Perturbation techniques in mathematics, physics, and engineering, 1964. ,
Mitropol ? ski? ?. Asimptoti?eskie metody v teorii neline? ?nyh kolebani? ?, Gosudarstv. Izdat. Tehn.-Teor. Lit, 1955. ,
Asymptotic methods in the theory of non-linear oscillations. Translated from the second revised Russian edition, International Monographs on Advanced Mathematics and Physics, 1961. ,
Vibration d'une barre avec une loi de comportement localement non linéaire, Proceedings of " Tendances des applications mathématiques en Tunisie, pp.479-485, 2009. ,
Double scale analysis of periodic solutions of some non linear vibrating systems, Bra] N. Ben Brahim. Vibration d'une barre avec une loi de comportement localement non linéaire. Communication au Congrès Smai, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00776184
Vibration of a bar with a law of behaviour locally nonlinear, pp.18-22, 2010. ,
Modulation of torsional waves in a rod with a crack, J.Acoust. Soc. AM, vol.3, issue.106, pp.1289-1291, 1999. ,
Théorie des vibrations. ApplicationàApplicationà la dynamique des structures, 1993. ,
Mechanical vibrations : theory and application to structural dynamics, 1997. ,
Numerical and experimental study for a beam system with local unilateral contact modelling satellite solar arrays, Proceedings of the 11th European spacecraft structures, materials and mechanical testing conference, 2009. ,
Finite element for a beam system with nonlinear contact under periodic excitation Ultrasonic wave propagation in non homogeneous media, springer proceedings in physics, pp.149-160, 2009. ,
Frequency sweep for a beam system with local unilateral contact modelling satellite solar arrays, Proceedings of " Tendances des applications mathématiques en Tunisie, pp.541-545, 2009. ,
Comparison of several numerical methods for mechanical systems with impacts, International Journal for Numerical Methods in Engineering, vol.51, issue.9, pp.1101-1132, 2001. ,
DOI : 10.1002/nme.206
URL : https://hal.archives-ouvertes.fr/hal-00814950
Non smooth deterministic or stochastic discrete dynamical systems. Applications to models with friction or impact. , Mechanical Engineering and Solid Mechanics Series, 2013. ,
Large-amplitude non-linear normal modes of piecewise linear systems, Journal of Sound and Vibration, vol.272, issue.3-5, 2004. ,
DOI : 10.1016/S0022-460X(03)00497-8
URL : https://hal.archives-ouvertes.fr/hal-01350797
Dilatation of a One-Dimensional Nonlinear Crack Impacted by a Periodic Elastic Wave, SIAM Journal on Applied Mathematics, vol.70, issue.3, pp.70-3735, 2009. ,
DOI : 10.1137/080741021
URL : https://hal.archives-ouvertes.fr/hal-00339279
Interaction between periodic elastic waves and two contact non-linearities. Mathematical Models and Methods in Applied Sciences Asymptotic expansion of vibrations with unilateral contact, Ultrasonic wave propagation in non homogeneous media, springer proceedings in physics, pp.173-182, 2009. ,
The method of strained coordinates for vibrations with weak unilateral springs, IMA Journal of Applied Mathematics, vol.76, issue.2, 2010. ,
DOI : 10.1093/imamat/hxq045
URL : https://hal.archives-ouvertes.fr/hal-00395351
The Duffing equation. Nonlinear oscillators and their behaviour, 2011. ,
Nonlinear normal modes, Part I: A useful framework for the structural dynamicist, Mechanical Systems and Signal Processing, vol.23, issue.1, pp.170-194, 2009. ,
DOI : 10.1016/j.ymssp.2008.04.002
URL : https://hal.archives-ouvertes.fr/hal-01357931
Physique théorique. Tome I. Mécanique.Deuxì emé edition revue et complétée, ´ Editions Mir, 1966. ,
Nonlinear modal analysis of mechanical systems with frictionless contact interfaces., " Comput. Mech Hall Introduction to Hamiltonian dynamical systems and the N-Body problem, pp.469-478, 1992. ,
URL : https://hal.archives-ouvertes.fr/hal-00413696
Applied asymptotic analysis, Graduate Studies in Mathematics, vol.75, 2006. ,
Frequency up-conversion and frequency down-conversion of acoustic waves in damaged materials, Physics Letters A, vol.301, issue.3-4, pp.281-290, 1991. ,
DOI : 10.1016/S0375-9601(02)00974-X
Introduction to perturbation techniques, 1981. ,
Perturbation methods in nonlinear dynamics In Nonlinear dynamics aspects of particle accelerators, Lecture Notes in Phys, vol.247, pp.238-314, 1985. ,
Resolving controversies in the application of the method of multiple scales and the generalized method of averaging., Nonlinear Dyn, pp.61-102, 2005. ,
The general problem of the stability of motion English translation by Fuller from Edouard Davaux's french translation Probì eme général de la stabilité du mouvement) 9 (1907)); this french translation is to be found in url, Russian in Kharkov. Mat. Obshch, 1892. ,
Méthodes nouvelles de la mécanique céleste, pp.1892-1899 ,
Periodic solutions of o.d.e. systems with a Lipschitz non linearity, 2011. ,
On a derivative-expansion technique and some comments on multiple scaling in the asymptotic approximation of solutions of certain differential equations, SIAM Rev, vol.20, issue.1, pp.79-105, 1978. ,
Averaging methods in nonlinear dynamical systems, 1985. ,
DOI : 10.1007/978-1-4757-4575-7
Détection vibroacoustique non linéaire d' endomagements dans une structure poutre, 2003. ,
Application of non-linear ultrasonic spectroscopy to health monitoring and damage detection in structures,. 38p, 75th Shock and Vibration Symposium, 2004. ,
Non destructive testing with non linear vibroacoustic, Septì eme colloque national en Calcul de structures, pp.603-608, 2005. ,
A perturbation method for evaluating nonlinear normal modes of a piecewise linear two-degrees-of-freedom system, Nonlinear Dynamics, vol.35, issue.3, pp.379-393, 2008. ,
DOI : 10.1007/s11071-008-9337-3