Dynamics of Flexible Beam Using a Component Mode Synthesis Based Formulation

Abstract

Abstract This paper establishes a new formulation strategy for a flexible beam with large rotational motion. The finite element based formulation, which was previously developed for the analysis of the ‘Spaghetti Problem’ by the present authors, is extended to realize a low order and high accuracy beam model using a kind of component mode synthesis method. The deformation of the flexible beam is modeled by a combination of a static mode represented by a shape function and an analytically evaluated vibration mode clamed at both ends with respect to the body coordinate system. The body coordinate system satisfies the condition that the x-axis connects both ends of the beam. To demonstrate the efficiency and validity of the flexible beam model in multibody dynamics, a 2-link flexible robot arm is modeled as a flexible multibody system consisting of some rigid bodies and two flexible beams. Its validity is indicated by good agreement between numerical simulations and the experimental results.