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.
