الفهرس 
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Abstract
Vibration is a mechanical phenomenon whereby oscillations occur about an
equilibrium point. The oscillations may be periodic, such as the motion of a
pendulum or random, such as the movement of a tire on a gravel road.
Mechanical vibrations span amplitudes from meters (civil engineering) to
nanometers (precision engineering). In many cases, vibration is undesirable and
causes detrimental effects on various systems as follows:
Failure: vibrations may cause structure failure such as, excessive strain
during transient events when a building responses to an earthquake, and
flutter phenomenon in bridges and plane wings when subjected to wind
excitation. Also failure may occur due to fatigue in mechanical parts in
machines.
Discomfort: vibrations reduce comfort such as noise and vibration in
helicopters, car suspensions and wind-induced sway of buildings.
Reduce accuracy during production of precision devices: many precision
industrial processes cannot take place if machinery is being affected by
vibration, for example, the production of semiconductor wafers.
Detrimental effects of vibrations increase more and more and should be
eliminated especially when mechanical resonance occurs. Mechanical resonance
is the tendency of a mechanical system to respond at greater amplitude when
the excitation frequency matches
than it does at other frequencies. It may cause great amplitude motions and
even catastrophic failure in improperly constructed structures including bridges,
buildings, and airplanes in a phenomenon known as resonance disaster. So
vibration reduction is of vital importance especially at resonance cases. The basic
concepts used to reduce vibrations are stiffening, damping, and isolation.
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Stiffening shifts the resonance frequency of the structure beyond the frequency
band of excitation. Damping reduces the resonance peaks by dissipating the
vibration energy. Isolation depends on preventing the propagation of
disturbances to sensitive parts of the systems. Vibration control systems can be
broadly classified as passive, active, and semi-active.
Passive control generally consists of spring and damper elements and no
computer control is associated with this type of control. The characteristics of
passive vibration absorbers are fixed by the mass, spring, and damper elements.
Passive vibration absorbers do not automatically change or optimize their spring
or damper characteristics based upon a changing environment. Therefore, they
are almost effective over a narrow range of disturbance inputs. The passive
vibration absorbers are designed based on a nominal mass load and disturbance
environment expected to be most encountered over the design life of the
structure. Passive vibration absorbers represent the majority of vehicular
vibration absorbers in use today due to their low cost of manufacturing and
maintenance when compared to other vibration absorbers. Also passive vibration
vibration absorbers may take the form of basic structural changes or the addition
of passive elements such as masses, springs, and fluid dampers or addition of
smart materials like piezoelectric materials (PZT). Authors in [1] studied
extensively the passive vibration absorbers. The response of a harmonically
excited system consisting of a nonlinear shaker emulates the machine coupled to
a passive vibration absorber is investigated in chapter 1 in this thesis. The model
Active vibration controller depends on application of a dynamic force in an
opposite fashion to the forces imposed by external vibration so that the
amplitude of the resultant force and the system response to external vibrations
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decrease. Active vibration controllers are typically composed of a spring element
and some type of force actuator. The primary damping or energy dissipation is
provided by the active force actuator which replaces the passive damper used in
passive vibration absorbers. Theoretically, both the spring and the damper in
passive vibration absorber could be replaced by a force actuator; however, this
is not typical due to practical system constraints. At a minimum, a spring is
usually necessary to provide support, even in the most advanced system designs.
Although they can be manufactured with a high degree of reliability, the rare
possibility of failure in operation must be taken into consideration. A passive
system may be required as a backup to prevent such failure from making a
complete disaster. The mathematical control law is developed and implemented
in software on a real-time computer processor, which drives the force actuator
through the interface circuits and thus determines the actuation force. Also
sensors which detect or measure the vibration and convert it to signals are
needed. The linear electromagnetic motor can be used as a dynamic force
actuator as in case of Bose Corporation automotive suspension system. Active
control methods are more costly than passive ones, but some vibration problems
are so intensive that active control methods alone can cure them. Active
vibration controllers are studied extensively in [3]. A semi-active vibration
controller is typically composed of a spring type element and a damper that is
continuously adjustable such as Magneto-Rheological damper or shortly MR
damper. The damper characteristics are continuously variable and can be
controlled by a computer algorithm. Since the adjustable damper is not capable
of supplying energy to the system, the system performance is limited compared
to the capability of the active vibration absorber. However, the semi-active
vibration controller is more stable than active vibration controllers. Semi-active
vibration controllers provide an alternative to active systems when the
performance improvement of the semi-active system over the passive system is
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adequate. In addition, a semi-active vibration absorbers may be less costly and
potentially more reliable than an active vibration absorbers. Semi-active
vibration controllers are studied extensively in [4].
Unfortunately, active and semi-active vibration controllers may suffer from
time/loop delays. Time delays are inevitable in any active control system as a
result of measuring system states, processing the control algorithms, control
interfaces, transport delay, and actuation delay. Presence of time delays imposes
strict limitations on the control system. With delays in measurement, the
ays in actuation. Thus time
delay reduces the compensation efficiency to the effect of disturbances. So
controller design and operation become complicated. Time delays can affect the
stability of the system. Thus control system with time delays became a subject
systems with loop delays. Many active vibration control techniques are studied
in this thesis to reduce the vibrations of a nonlinear beam in chapters 2 to 4.
This beam is subjected to dynamic instability due to occurrence of flutter
phenomenon. The mathematical models under study in this thesis are
represented by a second order ordinary differential equation, and the vibration
controller is represented also by another second order ordinary differential
equation. So the closed loop system consists of a coupled system of differential
equations and the main interest of the thesis is reducing vibrations of coupled
systems.
Flutter is a dangerous phenomenon which occurs when elastic structures are
subjected to aerodynamic forces. This aerodynamic forces are exerted on the
elastic structure by the fluid flow due to relative motion between the structure
ed
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by the fluid flow can cause a positive feedback to the structure. This positive
feedback increases oscillations which may lead to instability and cause flutter.
example the wing of a plane has two basic degrees of freedom or natural modes
of vibration: pitch and plunge (bending). where the pitch mode is rotational
and the bending mode is a vertical up and down motion at the wing tip. This
includes aircraft, buildings, telegraph wires, and bridges. The mathematical
-Bernoulli beam with
nonlinear curvature. This model was given by Warminski in [6]. The beam is
subjected to external harmonic excitation close to its first natural frequency,
also the beam is subjected to fluid flow which is modeled by a nonlinear damping
causes a positive feedback which is proportional to velocity of motion, so
oscillation system draws energy from the fluid flow and can increase vibrations
even in the case of free vibrations. However, it vanishes when motion stops so
vibrations resulted from fluid flow are called a self-excited vibrations. Selfexcited
oscillations are studied extensively in [7, 8]. The beam model under study
model. Interaction between forced vibrations and self-excited vibrations may
cause flutter. So our main purpose here is to reduce vibrations of the bending
mode in order to prevent occurrence of flutter. Chapter 2 presents a quantitative
analysis on the nonlinear behavior of the studied beam coupled to a positive
position feedback controller PPF. In chapter 3, we use the delayed positive
position feedback controller to reduce the bending mode vibrations of the beam
under study. In chapter 4, an improved saturation controller and a velocity
feedback controller are used together to eliminate the vibrations of the studied
beam.