This paper presents a reduced-order-modeling approach for nonlinear, multi-degree-of-freedom aerodynamic systems using multi-input Volterra theory. The method is applied to a two-dimensional, 2 degree-of-freedom transonic airfoil undergoing simultaneous forced pitch and heave harmonic oscillations. The so-called Volterra cross kernels are identified and shown to successfully model the aerodynamic nonlinearities associated with the simultaneous pitch and heave motions. The improvements in accuracy over previous approaches that effectively ignored the cross kernels by using superposition are demonstrated. Copyright

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Journal AIAA Journal
Balajewicz, M. (Maciej), Nitzsche, F, & Feszty, D. (2010). Application of multi-input volterra theory to nonlinear multi-degree-of-freedom aerodynamic systems. AIAA Journal, 48(1), 56–62. doi:10.2514/1.38964