Search

The three-dimensional free vibrations of an orbiter-towed tethered satellite system with nominally vertical tether during stationkeeping phase are studied analytically. The tether is modeled as an elastic continuum with mass and the orbiter and the subsatellite as two concentrated masses. The linearized equations of motion with variable coefficients are solved by means of a perturbation technique. An analysis of the order of magnitude of the different terms involved permits evaluation of the coupling between longitudinal and transversal in-plane vibrations coming to an approximate closed-form solution of the eigenvalue problem.

In this paper, the effect of boundary conditions on multiple interactive buckling in thin-walled members under compression is analyzed by means of the general theory of stability. The total potential energy is expanded to up to third-order terms to investigate structures with asymmetric postbuckling behavior; initial geometric imperfections are taken into account. Under simplifying assumptions, the nonlinear equations governing the postcritical behavior reduce to a linear eigenvalue problem that is independent of the geometric and mechanical properties of the column and depends on the boundary conditions only. Localization of the buckling patterns is verified when a large number of local buckling modes occur simultaneously. A continuum representation, based on the substitution of the algebraic eigenvalue problem with a differential equation, is proposed.