New concepts in damping generation and control: theoretical formulation and industrial applications

Abstract

These notes are finalized to a particular study of the damping mechanism in Hamiltonian systems, characterized indeed by the absence of any energy dissipation effect. It is important to make a clear distinction between the two previous concepts, since they seem to be somehow contradictory. A Hamiltonian system is characterized by an invariant total energy (the Hamiltonian H) that is equivalent to state any energy dissipation process is absent. This circumstance, especially from an engineering point of view, leads to the wrong expectation that the motion of any part of such a dissipation-free system, subjected to some initial conditions, maintains a sort of constant amplitude response. This is, although unexpectedly, a wrong prediction and the “mechanical intuition” leads, in this case, to a false belief. It is indeed true the converse: even in the absence of any energy dissipation mechanisms, mechanical systems can exhibit damping, i.e. a decay amplitude motion.