A 2-DOF Model of an Elastic Rocket Structure Under Circulatory Force

Abstract

It is intended, in this paper, to develop a mathematical and numerical model of an elastic space rocket structure as a Beck’s column excited by a follower (or circulatory) force. This force represents the rocket motor thrust that should be always in the direction of the tangent to the structure deformed axis at the base of the vehicle. We present a simplified two degree of freedom rigid bars discrete model. Its system of two second order nonlinear ordinary differential equations of motion are derived via Lagrange’s energy method, allowing for a general understanding of the main characteristics of the problem. The proposed equations consider up to third order (cubic) inertia, stiffness and forcing terms. Among other rich nonlinear dynamic behaviour of this model, depending on parameters and initial conditions choices, either stable or unstable limit cycle post-critical steady state solutions are possible. The latter is a form of flutter. Numerical simulations are carried out using Runge-Kutta’s 4th order algorithm in Matlab environment.