## ABSTRACT

D w N

w

x N

w

y h w 04 1

2 2∇ + ∂∂ +

∂ ∂ − ρ ω =

(6.1)

Let =x x a/ , =y y a/ . Since the horizontal sides are simply supported, we set

w(x,y) = W(x) sin(αy) (6.2)

where α = nπa/b. In view of Equation (6.2), Equation (6.1) becomes

+ − α − ω + α − α = ≤ ≤d W

dx N

d W

dx N W x( 2 ) ( ) 0, 0 1

(6.3)

Here the nondimensional parameters are

= = ω = ρ ωN N a D N N a D h a D/ , / , /1 1 2 2 2 2 2 2 4 (6.4)

Note that the frequency is normalized with respect to the width a instead of the height b as in Chapter 5.