Double modal transformation in continuous modelling

The modal transformation techniques, usually adopted in dynamic analyses, are based on the search for a space in which there are advantages in the solution or interpretation of the problem. Analogous transformation techniques have been recently developed with the aim of defining a space where a multidimensional random process is expressed by a linear combination of one-dimensional 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. This technique is developed by a continuous approach and is applied to the evaluation of the along-wind response of slender structures. The solution is provided in closed form.