2. What is vibration?
A continuous slight shaking movement : a series of
small, fast movements back and forth or from side
to side .
3. Definition of Mechanical
Vibration
Mechanical vibration is defined as the
measurement of a periodic process of
oscillations with respect to an equilibrium point.
9. Vibration
More often, vibration is undesirable,
wasting energy and creating unwanted
sound – noise!
The vibrational motions of
engines, electric motors,
other mechanical devices
which are usually the
results of imbalance in
rotating parts, uneven
friction, meshing gear, etc.
are typically unwanted!
10. Definitions
Periodic motion: A motion which repeats itself after equal
intervals of time.
Time period: Time taken to complete one cycle.
Frequency: Number of cycles per unit time.
Amplitude: The maximum displacement of a vibrating body
from its equilibrium position.
Natural frequency: When no external force acting on the
system after giving it an initial displacement, the body
vibrates. These vibrations are called free vibrations and their
frequency as natural frequency. It is expressed in rad/sec or
Hertz.
Fundamental Mode of Vibration: The fundamental mode of
vibration of a system is the mode having the lowest natural
frequency.
Damping: is the resistance to the motion of vibrating body.
Resonance: when the frequency of external excitation is
12. Frequency
Is the number of occurrences of a repeating
event per unit time
13. Natural Frequency
Is the frequency at which a system tends
to oscillate in the absence of any driving
or damping force
14. Damping
A reduction in the amplitude of an oscillatio
n or vibration as a result of energy .
15. Resonance
Is a phenomenon in which a vibrating system or
external force drives another system to oscillate
with greater amplitude at a specific preferential
frequency .
16. Stiffness
The extent to which it resists deformation in
response to an applied force .
17. Inertia
Is the resistance of any physical object to
any change in its state of motion; this
includes changes to its speed, direction or
state of rest .
18. Simple Harmonic Motion
The motion of a body about a fixed
point is called simple harmonic
motion.
The motion is periodic.
The motion of a simple pendulum is
simple harmonic in nature.
A body having simple harmonic motion
is represented by the equation.
X=Asin(wt)
19. Vibration Parameters
All mechanical
systems can be
modeled by containing
three basic
components:
spring, damper, mass
When these components are subjected to constant
force, they react with a constant
displacement, velocity and acceleration
20. Lumped (Rigid) Modelling Numerical Modelling
Element-based
methods
(FEM, BEM)
Statistical and
Energy-based
methods
(SEA, EFA, etc.)
Modelling of vibrating systems
21. Degree of Freedom (DOF)
• The number of degrees of freedom for a system is
the number of kinematically independent variables
necessary to completely describe the motion of
every particle in the system.
DOF=1
Single degree of freedom (SDOF)
DOF=2
Multi degree of freedom (MDOF)
23. Types of Vibration
Free undamped vibration
Free damped vibration
Forced damped vibration
Forced undamped vibration
Forced damped vibration under
harmonic motion of the base
Vibration of multi degree of freedom
systems
24. Free Vibration
Equilibrium pos.
When a system is initially disturbed by a displacement,
velocity or acceleration, the system begins to vibrate
with a constant amplitude and frequency depend on
its stiffness and mass.
This frequency is called as natural frequency, and
the form of the vibration is called as mode shapes
25. Forced Vibration
If an external force applied to a
system, the system will follow the
force with the same frequency.
However, when the force
frequency is increased to the
system’s natural frequency,
amplitudes will dangerously
increase in this region. This
phenomenon called as
“Resonance”
’
26. Damped Vibration
When the energy of a vibrating system is gradually
dissipated by friction and other resistances, the
vibrations are said to be damped. The vibrations
gradually reduce or change in frequency or intensity
or cease and the system rests in its equilibrium
position
