A Simplified Method for Deriving Equations of Motion For Continuous Systems with Flexible Members

Abstract

A method is proposed for deriving dynamical equations for systems with both rigid and flexible components. During the derivation, each flexible component of the system is represented by a "surrogate element" which captures the response characteristics of that component and is easy to mathematically manipulate. The derivation proceeds essentially as if each surrogate element were a rigid body. Application of an extended form of Lagrange's equation yields a set of simultaneous differential equations which can then be transformed to be the exact, partial differential equations for the original flexible system. This method's use facilitates equation generation either by an analyst or through application of software-based symbolic manipulation.