Force Damped Vibrations

this this slideshare presentation we discussed about difference of vibration system for forced damping here this is having with simple definition and for dynamic of machinery without equation and simple method.

1. FORCED VIBRATION &
DAMPING

2. Damping
a process whereby energy is taken from the
vibrating system and is being absorbed by
the surroundings.
Examples of damping forces:
internal forces of a spring,
viscous force in a fluid,
electromagnetic damping in galvanometers,
shock absorber in a car.

3. Free Vibration
Vibrate in the absence of damping and
external force
Characteristics:
the system oscillates with constant frequency and
amplitude
the system oscillates with its natural frequency
the total energy of the oscillator remains constant

4. Damped Vibration
The oscillating system is opposed by
dissipative forces.
The system does positive work on the
surroundings.
Examples:
a mass oscillates under water
oscillation of a metal plate in the magnetic field

5. Damped Vibration
Total energy of the oscillator decreases with
time
The rate of loss of energy depends on the
instantaneous velocity
Resistive force µ instantaneous velocity
i.e. F = -bv where b = damping
coefficient
Frequency of damped vibration < Frequency
of undamped vibration

6. Types of Damped Oscillations
Slight damping (underdamping)
Characteristics:
- oscillations with reducing
amplitudes
- amplitude decays
exponentially with time
- period is slightly longer.
constant a.......
4
3
3
2
2
1
====
a
a
a
a
a
a

7. Critical damping
No real oscillation
Time taken for the displacement to become
effective zero is a minimum.
Types of Damped Oscillations

8. Heavy damping (Overdamping)
Resistive forces exceed those of critical damping
The system returns very slowly to the
equilibrium position.
Types of Damped Oscillations

9. the deflection of the pointer is critically damped
Example: moving coil galvanometer
Damping is due to
induced currents
flowing in the metal
frame
The opposing couple
setting up causes the
coil to come to rest
quickly

10. Forced Oscillation
The system is made to oscillate by periodic
impulses from an external driving agent
Experimental setup:

11. Characteristics of Forced Oscillation
(1)
Same frequency as the driver system
Constant amplitude
Transient oscillations at the beginning which
eventually settle down to vibrate with a
constant amplitude (steady state)

12. In steady state, the system vibrates at the
frequency of the driving force
Characteristics of Forced Oscillation
(2)

13. Energy
Amplitude of vibration is
fixed for a specific driving
frequency
Driving force does work on
the system at the same rate
as the system loses energy
by doing work against
dissipative forces
Power of the driver is
controlled by damping

14. Amplitude
Amplitude of vibration
depends on
the relative values of
the natural frequency
of free oscillation
the frequency of the
driving force
the extent to which
the system is damped

15. Effects of Damping
Driving frequency for maximum amplitude becomes
slightly less than the natural frequency
Reduces the response of the forced system

16. Forced Vibration (1)
Adjust the position of the load on the driving
pendulum so that it oscillates exactly at a
frequency of 1 Hz
Couple the oscillator to the driving pendulum
by the given elastic cord
Set the driving pendulum going and note the
response of the blade

17. In steady state, measure the amplitude of
forced vibration
Measure the time taken for the blade to
perform 10 free oscillations
Adjust the position of the tuning mass to
change the natural frequency of free vibration
and repeat the experiment
Forced Vibration (2)

18. Plot a graph of the amplitude of vibration at
different natural frequencies of the oscillator
Change the magnitude of damping by rotating
the card through different angles
Plot a series of resonance curves
Forced Vibration (3)

19. Resonance
Resonance occurs when an oscillator is acted upon by a
second driving oscillator whose frequency equals the
natural frequency of the system
The amplitude of reaches a maximum
The energy of the system becomes a maximum
The phase of the displacement of the driver leads that of
the oscillator by 90°

20. Resonant System
There is only one value of the driving
frequency for resonance, e.g. spring-mass
system
There are several driving frequencies which
give resonance, e.g. resonance tube

21. THANK YOU