ABSTRACT
The present paper develops an appropriate optimization model for placing
frequencies of a typical wind rotor/tower structure in free torsional motion. The aim is
to avoid large amplitudes caused by the yawing-induced vibrations in the case of
horizontal-axis machines or rotational motion of the blades about the tower axis in
case of vertical-axis machines. This can be a major cause of fatigue failure and might
severely damage the whole structure of the wind generator. The mathematical
formulation considers a single pole tower configuration having thin-walled circular
cross section with constant taper along the tower height. The nacelle/rotor
combination is modeled as a rigid mass elastically supported at the top of the tower
by the torsional spring of the yawing mechanism. The resulting governing differential
equation of motion is solved analytically by transforming it into a standard form of
Bessel's equation, which leads to the necessary exact solutions for the frequencies
and mode shapes. Several cases of study are examined for different values of the
yawing stiffness and damping parameters by considering both conditions of locked
and unlocked yawing mechanism. Useful design charts are developed for placing the
frequencies at their needed target values with no penalty of increasing the total
structural weight of the system. In all, the developed model guarantees full
separation of the system frequencies from the critical exciting torsional frequencies
by the appropriate choice of the optimization design parameters.