Modelling and resonance of a flexible rod using a floating reference frame

A direct variational approach with a floating frame is presented to derive the ordinary differential equations of motion of a flexible rod, constant crank speed slider-crank mechanism. Potential energy terms contained in the derivation include beam-bending energy and energy in foreshortening of the rod tip (which were selected because of the importance of these terms in a pinned-pinned rod parametric resonance). A symbolic manipulator code is used to reduce the constrained equations of motion to unconstrained nonlinear equations. A linearized version of these equations is used to explore parametric resonance stability-instability zones by a monodromy matrix technique.