April 2016
Intermediate to advanced
297 pages
8h 37m
English
Content preview from Structural Acoustics
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112 Structural Acoustics: Deterministic and Random Phenomena
© 2011 by Taylor and Francis Group, LLC
Expressing the derivatives in nite-difference form, the total potential
energy of stretching and shearing relative to the xed axes can be written as
shown in Section 6.7.
6.2.1 Bending and Twisting Energy
The potential energy of bending and twisting of a cross-stiffened plate ele-
ment can be derived from the concept of an equivalent orthotropic plate. The
energy is
E D
x
D
y
B x
A
v
=
∂
∂
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
+
∂
∂
⎛
⎝
⎜
⎞
⎠
⎟
+
∫
1
2
2
2
2
2
2
2
2
ω ω
DD
w
x
w
y
D
w
x y
dA
xy
1
2
2
2
2
2
2
4
∂
∂
∂
∂
+
∂
∂ ∂
⎛
⎝
⎜
⎞
⎠
⎟
⎤
⎦
⎥
⎥
(6.6)
Using nite-difference approximations and transferring to the xed axes
(Equation ...
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