Nonlinear Dynamic Analysis of an Icosahedron Frame which Exhibits Chaotic Behavior

Abstract

The research question addressed is whether a lighter than air vehicle (LTAV), which uses an internal vacuum to become positively buoyant, can be designed to provide extended loiter for U.S. Air Force applications. To achieve a vacuum, internal gases are evacuated from the vessel, which creates a dynamic response in the supporting structural frame. This paper considers the frame of an icosahedron shaped LTAV subject to external atmospheric pressure evacuated at varying rates. A static finite element analysis documented in previous research revealed a snapback phenomenon in the frame members under certain loading conditions. A nonlinear chaotic response was observed when a dynamic analysis was conducted with the same boundary conditions used in the static analysis. The chaotic response for a variety of boundary conditions, generated by varying the rate of evacuation, similar to a ramp input, is determined. An analysis of the dynamic response is determined nonlinearly using a method that relies on a reference point distribution of external pressures to distribute the surface force across the frame. A novel method of combining the power spectral density with a Lyapunov exponent was used to determine the degree of nonlinearity and chaotic response for each boundary condition examined.