PSI - Issue 12

A. Cetrini et al. / Procedia Structural Integrity 12 (2018) 87–101

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Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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The Nrel FAST code models the components of the generator as rigid bodies, except for the tower and the blades which can also be defined as flexible. In contrast to the case of rigid bodies, whose configuration is defined by a maximum of six independent parameters, the configuration of a deformable body is defined by an infinite number of coordinates. However, for computational problems, infinite coordinates can’t be used, so it is necessary to h ave a finite number of degrees of freedom (Shabana (2005), Holm- Jorgensen(2009)). In most multibody modeling software this is done through an approach that, through or finite elements (ADAMS, SIMPACK) or, as in FAST, analytically, adopts modal modeling and modal truncation: the components of the deformation field are expressed as a linear combination, extended to a finite number of terms, of time functions (natural coordinates) and spatial functions (modes). FAST uses the reductive but simplifying hypothesis that the tower and the blades are fixed beams with distributed mass and stiffness. For these bodies it is possible to perform a modal truncation that only leads to the involvement of modal forms considered fundamental for the motion. In particular, referring to the case of a simple cantilever beam, defining with ( , ) the displacement of the beam axis line in only one direction (2): ( , ) = ∑∅ ( ) ( ) =1 (2) The Rayleigh-Ritz method allows to approximate the modal forms ∅ ( ) as the sum of a set of functions called "shape functions"(3): ∅ ( ) = ∑ ,ℎ ℎ ( ) ( = 1,2. . . ) (3) In FAST environment the modal forms are defined analytically by means of sixth grade polynomials of the following type (3): ∅ ( ) = ∑ ℎ ( ) ℎ 6 ℎ=2 (4) Regarding modal truncation, the number of modes is predefined and limited to four, associated with the first two bending modes in each of the two main planes of the component, i.e. two Fore-Aft (FA) modes and two Side-Side (SS) modes for the tower.

3. Theoretical bases and application of the method 3.1 Reference theory for the developed method

As mentioned in Section 1, this article presents a methodology that allows, under appropriate hypotheses, to reduce a complex support structure of a wind turbine to that of a simple cantilever beam in such a way as to guarantee an equivalence in static and dynamic terms. This allows simulating the reduced structure within the FAST software in an immediate way, without changing the source code. The developed method can be briefly summarized by Fig (1).