Effects of non-linearity due to large deflections in the derivation of frequency response data from the impulse response of structures

The impulse response of a non-linear, hardening-spring, resonant system and derived frequency response estimates by Fourier transformation are examined. A perturbation solution for the impulse response of a single-degree-of-freedom system with “cubic stiffness” is derived, this type of non-linearity being observed for structures at large deflections. Frequency response function characteristics derived from the Fourier transform of the perturbation solution are compared with those from computer solutions. The vector diagram method of frequency response function presentation is studied and the occurrence of pseudo-resonances in practical testing is discussed.