Extension of Davenport's Background/Resonant decomposition for the estimation of higher response moments

The non Gaussian buffeting analysis of a structure subjected to turbulent
wind may be advantageously performed with a Volterra approach. Although
this concept may be applicable to nonlinear structures, the scope
of this paper is limited to structures with a deterministic linear
behavior. In this case, the Volterra kernels take a simple explicit
expression and the statistical moments of the structural response
are simply recovered by a multi-dimensional integration of the corresponding
spectra. Because the multi-dimensional spectra of the loading are
usually determined numerically, these integrals have to be computed
numerically too. The computational burden necessary for the estimation
of these integrals turns out to be prohibitive as soon as high order
moments are required (beyond and including 4th moment). The numerical
conditioning is in fact again worse when the structural damping is
low as the Volterra kernels then exhibit very large gradients in the
frequency space, which are difficult to capture properly.

Because the timescales related to the dynamics of the structure and
to the random wind loading are well distinct, a nowadays customary
decomposition of the response into Background and Resonant contributions
(dating back to A. Davenport's earliest works) provides a very good
estimation of the second statistical moment. Recently the concept
has been extended to the Background/biResonant decomposition for the
estimation of the third statistical moment of the response. This paper
presents the extension to the computation of the fourth statistical
moment, with the only assumptions of slight damping and low-frequency
loading such as those that made Allan Davenport's Background/Resonant
(B/R) decomposition fruitful.

After some multiple scales considerations, the fourth moment of the
response is approximated as the sum of a background component, a tetraresonant
component and a mixed background-biresonant component. Mathematical
developments will be presented in the full paper along with illustrative
examples, while the current 4-page abstract just presents of a flavour
of it.