Date post: | 21-Apr-2017 |
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Engineering |
Upload: | manthan-kanani |
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FORCED VIBRATION & DAMPING
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.
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
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
Damped Vibration
Total energy of the oscillator decreases with time
The rate of loss of energy depends on the instantaneous velocity
Resistive force instantaneous velocity i.e. F = -bv where b = damping
coefficient Frequency of damped vibration < Frequency
of undamped vibration
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 aa
aa
aa
Critical damping No real oscillation Time taken for the displacement to become
effective zero is a minimum.
Types of Damped Oscillations
Heavy damping (Overdamping) Resistive forces exceed those of critical damping The system returns very slowly to the
equilibrium position.
Types of Damped Oscillations
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
Forced Oscillation
The system is made to oscillate by periodic impulses from an external driving agent
Experimental setup:
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)
In steady state, the system vibrates at the frequency of the driving force
Characteristics of Forced Oscillation (2)
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
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
Effects of Damping
Driving frequency for maximum amplitude becomes slightly less than the natural frequency
Reduces the response of the forced system
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
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)
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)
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
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
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