What is called vibration Analysis Design 5 Vibrations Objectives: What is called vibration Analysis Design ME 316 Lecture 7

Vibrations – What ? 1. Introduction Example 1: Equilibrium position 5 Vibrations – What ? 1. Introduction Example 1: Equilibrium position A displaced position K: stiffness ME 316 Lecture 7

Vibrations – what ? Example 2 Equilibrium position Displaced position 5 Vibrations – what ? Example 2 Equilibrium position Displaced position ME 316 Lecture 7

Vibrations – what ? Example 3 Damping External excitation or Forced 5 Vibrations – what ? Example 3 Damping External excitation or Forced Spring or elastic element ME 316 Lecture 7

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

Period: Time for one cycle (back and forth): T 5 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

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

2. Mathematical Expression or Model 5 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

2.1 Undamped free vibration 5 Vibrations 2.1 Undamped free vibration Step 2: Newton’s second law Circular frequency ME 316 Lecture 7

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

5 Vibrations B A ME 316 Lecture 7

5 Vibrations ME 316 Lecture 7

If the amplitude of vibration remains constant 5 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

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