Stability and non-stationary vibration analysis of beams subjected to periodic axial forces using discrete singular convolution

Dynamic instability of beams subjected to periodic axial forces is studied using the discrete singular convolution (DSC) method with the regularized Shannon\'s delta kernel. The principal regions of dynamic instability under different boundary conditions are examined in detail, and the non-stationary vibrations near the stability-instability critical regions have been investigated. It is found that the results obtained by using the DSC method are consistent with the analytical solutions, which shows that the DSC algorithm is suitable for the problems considered in this study. It was found that there is a narrow region of beat vibration existed in the vicinity of one side (o/o > 1) of the boundaries of the instable region for each condition.