Double modal transformation and wind engineering applications

Modal transformation techniques are usually adopted in structural dynamics with the aim of decoupling the equations of motion. They are based on the search for an abstract space in which the solution of the problem results simplified. Analogous transformation techniques have recently been developed with the aim of defining a space where a multivariate stochastic process is expressed by a linear combination of one-variate uncorrelated processes. This paper proposes a method, called double modal transformation, by which the dynamic analysis of a linear structure is carried out through the simultaneous transformation of the equations of motion and the loading process. By adopting this technique, the structural response is obtained through a double series expansion in which structural and loading modal contributions are superimposed. Its effectiveness and application are discussed with reference to two classic wind engineering problems—the alongwind response and the vortex-induced crosswind response of slender structures—which provide a wide panorama of the most relevant properties of this procedure.