Optimization

11Introduction

For this problem, L = 1 m and ρ = 7800 kg/m

3

. The rst cantilever fre-

quency is given by

f

L

EI

k

1

2

1

2

3 5156

=

π

.

(1.30)

where E is Young’s modulus of steel and its value is 2 × 10

11

N/m

2

. The

variable k is mass per unit length. The moment of inertia I for the rod is

given by

I d=

π

64

4

(1.31)

The optimization problem can be written as follows.

Minimize

π

ρ

4

2

d L (1.32)

subject to

1

2

3 5156

20

2

π

.

L

EI

k

≥

(1.33)

1.4 Solution with the Graphical Method

Having formulated the optimization problems in the previous section, it

is tempting for readers to get solutions for these problems. The graphical

method is a simple technique for locating ...