Near-irreversibility in a conservative linear structure with singularity points in its modal density

Abstract

Through two complementary approaches, using modal response and wave propagation, the analyses presented here show the conditions under which a decaying impulse response, or a nearly irreversible energy trapping, takes place in a linear conservative continuous system. The results show that the basic foundation of near-irreversibility or apparent damping rests upon the presence of singularity points in the modal density of dynamic systems or, analogously, in the wave-stopping properties associated with these singularities. To illustrate the concept of apparent damping in detail, a simple undamped beam is modified to introduce a singularity point in its modal density distribution. Simulations show that a suitable application of a compressive axial force to an undamped beam placed on an elastic foundation attenuates its impulse response with time and develops the characteristics of a nearly irreversible energy trap.

How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”

“…Homogenization is also involved in the analysis of dissipation effects in many particle systems in the attempt of describing a finite dimensional system (in which length and time scales may be relevant) through a continuum approximation by the Langevin equation in the context of Brownian motion (see e.g. [15], [18], [20]). In these papers, a perturbation analysis is proposed and a procedure for homogenization in stochastic system is found, based on the use of a special family of probability distributions.…”

Beyond Euler-Cauchy Continua: The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument

“…4, we provide a new proof of the following not very well-known fact in the theory of second-gradient materials: if edge tractions are constitutively presumed null on whatever edge, then the hyperstress takes a very special form whose information content is carried by a vector field. We surmise that inability to develop edge interactions be characteristic of certain second-gradient fluids, an issue that we take up in a forthcoming article [17], continuing a line of thought proposed by Podio-Guidugli [16].…”

Vibration absorption using non-dissipative complex attachments with impacts and parametric stiffness

“…7 the intrinsic properties of attachments are identified, which control the speed of energy sharing between a master and the attachment and the time the energy takes to be transferred back to the master. Several studies examined the conditions that, even in the absence of energy dissipation, prevent energy transport back to the master, which lead to the so called near-irreversibility condition [8][9][10] also confirmed by experimental tests. 11 Finally, the problem of an efficient design of a multi-degrees of freedom tuned-mass-damper has been also considered in the context of control theory.…”