Geology Reference
In-Depth Information
vibration) along with sensors and controllers
(analog or digital) to produce an actuation with the
right timing to counteract the resonant oscillation.
Due to remarkable advances in sensor, actuator
and, more importantly, computer technologies
in recent years active systems have become cost
effective solutions to most sound and vibration
control problems.
Fractional Derivative:
A generalization of
the well known derivative in the case when the
derivative order is a real number. A few definitions
of the fractional derivative are known and the most
popular ones are those proposed by Riemann and
Liouville, Caputo and by Grunwald and Letnikov.
Models with Fractional Derivative:
Models
which contain spring-pot elements. Differential
equations with fractional derivatives describe the
behaviour of such models.
Particle Swarm Optimization (PSO):
The
optimization method based on the study of social
behaviour in a self-organized population system
(i.e., ant colonies, fish schools). It is a non-gradient,
heuristic method which requires calculation of
the objective function only. This method is able
to find a global solution to non-convex optimi-
zation problem and problems which have many
local minima.
Passive Systems:
The most commonly applied
vibration control techniques are based on the use
of passive technologies. The majority of these
applications are based on passive damping using
viscoelastic materials. The traditional passive
damping methods include the use of broadband
dissipative solutions such as viscoelastic, viscous,
and friction dampers, as well as narrowband
reactive solutions such as tuned mass dampers.
Although most passive damping treatments are
inexpensive to fabricate, their successful appli-
cation requires a thorough understanding of the
vibration problem in hand and the properties of the
damping materials. Viscous dampers (dashpots),
tuned-mass dampers, dynamic absorbers, shunted
piezoceramic dampers, and magnetic dampers are
other mechanisms of passive vibration control.
Passive vibration control has its limitations such
as: lack of versatility, large size and weight when
used for low-frequency vibration control, and de-
tuning of tuned treatments.
Rheological Models:
One-dimensional consti-
tutive models for viscoelasticity based on spring,
dashpot, and spring-pot elements. The elements
may be connected in series or in parallel. In models
where the elements are connected in series the
strain is additive while the stress is equal in each
element. In parallel connections, the stress is ad-
ditive while the strain is equal in each element.
Semi-Active (Adaptive-Passive) Systems:
Refer to an adjustable passive vibration control
scheme, that is, the passive treatment can adjust
itself in response to changes in the structure.
For example, the stiffness, damping coefficient
or other variables of the passive control scheme
can change automatically so that optimal vibra-
tion mitigation is induced. These variable com-
ponents, also known as “tunable parameters” of
the control system, are re-tailored via a properly
developed semi-active control algorithm. Being
more versatile than passive control techniques
and more affordable (in terms of cost and energy
consumption) than active control schemes, has
made semi-active control methods very popular.
Spring-Pot Element (also known as the
Scott-Blair's Element):
An element which com-
bines elastic and viscous properties of spring and
dashpot elements. The spring-pot element satisfies
the constitutive equation:
u t
=
α
, where
u
( )
is the force in element,
c
and
α
are models
parameters and
D x t
t
( )
c D x t
t
( )
α
( )
is the fractional derivative
of the order
α
with respect to time
t
. The spring-
pot element is often schematically shown as
rhombus in rheological model diagrams. The
spring-pot element can be understood as an inter-
polation between the spring element and the
dashpot element: spring-pot is a spring when
α
= 0
and a dashpot when
α
=1
.
Transfer Function (also known as the System
Function or Network Function):
A mathemati-
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