Vibration Lecture 4 Notes

MCG 4308

Lecture 4

1 DOF: Free Undamped Vibrations

Mechanical Vibration Analysis 1 DOF, free undamped oscillator

Displacement

Although a simple model it represents ALL Mass

M

k

x

Spring Although a simple model, it represents ALL

Summary of Simple Harmonic Motion

Response is

Example 1: Effect of fuel on

frequency of an airplane wing

y Model wing as transverse

beam

y Model fuel as tip mass

y Ignore the mass of the

wing and see how the

frequency of the system

changes as the fuel is used

up

Energy Conservation in Oscillatory Motion

y Potential energy versus time

y Kinetic energy versus time

y Note Kinetic Energy is max when Potential energy is minimum and vice versa. Total energy is conserved.