Building Acoustics

94 Building acoustics

corresponding bending stiffness Bx and Bz. 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.

Figure 3.21 Rectangular plates in bending motion. Examples on mode shape.

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 Ex, Ez, υx,
υz and Gxz, 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

( 1 , 1 ) mode ( 1 , 2 ) mode

( 2 , 2 ) mode ( 2 , 3 ) mode

1 2 3 4 5 6 7 8 9 10

0

50

100

150

200

Natural frequency number

Frequency (Hz)