Department of Mechanical Engineering, LSU Session VI
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Transcript Department of Mechanical Engineering, LSU Session VI
MATLAB Tutorials
Session VI
Engineering Applications using MATLAB
Rajeev Madazhy
Email: [email protected]
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….
Department of Mechanical Engineering, LSU
Session VI
Command window….
Department of Mechanical Engineering, LSU
Session VI
Output….
Department of Mechanical Engineering, LSU
Session VI
Output….
Department of Mechanical Engineering, LSU
Session VI
Example 2: Four Bar Linkage….
C
y
B
A
Department of Mechanical Engineering, LSU
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
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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:
Department of Mechanical Engineering, LSU
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
Department of Mechanical Engineering, LSU
Session VI
Fountain.m
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Session VI
Fountain.m cont….
Department of Mechanical Engineering, LSU
Session VI
Piping.m
Department of Mechanical Engineering, LSU
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