Flexural-flexural oscillations of Beck's column subjected to a planar harmonic excitation

The non-linearly coupled flexural-flexural oscillations of a non-conservative column with two independent load parameters are investigated by analytical methods with the objective of determining the quantitative and the qualitative behavior of the response. The column is subjected to a planar periodic distributed load whose frequency is near the eigenfrequency of its free bending oscillations. The analytical results of the analysis are compared with those obtained by numerical integration of a set of non-linear differential equations obtained by the application of Galerkin's method to the original equations.