Nonlinear dynamic behaviour of joined lightweight structures [Elektronische Ressource] / Souheib Abdul Karim

Sakarim

Informations

• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2011
• Nombre de lectures: 25
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

LEHRSTUHL UND INSTITUT FÜR LEICHTBAU
Rheinisch-Westfälische Technische Hochschule Aachen



Nonlinear Dynamic Behaviour of
Joined Lightweight Structures


















Souheib Abdul Karim




Nonlinear Dynamic Behaviour of
Joined Lightweight Structures





Von der Fakultät für Maschinenwesen der Rheinisch-Westfälischen Technischen
Hochschule Aachen zur Erlangung des akademischen Grades eines Doktors der
Ingenieurwissenschaften genehmigte Dissertation

vorgelegt von
Souheib Abdul Karim





Berichter: Univ.-Prof. Dr.-Ing. H.-G. Reimerdes
Univ.-Prof.em Dr.-Ing. J. Ballmann

Tag der mündlichen Prüfung: 27.04.2011


Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.

Nonlinear Dynamic Behaviour of
Joined Lightweight Structures




Der Fakultät für Maschinenwesen
der Rheinisch-Westfälischen Technischen Hochschule
Aachen


vorgelegte Dissertation zur Erlangung des
akademischen Grades eines Doktors der
Ingenieurwissenschaften


von

Souheib Abdul Karim
Dedication



To my parents

Father and Mother

Who taught me that even the largest task can be accomplished
if it is done one step at a time.
Acknowledgments

I would like to sincerely and enthusiastically thanks to Prof. H.-G. Reimerdes for
his kindness and helpfulness. Throughout this thesis, his patience as a supervisor is
unlimited. His direction is priceless. While reviewing all my writing, his
recommendations were very constructive. Also, I am grateful to him for accepting
me to join his institute and opening the institute facilities to make this work
happen.
I must also acknowledge examination doctorate committee, Prof. J. Ballmann and
Prof. D. Moormann.
I thank also Dr.-Ing. Athanasios Dafnis for granting me his time as it needed in his
eventful schedules for enhancing my knowledge by his comments at various
stages of my Ph.D. course.
Most importantly, I would like to thank my parents, brothers, sister, my wife and
my kinds for their unconditional support, love and affection. Their encouragement
and never-ending kindness made everything easier to achieve.
Also, I would like also to thank my colleague in the institute for their kindness and
their continuous encourage.
Eventually, I also would like to thank the institute secretary and the technical
team, namely: It-team, Laboratory and workshop staff for on-time support in
different issues. Abstract
This study is primarily focused on investigating the linear and nonlinear behaviour of
beams and plates under dynamic loads. Additionally, it aims to provide a thorough
understanding of the interaction between the frictional joint and the joined part. To this
end, a new model for the joint has been suggested. It is intended to bridge the gap as
shown by the literature review. Further, the model is adjusted to mediate a trade-off
between low computation cost and acceptable prediction capability of true physics;
portability and integrability features are attributed so they can be implemented easily.
Practicability of the model is demonstrated by dynamic analysis. In particular, full
time series analysis was carried out twice, one time for a beam and one time for a
plate. In both cases, the stick-slip mechanism is allowed to interact with the
geometrical nonlinearity of the beam or the plate model on a flexible support.
Furthermore, for validation purposes, results from the plate model were compared to
results from literature, experiments and some applicable analytical solutions.
In order to make the results available, various computation software packages have
been used parallel with some in-house programs coded by MATLAB. Furthermore, a
variety of solution methodologies have been adopted such as finite element, finite
difference for spatial state variables discretization and a direct time integration scheme
for time domain variables. In order to evaluate the joint parameter impact on the built-
up structures, the damping due to stick-slip at the joint is estimated by evaluating the
dissipated energy.
The final results show that the suggested lumped model is able to capture some
realistic phenomena such as stick-slip and the interaction between the joint and the
geometrical nonlinearity of the joined components. Obviously, the model is able to
accommodate the damping due to the stick-slip at the joints. Hence, this allows for the
optimizing process for joint parameters based on damping and stability conditions.
In conclusion, in addition to the well-known vital role of the joint as a major
participant in the system damping, the results also show the contribution of the joint to
the overall behaviour. More precisely, the joint suppresses the high peaks of the
internal, in-plane forces compared with case of fully clamped boundary conditions.

Table of contents III

Table of contents
Abstract ............................................................................................................................I
Table of contents........................................................................................................... III
List of Figures ..............................................................................................................VII
List of Tables ............................................................................................................. XIII
1 Introduction .............................................................................................................. 1
1.1 Motivation........................................................................................................ 1
1.2 Literature Review............................................................................................. 5
1.2.1 Elasticity Theory Evolution ............................................................................ 6
1.2.2 Frictional Joints............................................................................................. 10
1.2.3 Stick-slip ....................................................................................................... 15
1.2.4 Damping........................................................................................................ 16
1.3 Objective of the Study.................................................................................... 16
1.4 Outline of the Thesis ...................................................................................... 18
2 Theoretical Background......................................................................................... 19
2.1 Types of Nonlinearity .................................................................................... 19
2.1.1 Contact Nonlinearity ..................................................................................... 19
2.1.2 Geometrical Nonlinearity.............................................................................. 20
2.1.2.1 Softening Type of Nonlinearity .......................................................... 20
2.1.2.2 Stiffening Type of Nonlinearity.......................................................... 21
2.1.3 Material Nonlinearity.................................................................................... 21
2.2 Friction ........................................................................................................... 22
2.2.1 Factors Affecting the Friction between Surfaces.......................................... 22
2.2.2 Static Coefficient of Friction......................................................................... 23
2.2.3 Dynamic Coefficient of Friction ................................................................... 23
2.3 Elasticity Theory ............................................................................................ 23
2.3.1 General Strain-Displacements Equations (Geometric-Logic) ...................... 24
2.3.2 Constitutive Equations (Stress-Strain Relation) ........................................... 25
2.3.3 Equilibrium Equations (Physical Law)......................................................... 26
2.3.4 Compatibility Equations ............................................................................... 26
2.4 Beam Theories ............................................................................................... 27 IV Table of contents

2.4.1 Strain-Displacement Equations..................................................................... 27
2.4.1.1 Small Strain and Moderate Rotation................................................... 28
2.4.1.2 Small Strain and Small Rotation......................................................... 28
2.4.2 Euler-Bernoulli Beam Theory....................................................................... 28
2.4.3 Geometrically Nonlinear Beam Theory........................................................ 30
2.4.4 Membrane Force Estimation......................................................