Stability of a system of circular rings reinforced with inextensible threads

Abstract

The paper deals with the problems of stability for a system of circular rings interconnected in such a way that the displacements of these rings, and the rotation angles of their sections at some points, coincide. This has been reduced to a certain variational problem with restrictions on the functions in question in the form of linear equations, and Fourier series are used to obtain a finite-dimensional approximation. The paper also presents the stability problem for a system of circular rings reinforced by inextensible threads that cannot resist compressive forces. In this case, constraints in the form of inequalities arise, and after finite-dimensional approximation the problem reduces to finding the bifurcation points for a nonlinear programming problem in the presence of inequality constraints.