Effect of damping and stiffness on the random vibration of non-linear periodic plates

Sonic fatigue analysis of large complex structures requires accurate prediction of the response of plates and shells. Life predictions based on linear plate theory have been shown to deviate significantly from experimental data when the structure is subjected to high acoustic loading. The accuracy of the analysis can be improved by considering the non-linearities of the structure. It is well known that the geometrical non-linearities of the plate yield a stiffness which increases non-linearly with the amplitude of vibration. The effect of this non-linearity becomes significant as the deflections approach the thickness of the plate. In addition to the non-linear stiffness it has been argued that non-linear damping also could play an important role in the vibration of plates. The argument is based on the observation that during random excitation of plates the power spectra resonance peaks broaden as the excitation level is increased. In this paper we present an investigation of this broadening phenomenon. For generality, both unstiffened and orthogonally stiffened plates are considered. It is shown that widening of the resonance peaks, can occur simply by the existence of the non-linear stiffness and without the introduction of non-linear damping. It is also shown that the method of equivalent linearization is not suitable for the study of the power spectra of the response of non-linear plates.