Remarks on optimization of impact damping for a non-ideal and nonlinear structural system

Abstract

It is intended, in this work, to present some research results on the optimization of an impact damper for a structural system excited by a non-ideal power source. In the model, the impact vibration absorber is, basically, a small free mass inside a box carved in the structure that undergoes undamped linear motions colliding against the walls of the box. Whenever the mass shocks against the walls of the box, an exchange of kinetic energy between the mass and the structure may be used to control the amplitude of the dynamic response of the structure. In this work, the structure is excited by a non-ideal power source, a DC electric motor installed on it, which may present the Sommerfeld effect. A non-ideal power source is one that interacts with the motion of the structure as opposed to an ideal source whose amplitude and frequency are fixed, independent of the displacements of the structure. Here, the dynamic response of the system is computed using step-by-step numerical integration of the equations of motion derived via a Lagrangian formulation. The optimization problem is defined considering as the objective function the maximum amplitude of the structure displacement, while the design variables are the weight of the free mass and the width of the carved box. Using the augmented Lagrangian method, several optimization problems are formulated, and, solving them, the best design to maximize the efficiency of the impact damper is obtained.