Multiple scales Analysis of the impact of a bending beam on a rigid surface
Promotor(s) : Denoël, Vincent
Date of defense : 26-Jun-2019/27-Jun-2019 • Permalink :
|Title :||Multiple scales Analysis of the impact of a bending beam on a rigid surface|
|Author :||Delcourt, Arnaud|
|Date of defense :||26-Jun-2019/27-Jun-2019|
|Advisor(s) :||Denoël, Vincent|
|Committee's member(s) :||Vanderheyden, Benoît
|Discipline(s) :||Engineering, computing & technology > Mechanical engineering|
|Institution(s) :||Université de Liège, Liège, Belgique|
|Degree:||Master en ingénieur civil physicien, à finalité approfondie|
|Faculty:||Master thesis of the Faculté des Sciences appliquées|
[en] The purpose of this master thesis is to study the behavior of a bent beam impacting
a rigid wall with the vibrating dynamics generated. This problem is recurrent in di erent
fields of engineering. One example is the drilling in petroleum industry.
Two approaches are investigated: the analytical and numerical fields. The first
objective is to study the leading order. Then, the purpose is to study the properties of the
behavior at the second order.
In the analytical part, the perturbation method is used to separate the slow (natural
vibration mode) and fast (impact of an infinitely long beam) dynamics. To solved
separately these two dynamics, the multi scales method is introduced and the matching
will occur to satisfy the complementary condition of no penetration.
In the numerical simulations, a nonsmooth solver is used to represent the
discontinuity. Indeed, with the activation of the unilateral constraint, a temporal
discontinuity appears. Moreover, at the borders of the contact, a spatial discontinuity
occurs. A er an analysis on the numerical parameters, the results obtained by
simulations are compared to those obtained theoretically.
For the majority of the results at leading order, the results obtained with both
analytical and numerical approaches are consistent. The high order have also been
introduced. However, we met troubles because of numerical errors and thus the only the
tendencies could be observed. The tracks given in the end of this document may be
investigated to get the matching.
Cite this master thesis
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