Applications of biorthogonal decompositions in fluid–structure interactions

Abstract

This paper is dedicated to the study of the orthogonal decomposition of spatially and temporally distributed signals in fluid–structure interaction problems. First application is concerned with the analysis of wall-pressure distributions over bluff bodies. The need for such a tool is increasing due to the progress in data-acquisition systems and in computational fluid dynamics. The classical proper orthogonal decomposition (POD) method is discussed, and it is shown that heterogeneity of the mean pressure over the structure induces difficulties in the physical interpretation. It is then proposed to use the biorthogonal decomposition (BOD) technique instead; although it appears similar to POD, it is more general and fundamentally different since this tool is deterministic rather than statistical. The BOD method is described and adapted to wall-pressure distribution, with emphasis on aerodynamic load decomposition. The second application is devoted to the generation of a spatially correlated wind velocity field which can be used for the temporal calculation of the aeroelastic behaviour of structures such as bridges. In this application, the space–time symmetry of the BOD method is absolutely necessary. Examples are provided in order to illustrate and show the satisfactory performance and the interest of the method. Extensions to other fluid–structure problems are suggested.