By J. Lerner, U. Boldfes
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Additional info for Wind Tunnels and Experimental Fluid Dynamics Research
In particular, in case of ﬂexible structures, it is known that the normal modes of vibration φj consist an optimum basis Φ for the representation of the structural response to a broadband loading (Géradin & Rixen, 2002). They are obtained by solving the eigenvalue problem: (K − ω 2j M)φj = 0 (13) where ω j represents the natural circular frequency. The ﬁrst three mode shapes of the considered structure are illustrated in Fig. 12. e. large wavelengths, as opposed, in this case, to the deep localization of loading components.
1997). This would be preformed by ﬁtting parametric estimates to the bispectrum of generalized forces and conducting higher order stochastic analyses as described in (Denoël & Degée, 2006; Gusella & Materazzi, 1998). 6. Acknowledgments The authors are grateful to CSTB (Nantes, France) and to BEG (Angleur, Belgium) for having provided a neat case study for the illustration of the proposed ideas. 7. References Baker, C. J. (2000). Aspects of the use of proper orthogonal decomposition of surface pressure ﬁelds, Wind and Structures 3(2): 97–115.
The base for these calculations is the introduction of a dynamic model in the next section, describing the behaviour of the system under the inﬂuence of loads, forces and torques. 2 Dynamics The dynamical equations of motion of the end effector can be described by mpE 0 0 I Mp r¨ 0 f + − E τE ω ˙ ω × (Iω) gC x¨ −w gE = AT f (6) 357 Wire Robot for Wind Tunnels Suspension Systems for Wind Tunnels Wire Robot Suspension Systems with mass matrix of end effector, Mp cartesian space vector of coriolis and centrifugal forces and torques, gC vector of generalized applied forces and torques.