**Introduction**

Vibration is one of the most common aspects of life. Many natural phenomena, as well as man-made devices, involve periodic motion of some sort. Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. Vibration can be desirable for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, o mobile phone or the cone of a loudspeaker. In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound. For example, the vibration motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the rotating parts, uneven friction or the meshing of gear teeth. Careful designs usually minimize unwanted vibration.

**Vibration Control System **

Structural vibration
control system is to control the vibration of the structure under unbalanced
forces by changing the stiffness, mass, damping and shape of the structure and
providing a certain amount of passive or active reaction forces.

Vibration control system
is classified as –

- ‣
Passive Control system
- ‣
Active Control system
- ‣
Semi – Active Control system

The passive control
system doesn’t require an external power source and being utilizes the
structural motion to isolate the vibrations so that response of structure can
be controlled. Active vibration control systems, also called active vibration
isolation or active vibration cancellation, are isolation systems that
dynamically react to incoming vibrations. That is, they sense incoming
vibrations and react to them, rather than passively reducing their effect by
virtue of their mechanical structure. The semi-active control system compromise
between the passive and active control system. The structural motion is
utilized to develop the control actions or forces through the adjustment of its
mechanical properties.

**Vibration Modeling **

There are usually two
different approaches to mathematical modeling: models made by equations
describing the physics of relevant phenomena, - these may be defined as
analytical models and empirical models, often called black box models.

In analytical model the
equation approximating the behavior of the various parts of the system, along
with the required approximations and simplifications, are written. Even if no
real-world spring behaves exactly like the linear spring, producing a force
proportional to the relative displacement, of its ends through a constant
called stiffness and even if no device dissipating energy is a true linear
damper, the dynamic of a mass-spring-damper system can be described, often to a
very good approximation, by the usual ordinary differential equation (ODE).

The behavior of some
systems, on the other hand, is so complex that writing equations to describe it
starting from the physical and geometrical characteristics of their structure
is forbiddingly difficult. Their behavior is studied experimentally and then a
mathematical expression able to describe it is sought, identifying the various
parameters from the experimental data. While each of the parameters m, c, and k
included in the equation of motion of the mass–spring–damper system refers to
one of the parts of the system and has a true physical meaning, the many
coefficients appearing in empirical models usually have no direct physical
meaning and refer to the system as a whole.

Once the model has been
built and the equations of motion written, there is no difficulty in studying
the response to any input, assuming the initial conditions are stated.

**Vibration Modeling
Considerations**

Mechanics of vibration is
not just a field for theoretical study. Design engineers had to deal with
vibration for a long time, but recently the current tendencies of technology
have made the dynamic analysis of machines and structures more important.

The following
considerations the designer has to make for designing a vibration model –

- ·
The load conditions the designer has to
take into account in the structural analysis of any member of a machine or a
structure can be conventionally considered as static, quasi-static or dynamic.
- ·
All possible environmental effects (creep,
corrosion, etc) must be taken into account.
- ·
If the deformations of the structure are
consistent with the regular working of the machine.
- ·
Fatigue must generally be taken into
account, and often the methods based on fracture mechanics must be applied.
- ·
Speed

**Vibration Modeling
Challenges **

The computational
predictions of the characteristics and the performance of a physical system are
based on the construction of a mathematical model, constructed from a number of
equations, whose behavior is similar to that of the physical system it
replaces.

The
complexity of the model depends on many factors that are the **first challenge**
the analyst has to make. The model must be complex enough to allow a realistic
simulation of the system’s characteristics of interest, but no more. The more
complex the model, the more data it requires, and the more complicated are the
solution and the interpretation of the results. Today it is possible to built
very complex models, but overly complex models yield results from which it is
difficult to extract useful insights into the behavior of the system.

It
may require long computation time (and thus high costs) if the model is
complex, or has characteristic that make numerical integration difficult, and
it allows the effects of changes of the values of the parameters to be
predicted only at the cost of a number of different simulations.

Another
most challenging part is elimination of additional energy sources, isolate the
system from external disturbances e.g. balancing, decrease of colliding bodies
mass etc.

The
damping is also an important parameter. It refers to mechanical dissipation
which is exchanged to heat. It causes the decrease of general efficiency of
machines and devices. In case when the undesirable vibrations cannot be eliminated
via constructional or parameters changes the damping should be introduced. It a
great challenge to maintain proper damping.

**Conclusion**

Vibration
models are useful not only to the designer but also to the test engineer in
interpreting the results of testing and performing all adjustments. The analyst
has the duty not only of building, implementing and using the models correctly
but also of updating and maintaining them. Before building the model, the
analyst must be certain about what he wants to obtain from it. In case of doing so, comes greater
challenges. The analyst must be able to cope with these challenges.

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