MATLAB Tutorials
Session VI
Engineering Applications using MATLAB
Rajeev Madazhy
Email: rmadaz1@lsu.edu
Dept of Mechanical Engineering
LSU
Department of Mechanical Engineering, LSU
Session VI
Last Session….
 Solving Double Integrals
 Ordinary Differential Equations
 Examples of ODE using MATLAB….
 Mention of DDE’s
Department of Mechanical Engineering, LSU
Session VI
Session VI Outline….
Engineering Applications using MATLAB….
 Solving non linear differential equations
 Algorithm analysis for four bar linkage problem
 Other mechanical problems
Department of Mechanical Engineering, LSU
Session VI
Solving non-linear Diff Equation….
 Same as linear differential equations (use ode45)
 Incorporate differences in the function
 Consider the previous example of spring-mass-damper system
 let there be an external force of 0.1*sin(w*t) where w is the
frequency of the input and the value of c and k varies as follows
C=1 for x(1)>0.5m/s and 5 for x(1)<=0.5m/s
K=10 for x(2)>=-0.25m and 20 for x(2)<-0.25
Department of Mechanical Engineering, LSU
Session VI
Function….
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Session VI
Command window….
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Session VI
Output….
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Session VI
Output….
Department of Mechanical Engineering, LSU
Session VI
Example 2: Four Bar Linkage….
C
y
B


A
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
D
x
Session VI
Algorithm analysis….
 The lengths of AB, BC, CD, DA are known
 To determine the coordinate (x, y) of point C at each
rotation angle of ABD or .
 Basic formula.
B
c
a
C
b
A
c  a  b  2ab cos(C )
2
2
2
Department of Mechanical Engineering, LSU
Session VI
Cont….
Step 1: Calculate length of BD

Step 3: Calculate angle 
Step 2: Calculate angle
Step 4: The coordinate of point C is as follows:
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Session VI
Cont….
xC  DA  CD cos(   )
yC  CD sin(   )
( If 0<  <pi )
xC  DA  CD cos(   )
( If pi < <2pi )
yC  CD sin(   )
Department of Mechanical Engineering, LSU
Session VI
MATLAB program….
Department of Mechanical Engineering, LSU
Session VI
MATLAB program….
Department of Mechanical Engineering, LSU
Session VI
MATLAB program….
Department of Mechanical Engineering, LSU
Session VI
MATLAB program….
Department of Mechanical Engineering, LSU
Session VI
Animated output….
Department of Mechanical Engineering, LSU
Session VI
Moving block in an inclined plane….
N
(x1,y1)
v1
N
Moving object from (x1,y1) to
(x2,y2). The friction
coefficient is =0.1. The
starting velocity at 1 is v1.
Calculate v2 (velocity at 2), t
(time), and a (acceleration)
mgcos

mgsin

(x2,y2)
v2
mg
Department of Mechanical Engineering, LSU
Session VI
MATLAB Program….
Department of Mechanical Engineering, LSU
Session VI
Output….
Department of Mechanical Engineering, LSU
Session VI
Determining Diameter of the pipe
from the flow rate….
d
L
Q
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Session VI
Fountain.m
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Session VI
Fountain.m cont….
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Session VI
Piping.m
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Session VI
Piping.m cont…
Department of Mechanical Engineering, LSU
Session VI
Recap….
What have we learnt today?
Engineering Applications using MATLAB….
 Solving non linear differential equations
 Algorithm analysis for four bar linkage problem
 Other mechanical problems
Department of Mechanical Engineering, LSU
Session VI
Thank You
Department of Mechanical Engineering, LSU
Session VI