A multiple timescale approach of bispectral correlation

The paper develops an approximate semi-analytical solution for the computation of third statistical cross-moments modal responses in a stochastic dynamic analysis. These moments would require heavy twofold numerical integration general context but are drastically simplified proposed formulation by taking advantage assumed distinctness between low characteristic frequency loading and natural frequencies structure. This condition is typically respected acknowledged wind engineering where buffeting analysis large structures hinges on Background/Resonant decomposition. As such, extends to order existing developments estimation variances covariances. It allows spectral be conducted within reasonable amount time. also reveals existence three main components response: background, bi-resonant tri-resonant. latter one specific this very own problem shown important when sum two equal one, although structural behavior linear. Mathematics highlight other findings which then illustrated minimum working example, easily reproducible readers. Overall, it clearly demonstrates benefits decomposition terms both behavioral comprehension computational consumption.