The use of orthogonal decomposition tools in analyzing the wind effect on structures

Due to the geometric complexity, the flexibility which induces large displacement and the usually very small inherent damping, several aspects have to be taken into account during the design stage of stayed or suspended large span structures. The analysis of wind induced vibration is one of the main and more cumbersome topics. In fact, it requires, for instance, the evaluation of the pressure coefficients, the structural response analysis, the investigation of possible aeroelastic effects, etc, up to the design of additional energy dissipative systems to reduce the vibrations themselves, if necessary. The main objective of this paper is to study the structural response to the wind action and its mitigation whit relatively simple analysis tools which allow to control the numerical results without using heavy analysis software and without significantly loose precision and stochastic information. The appropriate use of orthogonal decomposition techniques is very helpful at this purpose. As a matter of fact, the scientific community is still debating about the effectiveness and the physical meaning of the orthogonal decomposition techniques in their different forms. Furthermore, the scientific literature often reports these techniques without considering their effective helpfulness in the structural design. In the present paper, the main orthogonal decomposition procedures are treated and their possible use in analyzing structures subjected to the wind action is shown. Orthogonal decomposition consists in projecting a generally multivariate stochastic field on an appropriate orthogonal base, to point out some specific aspects of the represented stochastic process. The first possible application of this technique concerns the simplification of pressure fields representation. An unsteady multivariate pressure field can be usefully simplified by projecting (Proper Orthogonal Decomposition - POD) it on the space generated by the eigenvectors of the covariance matrix of the original field. Two main advantages can be achieved by this technique. Firstly, the new fields (pressure modes) are mutually uncorrelated, giving rise to noteworthy advantages in evaluating the quasi-steady contribution to the structural response. Secondly, the energy content of the complete multivariate field is usually well represented by few components in the transformed space, allowing the representation of the effective pressure field by mean of few pressure modes. A possible third advantage, which is still debated by the scientific community, consists in the physical correlation between pressure modes and aerodynamic phenomena (such as incident wind turbulence, vortex shedding, etc.). The representation of local loads (were the non-Gaussianity may be important) will be also discussed. Another possible application consists in projecting the pressure fields on the space generated by the structural modal shapes. This results very helpful in evaluating the resonant contribution to the structural response. Sometimes, the double projection on both the covariance matrix eigenvectors and modal shapes allows further simplifications. A variant of the classical POD consists in evaluating different covariance matrices for different frequency ranges and in performing the projection for each of these frequencies. In other words, the power spectral density matrix is subdivided into a certain amount of frequency ranges and each of these ranges is treated separately, giving rise to different eigenvalues and eigenvectors sets. Sometimes, this procedure can allow to better correlate the pressure modes to physical phenomena, with respect to the classical POD. On the other hand, the increased numerical effort can vanish the pressure field simplification advantages. When wind tunnel tests are unavailable or insufficient to adequately describe the complete three-dimensional stochastic process, the pressure fields are numerically evaluated by mean of the artificial simulatio...