Systematic closed form modeling of hybrid parameter multiple body systems

Abstract

Presented in this paper is a systematic approach to modeling non-holonomic hybrid parameter multiple body systems. The continuum bodies are represented with the postulates usually associated to the non-linear theories, the Timoshenko (like) beam theories, the higher order plate and shell theories, and the rational theories (e.g. rods) with intrinsic rotary inertia properties. The methodology is an extension of previous work. It is founded in variational principles, but uses vector algebra to eliminate tedium. The variational nature of the methodology allows rigorous equation formulation providing not only the complete non-linear hybrid differential equations, but also the boundary conditions. The methodology is formulated satisfying general non-holonomic constraints; it produces a minimal realization. The spatial dimensions of the continuua are not restricted and the inter-body connections are completely general. To demonstrate the application of the technique, a two-link elastic pendulum or manipulator is modeled. The algorithmic modeling steps are demonstrated. Numerical simulations are presented.