Nonlinear Vibrations and Instability of Shallow Pyramidal Trusses

Abstract

Pyramidal space trusses are a basic component of several structures, from carbon nanostructures to large geodesic domes. These structures, such as the classical Von Mises truss, have a highly non-linear response in the presence of static and dynamic loads. The geometric nonlinearity is particularly significant, even at low load levels when these structures are shallow, that is, has a small height to base ratio. This paper presents an exact non-linear formulation for a shallow pyramidal truss composed of n equally spaced bars. Based on this formulation, the loss of stability and nonlinear vibrations of these structures under static and dynamic loads is analyzed. To understand its nonlinear behavior, time responses, phase portraits, bifurcation diagrams, energy profiles and basins of attraction are obtained. The results highlight the complex nonlinear dynamics of this class of structures and its major influence in design.