Civil Engineering Reference
In-Depth Information
corresponding bending stiffness
B
x
and
B
z
. In several cases, one may apply the geometric
average of the stiffness in these two directions to characterize the panel stiffness but this
may also turn out to be completely wrong, e.g. when calculating the natural frequencies.
(1,1) mode
(1,2) mode
(2,2) mode
(2,3) mode
Figure 3.21
Rectangular plates in bending motion. Examples on mode shape.
200
150
100
50
0
1
2
3
4
5
6
7
8
9
10
Natural frequency number
Figure 3.22
Natural frequencies (eigenfrequencies) of a 180 mm thick concrete slab, dimensions 4.0 by 6.0
metres; the frequencies of the first 10 modes of the slab that is simply supported.
We shall characterize the orthotropic plate using the material properties
E
x
, E
z
,
υ
x
,
υ
z
and
G
xz
, i.e. by the elasticity modulus and Poisson's ratio for the two directions
together with the shear modulus. There are really four independent quantities only as
taking symmetry into consideration gives
