Tower Design and Manufacture - Small Wind Turbines: Analysis, Design, and Application - page 209

Here is a snapshot of the execution of the m-file in the Matlab command
window for the IEC SLM Load Case H:
The comparison of the maximum stress at each height from the program with
the FEA results is shown in Fig. 10.3 ; the simple analysis is reasonably accurate.
The maximum axial stress due to the turbine weight and the tower self-weight is
1.2 MPa, which is very small. The important wind loads and tower parameters are
either output in the Matlab session copied below the program listing or are con-
solidated in Table 10.3 . The turbine contributes about 20% of the horizontal force
and about one-third the base overturning moment, demonstrating why monopole
towers need more mass, and are more expensive than the other types.
Table 10.3 demonstrates that the tower top deflection is also reasonably well
estimated. The following rows show the natural frequency calculations. Method A
approximates the stiffness as the total horizontal force divided by the turbine
deflection as calculated above, the natural frequency can be found as the square root
of stiffness divided by tower mass. It is easy, however, to show that for a constant
diameter tower without a turbine and its thrust, that this very crude method will
under-estimate the lowest natural frequency by the factor 1/(0.56p) = 0.568,
Exercise 10.14. Method A is more accurate for the combined turbine and tower.
This is undoubtedly because the turbine mass is concentrated at the top of the tower
and this suggests Method B wherein the effective mass of the tower is set to 0.23m t .
This factor comes from the standard analysis of the natural frequency of concen-
trated mass and force on top of a constant diameter column, e.g. pp. 127-128 of Rao
[ 14 ] which gives the effective column mass quoted above. Furthermore, the axial
load due to the turbine weight and tower mass is so small that it will not greatly alter