文档介绍：Journal of Sound and <ibration (2002) 251(1), 1}12
doi:.3806, available online at
A MATHEMATICAL MODEL FOR WIND TURBINE BLADES
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Forskningscenter Ris , Pr vestationen for <indm ller, Postboks 49, DK-4000 Roskilde, Denmark.
E-mail: abau@
(Received 14 February 2000, and in ,nal form 21 March 2001)
Amathematical model for an elastic wind turbine blade mounted on a rigid test stand is
derived pared with experimental results. The linear equations of motion describe
small rotations of the test stand, blade lateral de#ections and rotation of the chord. Warping,
extension and tilt of the cross-sections are slaved to the dependent minimal co-ordinates in
order to reduce the number of state variables. Using the principle of virtual work,
a procedure is employed bines the volume discretization of general &&solid'',or
shell-type "nite elements (FE), with the approach of global form functions (stretching over
the whole blade length). The equations of motion are solved as an eigenvalue problem and
the results pared with an experimental modal analysis of a 19 m long blade. The
computed eigenfrequencies "t well, but the mathematical model underestimates the pitch
motion of the blade chord. Parameter studies show the e!ect of warping. Despite the few
degrees of freedom and uncertainties in the model parameters, the mathematical model
approximates the measured blade dynamics well.
2002 Elsevier Science Ltd.
1. INTRODUCTION
Rod models, such as beams and strings, have essentials pared with general
solid or shell-type "nite-element (FE) models when describing slender solid bodies. The
co-ordinates are intuitively related to the motion of the physical system, signi"cantly fewer
degrees of freedom can be chosen and the range of eigenvalues is restricted to the relevant
low frequencies.
However, all well-known rod models are limited to symmetric cross-sections. They can be
extended to account, ., for el