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In this paper we deal with the flow of natural convection between two vertical planes with horizontal temperature gradient. We show that periodic steady flow occur when Rayleigh number increases. Critical values are obtained numerically and a nonlinear analysis is presented according to Center manifold method. 相似文献
2.
Models involving maximal monotone term and history (delay) term are considered in a mathematical and numerical point of view. 相似文献
3.
Perturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched. Among them, normal form theory provides a reliable method for systematically simplifying dynamical systems via nonlinear change of coordinates, and is also used in a mechanical context to define Nonlinear Normal Modes (NNMs). The main recognized drawback of perturbation methods is the absence of a criterion establishing their range of validity in terms of amplitude. In this paper, we propose a method to obtain upper bounds for amplitudes of changes of variables in normal form transformations. The criterion is tested on simple mechanical systems with one and two degrees-of-freedom, and for complex as well as real normal form. Its behavior with increasing order in the normal transform is established, and comparisons are drawn between exact solutions and normal form computations for increasing levels of amplitudes. The results clearly establish that the criterion gives an upper bound for validity limit of normal transforms. 相似文献
4.
Jérôme Bastien Claude-Henri Lamarque 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(5):393-407
Persoz’s gephyroidal model, which consists of elementary rheological models (dry friction element and linear spring), can
be covered by the existence and uniqueness theory for maximal monotone operators. Moreover, classical results of numerical
analysis allow one to use a numerical implicit Euler scheme, with convergence order of the scheme equal to one. Some numerical
simulations are presented. 相似文献
5.
Alireza Ture Savadkoohi Claude-Henri Lamarque Zoran Dimitrijevic 《Nonlinear dynamics》2012,70(2):1473-1483
The concept of the vibratory energy transfer between a linear master DOF and a nonsmooth nonlinear energy sink (NES) in the presence of gravity forces is studied. Different invariant manifolds of the system at different time scales are revealed and necessary conditions for leading the behavior of the system to strongly modulated response (SMR) are enlightened. 相似文献
6.
7.
Vaurigaud Bastien Ture Savadkoohi Alireza Lamarque Claude-Henri 《Nonlinear dynamics》2011,66(4):763-780
In this paper, we study a Targeted Energy Transfer (TET) problem between a p degrees-of-freedom (dof) linear master structure and several coupled parallel slave Nonlinear Energy Sink (NES) systems.
In detail, each lth dof l=1,2,…,p contains n
l
parallel NES; so the linear structure has (n
1+n
2+⋅⋅⋅+n
l
+⋅⋅⋅+n
p
) NES. We are interested to study analytically the TET phenomenon during the first mode of the compound system. To this end,
complexification, averaging, and multiple scales methods are used. 相似文献
8.
We present new analytical approach to the problem of energy pumping in strongly non- homogeneous nonlinear two-degree-of-freedom
(2DOF) systems with single anchor spring under condition of initial impact. Energy pumping is a passive, almost irreversible
transfer of mechanical energy from the main substructure of the system to the light auxiliary attachment. The mechanism of
energy pumping in the system under consideration is a resonance capture. The approach is based on application of Laplace transformation
to the principal asymptotic approximation of the equations of motion in complex form and using the power expansion of the
solution in terms of time. Obtained temporal dependence of the system energetic characteristics gives a tool for estimation
of energy pumping efficiency. In particular, we show that the system without an anchor spring in attachment is more efficient
than the system with such a spring. Numerical simulations confirm the analytical results. 相似文献
9.
Frédéric Bernardin Michelle Schatzman Claude-Henri Lamarque 《Comptes Rendus Mathematique》2004,338(11):837-842
The existence and uniqueness of solutions to multivalued stochastic differential equations of the second order on Riemannian manifolds are proved. The class of problem is motivated by rigid body and multibody dynamics with friction and an application to the spherical pendulum with friction is presented. To cite this article: F. Bernardin et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
10.
Alireza Ture Savadkoohi Bastien Vaurigaud Claude-Henri Lamarque Stéphane Pernot 《Nonlinear dynamics》2012,67(1):37-46
In this paper governing equations of general multi degrees of freedom (dof) systems with trees of parallel Nonlinear Energy
Sink (NES) devices at each dof are derived. Then these equations are summarized for a 4 dof structure with two parallel NES
at the 4th dof in order to control the first mode of the system. A prototype four storey structure with two parallel NES at the top
floor is studied experimentally. The NES of the mentioned system is designed by endowing the suggested method in the Part
I of this paper. A couple of experimental tests are carried out on the structure at the DGCB laboratory of the ENTPE, France.
The aim is to control the first mode of the compound nonlinear system by demonstrating the efficiency of the parallel NES
systems on the intended task. 相似文献
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