The dynamical modelling of elastic multibody systems.

Abstract

A modelling technique is presented for determining the time response of a system of bodies (rigid or flexible) which undergo large elastic deformations, coupled with large nonsteady translational and rotational motions. The derivations of the governing equations of motion are based on Lagrange's form of d'Alembert's principle. The general dynamical equations of motion are expressed in terms of stress and strain tensors, kinematic variables, the velocity and angular velocity coefficients, and generalized forces. These equations are derived systematically. The formulation of the general dynamical equations of motion are discussed in detail. Numerical simulations that involve finite elastic deformations coupled with large nonsteady rotational motions are presented for a beam attached to a rotating base and for the same beam with an end body. Effects such as centrifugal stiffening and softening, membrane strain effect, and vibrations induced by Coriolis forces are accommodated. The effects of rotary inertia as well as shear deformation are included in the equations of motion. These simulations demonstrate the capability of the general dynamical formalism in handling multibody (rigid or flexible) dynamics. An efficient recursive formulation of multibody dynamics is derived, based on the general dynamical equations of motion, which, in turn, are obtained from Lagrange's form of d'Alembert's principle. The efficiency derives from recurrence relations of the (angular) velocity coefficients, (angular) velocities, (angular) accelerations, and generalized forces. Kinematic relations between contiguous bodies that are connected by revolute or prismatic joints are defined by relative joint coordinates. Intermediate reference frames are introduced for convenience in defining various joint displacements between the interconnected deformed bodies. In this thesis, we restrict the discussion to open-loop kinematic chains, composed of bodies connected by joints. A beam rigidly attached at its outer end to a rotating base is studied to illustrate this recursive formulation.