Mechanical Vibrations Jeff Rhoads and Terry Ballinger MSU 2006.

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Presentation transcript:

Mechanical Vibrations Jeff Rhoads and Terry Ballinger MSU 2006

What is Vibration?

Scientific Definition Scientific Definition Any motion that repeats itself after an interval of time

What is Vibration? Scientific Definition Scientific Definition Engineering Definition Engineering Definition Any motion that repeats itself after an interval of time Deals with the relationship between and oscillatory of mechanical systems Deals with the relationship between forces and oscillatory motion of mechanical systems

Why is Vibration Important? November 7, 1940 The Tacoma Narrows Bridge Disaster

Why is Vibration Important? Amplitude of oscillation reached 14 feet!

What was the cause?

Vortex Shedding …Caused Wind-Induced Vibration (?)

Why is Vibration Important?

Wing Flutter Failures

Basic Concepts Every object has: at which it “likes” to vibrate Frequencies at which it “likes” to vibrate of vibration Characteristic geometries of vibration

Basic Concepts Every object has: at which it “likes” to vibrateç Frequencies at which it “likes” to vibrateç of vibration Characteristic geometries of vibration

Modeling Vibration The Ingredients: 1. Inertia (stores kinetic energy) 2. Elasticity (stores potential energy) 1 Realistic Addition: 3. Energy Dissipation

Modeling Vibration The Ingredients: 1. Inertia (stores kinetic energy) 2. Elasticity (stores potential energy) 1 Realistic Addition: 3. Energy Dissipation 2

Modeling Vibration The Ingredients: 1. Inertia (stores kinetic energy) 2. Elasticity (stores potential energy) 1 Realistic Addition: 3. Energy Dissipation 3 2

Modeling Vibration The Ingredients: 1. Inertia (stores kinetic energy) 2. Elasticity (stores potential energy) 23 1 Realistic Addition: 3. Energy Dissipation

Modeling Vibration The Ingredients: 1. Mass, m 2. Stiffness, k kc m Realistic Addition: 3. Damping, c

How is this model useful? kc m

Basic Concepts Resonance

Basic Concepts A vibration of large amplitude A vibration of large amplitude Occurs when an object is forced near its natural frequency Occurs when an object is forced near its natural frequency Resonance

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

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

Vibration Absorbers Used to eliminate vibration of an object Used to eliminate vibration of an object Object (that vibrates too much)

Vibration Absorbers Used to eliminate vibration of an object Used to eliminate vibration of an object Object Vibration Absorber (that vibrates too much) (‘absorbs’ vibration)

Vibration Absorbers Used to eliminate vibration of an object Used to eliminate vibration of an object Object Vibration Absorber (that vibrates too much) Choose these to eliminate motion of object.

Vibration Absorbers

Mode Shapes “Characteristic Geometry” of Vibration Mode Shapes Resonance Natural Frequencies

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