Department of Mechanical Engineering, LSU Session VI

MATLAB Tutorials

Session VIEngineering Applications using MATLAB

Rajeev MadazhyEmail: 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(*t) where 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

A

B

C

D

Example 2: Four Bar Linkage….

x

y

Department of Mechanical Engineering, LSU 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.

)cos(2222 Cabbac

a

b

c

C A

B

Department of Mechanical Engineering, LSU Session VI

Step 1: Calculate length of BD

Step 2: Calculate angle

Step 3: Calculate angle

Step 4: The coordinate of point C is as follows:

Cont….

Department of Mechanical Engineering, LSU Session VI

)cos( CDDAxC( If 0< <pi ))sin( CDyC

)cos( CDDAxC ( If pi < <2pi )

)sin( CDyC

Cont….

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

mgmgsin

mgcos

N(x1,y1) v1

(x2,y2) v2

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)

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….

Q

d

L

Department of Mechanical Engineering, LSU Session VI

Fountain.m

Department of Mechanical Engineering, LSU 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