Mechanical Vibrations

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Mechanical Vibrations
Jeff Rhoads and Terry Ballinger
MST _at_ MSU 2006
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What is Vibration?
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What is Vibration?

• Scientific Definition

Any motion that repeats itself after an interval
of time
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What is Vibration?

• Scientific Definition

Any motion that repeats itself after an interval
of time

• Engineering Definition

Deals with the relationship between forces and
oscillatory motion of mechanical systems
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Why is Vibration Important?
The Tacoma Narrows
Bridge Disaster
November 7, 1940
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Why is Vibration Important?
Amplitude of oscillation reached 14 feet!
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What was the cause?
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Vortex Shedding
Caused Wind-Induced Vibration (?)
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Why is Vibration Important?
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Why is Vibration Important?
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Why is Vibration Important?
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Wing Flutter Failures
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Basic Concepts

• Every object has

• Frequencies at which it likes to vibrate

• Characteristic geometries of vibration

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Basic Concepts

• Every object has

• Frequencies at which it likes to vibrateç

• Characteristic geometries of vibration

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Modeling Vibration

• The Ingredients
• Inertia (stores kinetic energy)
• Elasticity (stores potential energy)

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• Realistic Addition
• Energy Dissipation

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Modeling Vibration

• The Ingredients
• Inertia (stores kinetic energy)
• Elasticity (stores potential energy)

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2

• Realistic Addition
• Energy Dissipation

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Modeling Vibration

• The Ingredients
• Inertia (stores kinetic energy)
• Elasticity (stores potential energy)

1
2

• Realistic Addition
• Energy Dissipation

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Modeling Vibration

• The Ingredients
• Inertia (stores kinetic energy)
• Elasticity (stores potential energy)

1
2
3

• Realistic Addition
• Energy Dissipation

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Modeling Vibration

• The Ingredients
• Mass, m
• Stiffness, k

m
k
c

• Realistic Addition
• Damping, c

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How is this model useful?
m
k
c
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Basic Concepts

• Resonance

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Basic Concepts

• Resonance

• A vibration of large amplitude
• Occurs when an object is forced near its natural
  frequency

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Resonance

• A vibration of large amplitude
• Occurs when an object is forced near its natural
  frequency

Object
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Resonance

• A vibration of large amplitude
• Occurs when an object is forced near its natural
  frequency

Object
Model
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Vibration Absorbers

• Used to eliminate vibration of an object

Object
(that vibrates too much)
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Vibration Absorbers

• Used to eliminate vibration of an object

Vibration Absorber
(absorbs vibration)
Object
(that vibrates too much)
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Vibration Absorbers

• Used to eliminate vibration of an object

Vibration Absorber
Choose these to eliminate motion of object.
Object
(that vibrates too much)
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Vibration Absorbers
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Mode Shapes

• Characteristic Geometry of Vibration

• Mode Shapes
• Resonance
• Natural Frequencies