1. What is called vibration Analysis Design5
Vibrations
Objectives:
What is called vibration
Analysis
Design
ME 316 Lecture 7

2. Vibrations – What ? 1. Introduction Example 1: Equilibrium position5
Vibrations – What ?
1. Introduction
Example 1:
Equilibrium position
A displaced position
K: stiffness
ME 316 Lecture 7

3. Vibrations – what ? Example 2 Equilibrium position Displaced position5
Vibrations – what ?
Example 2
Equilibrium position
Displaced position
ME 316 Lecture 7

4. Vibrations – what ? Example 3 Damping External excitation or Forced5
Vibrations – what ?
Example 3
Damping
External excitation or Forced
Spring or elastic element
ME 316 Lecture 7

5. Force or moment / displacement or angle 5
Vibrations – What ?
Stiffness:
a measure of how difficult to make a system or an object deform or change its configuration
Force or moment / displacement or angle
Force needed to produce one unit displacement K?
ME 316 Lecture 7

6. Period: Time for one cycle (back and forth): T5
Vibrations – What ?
Free vibration
Force vibration
Un-damped
Damped
Period: Time for one cycle (back and forth): T
Frequency: How many cycles per second -> f=1/T
ME 316 Lecture 7

7. Amplitude: maximal displacement away from equilibrium point.5
Vibrations – What ?
Amplitude: maximal displacement away from
equilibrium point.
Damping: a process that makes motion degrading. In vibration, the damping makes a periodic motion tends to be zero.
Vibration control: to make a periodic motion system in terms of amplitude attenuation and change the natural frequency.
ME 316 Lecture 7

8. 2. Mathematical Expression or Model5
Vibrations - Analysis
2. Mathematical Expression or Model
Mathematical representation of the physics of a concerned entity. In developing a model, we need to have some assumptions
2.1 Undamped free vibration
Step 1: Free diagram. Take the figure in example 1 as an example.
ME 316 Lecture 7

9. 2.1 Undamped free vibration5
Vibrations
2.1 Undamped free vibration
Step 2: Newton’s second law
Circular frequency
ME 316 Lecture 7

10. Features of governing equation: - ordinary differential equation 5
Vibrations
Features of governing equation:
- ordinary differential equation
- homogeneous
- second order
- linear
- constant coefficient
X=A sin pt + B cos pt
ME 316 Lecture 7

11. 5
Vibrations B A
ME 316 Lecture 7

12. 5
Vibrations
ME 316 Lecture 7

13. If the amplitude of vibration remains constant5
Vibrations
Natural Frequency:
when a body or system of connected bodies is given an initial displacement from its equilibrium position and released, it will vibrate with a definite frequency
Undamped vibration:
If the amplitude of vibration remains constant
ME 316 Lecture 7

14. Determine the period of vibration for the simple pendulum.5
Vibrations
Example
Determine the period of vibration for the simple pendulum.
Bob has a mass m and is attached to a cord of length l. Neglect the size of the bob
ME 316 Lecture 7