A reduced eigenproblem formulation for Variable Geometry Trusses

Abstract

One important problem in the dynamic analysis of Variable Geometry Trusses (VGTs) is the evolution of frequencies and vibration modes in different positions along their movement, which usually involves large changes in their geometry. The calculation of modes and frequencies in every position may result in a prohibitive computational cost when using conventional solution methods for the dynamic eigenproblem. To reduce computational cost, and to better understand the dynamic behaviour of these systems, a methodology has been developed which estimates natural frequencies and vibration modes in a specific position from their values in a previous one. Thus, the derivatives of the natural frequencies and modes are obtained in a limited set of positions and a linear estimate is developed to extrapolate the values of the natural frequencies and modes to the rest. In order to verify the quality of the extrapolation of the reduced eigenproblem formulation, some suitable error estimators are used.