Tower Design and Manufacture - Small Wind Turbines: Analysis, Design, and Application - page 205

d 2 x

dy 2 ¼ M ðÞ

ð 10 : 16 Þ

EI ðÞ

Anticipating difficulties in analytically determining the double integral, the
solution may be sought under the restriction that t d 0 , in which case

Þ 3 I ð y Þ 0 : 43792td 0 þ d 1 y ð ð 10 : 17 Þ

With this simplification, the double integration of ( 10.16 ) using ( 10.5 ) and ( 10.17 )
may be obtained, for example, using the symbolic mathematics capability of
Matlab, but the result appears very cumbersome.
Alternatively, ( 10.16 ) can be rewritten as two first order ordinary differential
equations and solved using Matlab's built-in Runge-Kutta routines, as was the
equation for starting in Chap. 6 .

Fig. 10.2 The Aerogenesis 5 kW turbine on its 18 m monopole tower. The gin pole for raising
and lowering is attached near the base. The right side photo shows the turbine before being raised
(photos from Paul Peterson)