this problem is multivalued, a special procedure for sorting the most converged Floquet exponents is used. The bifurcations position and type are detected by observing the Floquet exponents crossing the imaginary axis.

See the references [9] and [10] for more details about Hill's method.

What is the advantage ?

Because the series contains a great deal of information, the control of the continuation and the detection of bifurcation is much easier than with classical predictor-corrector algorithms.

What is difficult in ManLab ?

For an easy computation of the series in Manlab, the system of equation R(U)=0 must be first written under a polynomial form with a quadratic non-linearity. This is usually the most difficult task for a beginner.

Programming languages

Manlab is written in the Matlab language, using an object-oriented approach. A graphical interface permits to control the continuation and to analyse the results interactively.

For enhancing the continuation of periodic orbits using HBM (which leads to very large algebraic systems) and for the Hill stability analysis, a Fortran acceleration is also provided.

Availability

The package is freely available for scientific use. ManLab is a typical research program which is provided "as is", with no guarantee whatsoever.

Download

Administrateur du Site — 2009-03-30T15:28:01Z

Download Manlab

Manlab is freely available under the terms of the Cecill license agreement

Latest version of the 30th of August 2019:

Package
MANLAB 4.1.7

Previous versions:

Type	Version	Date	File
Package	4.1.5	May 28th 2019	MANLAB 4.1.5
Package	4.1.3	December 19th 2018	MANLAB 4.1.3
Package	4.1.2	August 30th 2018	MANLAB 4.1.2
Package	4.0	April 20th 2018	MANLAB 4.0
User-guide	4.0	April 20th 2018	userguide-4.0
Package	3.0rev2	October 2014	MANLAB v3.0rev2 (beta) Documentation unavailable at the moment. No examples given. Development version.
Package	2.0rev1	October 4th 2011	MANLAB 2.0-rev1 Some bugs have been fixed
Documentation	2.0	October 4th 2011	MANLAB 2.0-rev1 User Guide
Package	2.0	November 8th 2010	MANLAB 2.0
Documentation	2.0	November 8th 2010	MANLAB 2.0 User Guide
Package	1.0	April 3rd 2009	MANLAB 1.0
Documentation	1.0	April 3rd 2009	MANLAB 1.0 User Guide

References for MANLAB

Bruno Cochelin, louis — 2009-01-29T21:41:42Z

Book

Méthode Asymptotique Numérique (in french) by B. Cochelin, N. Damil and M. Potier-Ferry. Hermes Sciences, Lavoisier 2007.

Articles

L. Guillot, A. Lazarus, O. Thomas, C. Vergez, B. Cochelin "A purely frequency based Floquet-Hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems", Journal of Computational Physics, vol. 416, 2020.

L. Guillot, B. Cochelin, C. Vergez "A Taylor series-based continuation method for solutions of dynamical systems", Nonlinear Dynamics, p. 1-19, 2019.

L. Guillot, C. Vergez, B. Cochelin "Continuation of periodic solutions of various types of delay differential equations using asymptotic numerical method and harmonic balance method", Nonlinear Dynamics, vol. 97(1), p. 123-134, 2019.

L. Guillot, B. Cochelin, C. Vergez "A generic and efficient Taylor series–based continuation method using a quadratic recast of smooth nonlinear systems", International Journal of Numerical Methods in Engineering, vol. 119(4), p. 261-280, 2019.

L. Guillot, P. Vigué, C. Vergez, B. Cochelin "Continuation of quasi-periodic solutions with two-frequency Harmonic Balance Method", Journal of Sound and Vibration, vol. 394, p. 434-450, 2017.

P. Vigué, C. Vergez, S. Karkar, B. Cochelin "Regularized friction and continuation: Comparison with Coulomb's law", vol. 389, p.350-363, 2017.

S. Karkar, B. Cochelin, C. Vergez "A comparative study of the harmonic balance method and the orthogonal collocation method on stiff nonlinear systems", Journal of Sound and Vibration, vol. 333, num. 12, p. 2554-2567, 2014.

