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

2. What is Vibration?

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

4. 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

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

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

7. What was the cause?

8. Vortex Shedding …Caused Wind-Induced Vibration (?)

9. Why is Vibration Important?

12. Wing Flutter Failures

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

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

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

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

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

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

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

20. How is this model useful? kc m

21. Basic Concepts Resonance

22. 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

23. 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

24. 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

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

26. 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)

27. 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.

28. Vibration Absorbers

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