Short Notes: Resonance | Short Notes for Mechanical Engineering PDF Download

 Page 1


Resonance
R e s o n a n c e
• When the frequency of external force(driving frequency) is equal to the natural 
frequency of a vibrating body, the amplitude of vibration becomes excessively 
large. This phenomenon is known as resonance.
• If an object is being forced to vibrate at its natural frequency, resonance will 
occur and you will observe large amplitude vibrations. The resonant frequency 
is f0.
• The amplitude of the resonance peak decreases and the peak occurs at a 
lower frequency.
Page 2


Resonance
R e s o n a n c e
• When the frequency of external force(driving frequency) is equal to the natural 
frequency of a vibrating body, the amplitude of vibration becomes excessively 
large. This phenomenon is known as resonance.
• If an object is being forced to vibrate at its natural frequency, resonance will 
occur and you will observe large amplitude vibrations. The resonant frequency 
is f0.
• The amplitude of the resonance peak decreases and the peak occurs at a 
lower frequency.
P h ase and R esonance
• The phase relationship between the driving oscillation and the oscillation of 
the object being driven is different at different frequencies.
° Below resonance,e they are in phase with each other.
° At resonance, the phase relationship is 90° or tt/2 rad.
° Above resonance, the phase relationship is 180° or tt rad.
• All structures have a resonant frequency.
• If you impact the structure with enough force to make it move, it will vibrate 
briefly at its natural frequency.
• A structure will have a resonant frequency in each of its 3 directional planes 
(x, y and z, or as we call them, horizontal, vertical and axial).
• Resonance serves to amplify the vibration due to whatever vibration force is 
present at (or near) that resonant frequency.
• It is important to note that resonance does not cause vibration, it amplifies it.
• Resonance problems occur in two primary forms. They are:
Critical speeds
• It occurs when a component rotates at its own natural frequency.
° A "critical speed" is simply when the rotational speed (rpm) coincides 
with the natural frequency of the rotor (cpm).
° The tiniest amount of residual unbalance (something that is always 
present) is enough to cause huge amounts of vibration when rotating at 
a critical.
° Rotors that are sped up or slowed down slowly are susceptible to this 
(i.e. turbines). In these cases, the critical speed is usually well known.
Structural resonances
• This is far more common than a critical speed problem. It becomes a problem 
when some forcing frequency comes close (+/-10%) to the resonant (natural) 
frequency of a structure.
o The structure can be the machine housing itself or some nearby 
structure such as a hand rail or I-beam. 
o The structure itself will vibrate excessively - do not confuse with a 
critical speed.
° The "shape" of the structure's vibration is an important clue and is known 
as a "mode shape".
Page 3


Resonance
R e s o n a n c e
• When the frequency of external force(driving frequency) is equal to the natural 
frequency of a vibrating body, the amplitude of vibration becomes excessively 
large. This phenomenon is known as resonance.
• If an object is being forced to vibrate at its natural frequency, resonance will 
occur and you will observe large amplitude vibrations. The resonant frequency 
is f0.
• The amplitude of the resonance peak decreases and the peak occurs at a 
lower frequency.
P h ase and R esonance
• The phase relationship between the driving oscillation and the oscillation of 
the object being driven is different at different frequencies.
° Below resonance,e they are in phase with each other.
° At resonance, the phase relationship is 90° or tt/2 rad.
° Above resonance, the phase relationship is 180° or tt rad.
• All structures have a resonant frequency.
• If you impact the structure with enough force to make it move, it will vibrate 
briefly at its natural frequency.
• A structure will have a resonant frequency in each of its 3 directional planes 
(x, y and z, or as we call them, horizontal, vertical and axial).
• Resonance serves to amplify the vibration due to whatever vibration force is 
present at (or near) that resonant frequency.
• It is important to note that resonance does not cause vibration, it amplifies it.
• Resonance problems occur in two primary forms. They are:
Critical speeds
• It occurs when a component rotates at its own natural frequency.
° A "critical speed" is simply when the rotational speed (rpm) coincides 
with the natural frequency of the rotor (cpm).
° The tiniest amount of residual unbalance (something that is always 
present) is enough to cause huge amounts of vibration when rotating at 
a critical.
° Rotors that are sped up or slowed down slowly are susceptible to this 
(i.e. turbines). In these cases, the critical speed is usually well known.
Structural resonances
• This is far more common than a critical speed problem. It becomes a problem 
when some forcing frequency comes close (+/-10%) to the resonant (natural) 
frequency of a structure.
o The structure can be the machine housing itself or some nearby 
structure such as a hand rail or I-beam. 
o The structure itself will vibrate excessively - do not confuse with a 
critical speed.
° The "shape" of the structure's vibration is an important clue and is known 
as a "mode shape".
° Testing for the structure's natural frequency is crucial (required) to 
confirming a resonance problem.
• Resonance, once diagnosed, can be simple to correct. It can also be 
extremely complex and difficult to correct.
• One method for determining a critical speed is a "Coast Down/Start Up Plot".
• This plot consists of the lx vibration amplitude being collected 
simultaneously with a lx rpm phase reading as the machine coasts to a stop 
or goes from stopped to full running speed.
• This test requires a lx rpm reference (from a photoeye or some other speed 
tracking signal) in order to track the amplitude and phase at that frequency.
• Two things are observed as the rotor passes through a critical:
° The lx rpm amplitude will increase until the rotor reaches it's critical and 
then decrease to the normal level as the speed continues to change.
° Phase will shift 180° as the rotor passes through the critical. This is due 
to the rotor changing from a rigid rotor (while operating below it's 
critical) to a flexible rotor (while operating above it's critical
• If the measured response of the structure (i.e. it's resonant frequency) is 
within about 10% of the forcing frequency (i.e. the rpm of the machine 
although it can be at any frequency), resonance should be considered a 
problem. The closer the two frequencies are, the more of a problem it is.
To correct a resonance problem, there are 4 methods:
• Stiffen the structure - This method raises the resonant frequency of the 
structure.
• Add mass to the structure - This method lowers the resonant frequency.
• Change exciting frequency - Change the speed of the machine.
• Add a dynamic absorber to the structure - This method attaches the 
equivalent of a tuning fork to the structure. This attachment is tuned to have 
the same resonant frequency as the structure and sets up an out-of-phase 
signal that has the effect of cancelling out (reducing) the signal being 
generated by the structure. The dynamic absorber must be properly sized to 
handle the forces being generated.