Recent advances in the application of functional series to non-linear structures

The Volterra and Wiener kernels of non-linear systems have been studied for some time now. The multidimensional Fourier transforms of Volterra and Wiener kernels are higher order frequency response functions (FRF's). Higher order FRF's can successfully be measured for non-linear structural systems as is demonstrated. These can predict aspects of the system behavior unobtainable from measurements of first order FRF's. By considering the measured FRF's of a structure as Volterra kernel transforms it is possible to curve fit a non-lindear multi-degree-of-freedom parametric model to FRF data. Analysis techniques for linear structures of measuring and curve fitting to first order FRF's can thus be extended to non-linear systems by the measurement of second and third order FRF's. © 1989.