Mechanical Vibrations Jeff Rhoads and Terry Ballinger MST @ MSU 2006.

Mechanical Mechanical VibrationsVibrations

Jeff Rhoads and Terry BallingerJeff Rhoads and Terry Ballinger

MST @ MSU2006

What is Vibration?What is Vibration?


Scientific DefinitionScientific DefinitionAny motion that repeats itself after an Any motion that repeats itself after an interval of timeinterval of time


Scientific DefinitionScientific Definition

Engineering DefinitionEngineering Definition

Any motion that repeats itself after an Any motion that repeats itself after an interval of timeinterval of time

Deals with the relationship between Deals with the relationship between forces and oscillatory and oscillatory motion of mechanical of mechanical systemssystems

Why is Vibration Why is Vibration Important?Important?

November 7, 1940

The Tacoma NarrowsBridge Disaster


Amplitude of oscillation reached 14 feet!

What was the cause?

Vortex SheddingVortex Shedding

…Caused Wind-Induced Vibration (?)

Wing Flutter FailuresWing Flutter Failures

Basic ConceptsBasic Concepts

Every object has:Every object has: Frequencies at which it “likes” to vibrate at which it “likes” to vibrate

Characteristic geometries of vibration of vibration


Every object has:Every object has: Frequencies at which it “likes” to vibrateç at which it “likes” to vibrateç

Characteristic geometries of vibration of vibration

Natural

Frequencies

Mode

Shapes

Modeling VibrationModeling Vibration

The Ingredients:The Ingredients:1.1. InertiaInertia (stores kinetic energy)(stores kinetic energy)

2.2. ElasticityElasticity (stores potential (stores potential energy)energy)

1

Realistic Realistic Addition:Addition:

3.3. Energy DissipationEnergy Dissipation




1



2




1


3.3. Energy DissipationEnergy Dissipation3

2




2 3

1




The Ingredients:The Ingredients:1.1. Mass, Mass, mm

2.2. Stiffness, Stiffness, kk

k c

m

Realistic Addition:Realistic Addition:3.3. Damping, Damping, cc

x

How is this How is this model model useful?useful?

k c

m

x


Resonance


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

frequencyfrequency

Resonance

ResonanceResonance A vibration of large amplitudeA vibration of large amplitude Occurs when an object is forced Occurs when an object is forced

near its natural frequencynear its natural frequency

Object

ResonanceResonance A vibration of large amplitudeA vibration of large amplitude Occurs when an object is forced Occurs when an object is forced

near its natural frequencynear its natural frequency

m

ck

x

t

M

e

Object Model

Vibration AbsorbersVibration Absorbers Used to eliminate vibration of an objectUsed to eliminate vibration of an object

Object(that vibrates too much)


Object

Vibration Absorber

(that vibrates too much)

(‘absorbs’ vibration)


Object

Vibration Absorber

(that vibrates too much)

Choose these to eliminate motion

of object.

Vibration AbsorbersVibration Absorbers

Mode ShapesMode Shapes““Characteristic Geometry” of VibrationCharacteristic Geometry” of Vibration

• Mode Shapes

• Resonance

• Natural Frequencies

Mechanical Vibrations Jeff Rhoads and Terry Ballinger MST @ MSU 2006.

Documents

Transcript of Mechanical Vibrations Jeff Rhoads and Terry Ballinger MST @ MSU 2006.