Timoshenko beams and flexible multibody system dynamics

Abstract

A method for the dynamic analysis of flexible multibody systems that accounts for rotary inertia and shear deformation effects is presented. Flexible components in the system are discretized by using the finite element method. Because of the large rotations of the system components, a set of reference co-ordinates are employed to describe the motion of a selected body reference. Kinetic and strain energies are derived for each element, thus identifying the element mass and stiffness matrices which account for the rotary inertia and shear deformation effects. A new set of time invariant element matrices that describe the coupling between the reference motion and elastic deformations is developed. These matrices need be evaluated only once in advance for the dynamic analysis. It has been, shown that the form of these matrices as well as the mass and stiffness matrices are significantly affected by the inclusion of rotary inertia and shear deformation. The formulation presented in this paper is exemplified by a two-dimensional flexible multibody aircraft. Numerical results indicate that rotary inertia and shear have a significant effect on the dynamic response of large scale flexible multibody systems with large angular rotations and in which the reference motion and elastic deformation are coupled.