PARAMETRIC INSTABILITY OF A LEIPHOLZ COLUMN UNDER PERIODIC EXCITATION

In this paper, the parametric instability of a Leipholz column under four boundary conditions is examined. The study of this prototypical model is intended to provide a basic understanding of the disc brake pad instability. The distributed, follower-type axial load is assumed to be uniform and periodic. Instability regions are obtained and the existence of combination resonances of the sum and difference types is discussed for each set of boundary conditions. It is found that the combination resonance of the sum type exists in all the cases of boundary conditions considered, but the difference type exists only in the cases of clamped-simply supported and clamped-free boundary conditions. The combination resonance is shown to be as important as the simple parametric resonance. Results, when compared to a column under a periodic end load, show that the instability characteristics of these two columns are considerably different. The effect of a constant axial load is to shift the instability regions along the frequency axis.