General dynamical equations of motion for elastic body systems

Abstract

A modeling technique capable of determining the time response of a single body (rigid or flexible) that is, in general, undergoing large elastic deformations, coupled with large, nonsteady translational and rotational motions, is presented. 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. The formulation of these equations is 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. 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 also included in the equations of motion. Although discussions here are restricted to a single body, the formulation allows the capability of a general dynamical formalism for handling multibody (rigid or flexible) dynamics.