Civil Engineering Reference
In-Depth Information
Figure 5.6
Aerodynamic admittance—
experimental data and fitted function (Vickery,
1965, 1968).
For open structures such as lattice frame towers which do not disturb the flow greatly,
χ
2
(n)
can be determined from the correlation properties of the upwind velocity
fluctuations (see Section 3.3.6). This assumption is also made for solid structures, but
χ
2
(n)
has also been obtained experimentally.
Figure 5.6 shows some experimental data with an empirical function fitted. Note that
χ(n)
tends towards 1.0 at low frequencies and for small bodies. The low-frequency gusts
are nearly fully correlated and fully envelope the face of a structure. For high frequencies
or very large bodies, the gusts are ineffective in producing total forces on the structure,
due to their lack of correlation, and the aerodynamic admittance tends towards zero.
To obtain the mean-square fluctuating deflection, the spectral density of deflection
given by Equation (5.8) is integrated over all frequencies:
(5.10)
The area underneath the integrand in Equation (5.10) can be approximated by two
components,
B
and
R,
representing the 'background' and resonant parts, respectively
(Figure 5.7).
Thus,
(5.11)
