Environmental Engineering Reference
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9.2 Vibration-Based Damage Detection of Rotational Wind
Turbine Blades
9.2.1 Structural Dynamic Model of Rotating Blades
A general horizontal axis wind turbine (HAWT) consists of three basic parts: the
tower, the nacelle, and the blades. The blades are fixed to the hub; see Fig. 9.1 .In
general, this system can be considered as flexible bodies attached to moving
supports, which have been described in a number of technical papers considering
rotating machinery, helicopter rotor blades, and so on.
A stationary linear dynamical model for the blade in still conditions is generally
suitable for structural dynamic analysis:
::
ðÞþ C _ Z ðÞþ KZ ðÞ¼ t ðÞ
M Z
ð 9 : 1 Þ
where M, C and K are the mass, damping, and stiffness matrices, respectively, their
dimensions are n 9 n, which is the degrees of freedom of the structure. Z collects
the displacements of the degrees of freedom of the structure, and its dimension is
n 9 1; the external force v is modeled as a nonstationary white noise.
However, for a rotational blade, because of the axial loads, such as centrifugal
forces and changing gravity forces, on the blade effect the lateral and torsional
deflections, the out-of-plane stiffness of a structure can be significantly affected by
the state of in-plane stress in the structure. This coupling between the in-plane
stress and transverse stiffness known as stress stiffening (or dynamic stiffening and
geometric stiffening), first proposed by Kane et al. [ 39 ], is most pronounced in the
blade structure. In this case, the conventional small-deflection theory models used
in the nonrotating structures is no longer suitable. Kane et al. considered the
system stiffness to be K = K s + K d , in which K s is the structural stiffness and K d
depends on the angular velocity, based on the accurate description of the defor-
mation of an elastic beam with a large overall motion [ 39 ]. In the past 20 years, a
number of researchers have observed and investigated this topic, and several
analytical approaches have been proposed to include stress stiffening terms in the
Fig. 9.1 Typical horizontal axis wind turbine blades
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