Modelling of a moveable beamlike complex system

Abstract

In this paper, the model of the beam with a variable geometry is considered. Thanks to a more accurate model and a better control of systems with variable geometry, one can get a significant reduction in maintenance costs and increase the durability and reliability of the entire system. This article presents a method for modeling the telescope beam of variable length and orientation. Changing the length of the extension element influences a change of the cross-sectional area of the external element and the total change in the stiffness of the system. During rotation, the slender structure vibrations occur, which may cause small relative movements. These local vibrations can change the direction of the resultant force. Because such small movements are not reflected in the geometry, this effect can be considered by changing the stiffness matrix. This effect is called spin softening. The global motion of a flexible beam is a composition of rotations and unwanted vibrations, which can be critical if the stiffness of the structure is not high enough, compared with the external dynamic load. The mathematical model of the considered beam is shown. In the model, damping, nonlinearly variable cross section of the component elements, and interactions between principal and relative motions are considered.