A systematic study of the stability of the rod is carried out, elastically fixed at one end from angular and linear displacements, and loaded at the other with potential and tracking forces, is carried out. A dynamic method is applied with the representation of perturbed motion in the form of a series expansion according to the natural forms of vibrations of a system with a reduction of a system with distributed parameters to a system with a finite number of degrees of freedom. Based on the Rouse–Hurwitz criterion, sufficient conditions are formulated to determine the boundaries of divergence and flutter. The analysis of the dependence of the position of the boundaries of the stability region on the rigidity of the fastening parameters of the rod is carried out. Based on the method of direct solution of a homogeneous boundary value problem and the optimization method for special cases of elastic fixation and energy dissipation, the change in characteristic parameters at the intersection of the stability domain is demonstrated.
No takes yet. Share an insight, caveat, or question.
Radin et al. (2024) studied this question.
Synapse has enriched 5 related papers. Consider them for comparative context: