The local and global instability and vibration of systems subjected to non-conservative loading

The paper presents the results of theoretical and numerical studies on the slender, geometrically nonlinear system supported at the loaded end by a spring of a linear characteristic and subjected to non-conservative (generalized Beck's) loading. The boundary problem was formulated based on the Hamilton principle and then solved using, due to the nonlinearity, the small parameter method. The bifurcation force depending on system parameters and local and global instability regions has been determined in the study, and the characteristic curves have been plotted in the load-free vibration plane.