This document provides an introduction to mechanical vibrations. It defines vibration as oscillations about an equilibrium position and notes they are common in everyday life, with useful applications like compressors but also harmful effects like noise and fatigue. Key vibration concepts discussed include the spring-mass-damper model, natural frequency, degrees of freedom, simple harmonic motion, and different types of vibrations such as free, forced, damped, and random vibrations. Vibrations can be longitudinal, transverse, or torsional depending on the direction of particle motion. Examples of resonant vibrations in bridges and helicopters are provided.
6. 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
7. Basic concept of vibration
• Discovery of musical instruments like drums,
“vibrations” became a point of interest for the
scientists.
• When the body is displaced by the application
of external force, the internal forces in the
form of elastic / potential energy try to bring
the body to its original position. At equilibrium
elastic energy is converted into kinetic energy
and body continues to move in opposite
direction because of it.
9. Important Definitions
• Periodic motion: a motion which repeats itself
after equal interval of time.
• Time period (T) : time taken to complete one
cycle.
• Frequency: no. of cycles per unit time
angular frequency (ω)= 1/T (rad/sec)
Frequency(n)= 2π/T (Hertz)
• Amplitude(A): Maximum displacement of a
body from its equilibrium position.
10. • Natural frequency: when no
external force acts on the system
after giving an initial displacement,
the body vibrates. These vibrations
are called free vibrations and their
frequency as natural frequency.
• Degree of freedom: the
minimum number of independent co-
ordinates required to specify the
motion of a system at any instant is
known as DOF of the system
11. • Simple Harmonic Motion (SHM) :
Motion of a body is too and fro about a fixed
point is called simple harmonic motion. The
motion is periodic and its acceleration is always
directed towards the mean position and is
proportional to its distance from mean
position.
Let a body having SHM is represented by eq.
12. Types of vibrations
Free vibration:
Initial disturbance, system left to vibrate without
influence of external forces..
Equilibrium pos.
13. 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”
’
14. Damped and Undamped
vibrations
• If the system has a damper,
the motion of the system will
be opposed by it and the
energy of the system will be
dissipated in friction. This type
of vibration is called damped
vibration.
• On the contrary, the system
having no damper is known as
undamped vibrations.
15. Deterministic and random vibration
• Deterministic vibration: Can be described by implicit mathematical function
as a function of time.
• Random vibration: Cannot be predicted. Process can be described by
statistical means.
16. Longitudinal, Transverse and
Torsional Vibrations
• If the mass m moves up and down
parallel to the spindle axes, it is said to
executes longitudinal vibrations.
17. • When the particles of the body or shaft move
perpendicular to the axes of the shaft, the
vibrations so causes are known as transverse.
• If the spindle get alternately twisted and
untwisted on account of vibratory motion of
the suspended disc, it is called to be
undergoing torsional vibrations