B.Cochelin, M. Medale "Power series analysis as a major breakthrough to improve the efficiency of Asymptotic Numerical Method in the vicinity of bifurcations." Journal of Computational Physics vol. 236, p. 594-607, 2013.- (download HAL version).

S. Karkar, B. Cochelin, C. Vergez "A high-order, purely frequency based harmonic balance formulation for continuation of periodic solutions: The case of non-polynomial nonlinearities", Journal of Sound and Vibration vol. 332, num. 4, pp. 968-977, 2013.

O. Thomas, A. Lazarus and C. Touzé "A harmonic-based method for computing the stability of periodic oscillations of non-linear structural systems", Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2010, August 2010, Montreal, Canada.

A. Lazarus and O. Thomas "A harmonic-based method for computing the stability of periodic solutions of dynamical systems", Comptes Rendus Mécanique, 338(9), pp. 510-517, 2010.

B. Cochelin C. Vergez. "A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions", Journal of Sound and Vibration, 2009.(download HAL version).

S. Baguet B. Cochelin. '' On the behaviour of the ANM continuation in the presence of bifurcations'', Comm. In Numer. Meth. in Engng,Vol 19, N° 6, p459-471, 2003.

J.M. Cadou, M. Potier-Ferry, B. Cochelin and N. Damil "Asymptotic Numerical Method for stationary Navier-Stokes equation and with Petrov-Galerkin formulation", Int. J. Numer. Methods Engng, Vol 50, p 825-845, 2001

H. Zarouni, B. Cochelin and M. Potier-Ferry. "Asymptotic-numerical methods for shells with finite rotations" Computer Methods in Applied Mecahnics and Engineering, Vol 175, 71-85, 1999.

A. Najah, B. Cochelin, N. Damil and M. Potier-Ferry. "A critical review of Asymptotic-Numerical Method"" Archives of Computational Methods in Engineering, Vol 5, 31-50, 1998

B. Cochelin. " A path following technique via an Asymptotic-Numerical method" Computers & Structures, Vol 53, N° 5, p 1181-1192, 1994.

B. Cochelin, N. Damil and M. Potier-Ferry. " Asymptotic-Numerical Methods and Padé approximants for non- linear elastic structures" Int. J. Numer. Methods Engng , Vol 37, p 1187-1213, 1994.

PhD. Theses

L. Guillot "On a quadratic formalism for the continuation of the solutions of dynamical systems and their bifurcations - Applications to reed instruments", PhD Thesis, Aix-Marseille University, 2020 (supervisors : C.Vergez and B.Cochelin)

Below, a package containing the articles (author's versions) from the PhD Thesis to download :


Papers from L.Guillot PhD

P. Vigué "Solutions périodiques et quasi-périodiques de systèmes dynamiques d'ordre entier ou fractionnaire - Applications à la corde frottée", PhD Thesis, Aix-Marseille University, 2017 (supervisors : C.Vergez and B.Cochelin)

S. Karkar "Méthodes numériques pour les systèmes dynamiques non linéaires. Application aux instruments de musique auto-oscillants", PhD Thesis, Aix-Marseille University, 2012. (supervisors : B. Cochelin and C. Vergez)

Contacts manlab 2.0

Bruno Cochelin, Manlab, Sami Karkar, Stephane Lejeunes — 2009-01-29T20:04:46Z

Contact

Today, Manlab is maintained and upgraded by:

Louis Guillot, Laboratoire de Mécanique et d'Acoustique Marseille, France.
Bruno Cochelin, Materials and Structures team, Laboratoire de Mécanique et d'Acoustique Marseille, France.
Christophe Vergez, Sounds team, Laboratoire de Mécanique et d'Acoustique Marseille, France.

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Screen shot

Bruno Cochelin — 2009-01-29T09:29:02Z

Screenshots

Bifurcation diagram of a small system with two equations

Bifurcation diagram of an elastic half ring subjected to a point load. A Finite Element program is included in ManLab for analysis of large displacement of elastic structures.

Computation of the periodic solutions of the Van der Pol oscillator using the harmonic balance method and ManLab

A bifurcation diagram showing many bifurcations