ME 4213
Lecturer :
Vibration Theory and Applications
G. Leng
Assoc. Prof. Gerard Leng
Office: E2-02-37, Tel : 6 516 6548
E-mail: mpelsb@nus.edu.sg,
Course Website : http:/dynlab.mpe.nus.edu.sg/mpelsb/
Text Books:
S. Rao, Mechanical Vibrations (SI ed), Pre
=
=
0
0
G. Leng, ME Dept, NUS
where C1 is a constant to be determined by initial conditions.
0.732
a = C1
1
Both equations implies that a1/ a2 = 0.732. For convenience we set
a2 = 1 and the solution takes the form :
cannot be independent (Why ? ).
1.366
=
a cos (t + )
G. Leng, ME Dept, NUS
2. Substitute (1) in the EOM : M x + K x = 0
x
1. Suppose the vibration takes the form
1.2 Characteristic equation for a MDOF system
(1)
=
0
(4)
(3)
G. Leng, ME Dept, NUS
This is the characteristic equation of the MDOF
k
m
x1
G. Leng, ME Dept, NUS
k
2m
x2
k
+ve
Example : Derive the EOM for the 2 DOF spring mass system
1.1 Deriving the Equations of Motion
1. Equations of motion for MDOF Vibration
k
x2
G. Leng, ME Dept, NUS
Hence by Newtons second law, the EOM is :
Force
Wind blast
G. Leng, ME Dept, NUS
Example USAFRL Articulated Total Body (ATB) Model
G. Leng, ME Dept, NUS
International
1) ISO 2017 - Vibration & Shock - Isolators
2) ISO 2631 Guide for the Evaluation of Human Exposure to Whole
Body Vibration
UK
1) BS 3015
G. Leng, ME Dept, NUS
Recap : How many DOF does a rigid body have ?
A system that requires more than 1 variable to describe its
configuration.
Simple answer
Question : What is a MDOF System ?
G. Leng, ME Dept, NUS
Recap : How many DOFs does an elastic (no
G. Leng, ME Dept, NUS
or
Some of the essentials for dealing with mechanical vibrations
as an engineer
Continuous Systems
Part II : Multi Degrees of Freedom Systems &
ME 4213
Mechanical Vibration
: E2-02-37
: mpelsb@nus.edu.sg
Office
E-mail
Website
G. Leng