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.
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ABSTRACT: Studies on prototypical systems that consist of a set of complex attachments, coupled to a primary structure characterized by a single degree of freedom system, have shown that vibratory energy can be transported away from the primary through use of complex undamped resonators. Properties and use of these subsystems as by energy absorbers have also been proposed, particularly using attachments that consist of a large set of resonators. These ideas have been originally developed for linear systems and they provided insight into energy sharing phenomenon in large structures like ships, airplanes, and cars, where interior substructures interact with a master structure, e.g., the hull, the fuselage, or the car body. This paper examines the effects of nonlinearities that develop in the attachments, making them even more complex. Specifically, two different nonlinearities are considered: 1 Those generated by impacts that develop among the attached resonators, and 2 parametric effects produced by time-varying stiffness of the resonators. Both the impacts and the parametric effects improve the results obtained using linear oscillators in terms of inhibiting transported energy from returning to the primary structure. The results are indeed comparable with those obtained using linear oscillators but with special frequency distributions, as in the findings of some recent papers by the same authors. Numerically obtained results show how energy is confined among the attached oscillators.The Journal of the Acoustical Society of America 01/2009; 40:2306-2314. · 1.65 Impact Factor
- 8th International Conference on Structural Dynamics, EURODYN 2011, Leuven, Belgium; 01/2011
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ABSTRACT: Navier–Cauchy format for Continuum Mechanics is based on the concept of contact interaction between sub-bodies of a given continuous body. In this paper, it is shown how—by means of the Principle of Virtual Powers—it is possible to generalize Cauchy representation formulas for contact interactions to the case of Nth gradient continua, that is, continua in which the deformation energy depends on the deformation Green–Saint-Venant tensor and all its N − 1 order gradients. In particular, in this paper, the explicit representation formulas to be used in Nth gradient continua to determine contact interactions as functions of the shape of Cauchy cuts are derived. It is therefore shown that (i) these interactions must include edge (i.e., concentrated on curves) and wedge (i.e., concentrated on points) interactions, and (ii) these interactions cannot reduce simply to forces: indeed, the concept of K-forces (generalizing similar concepts introduced by Rivlin, Mindlin, Green, and Germain) is fundamental and unavoidable in the theory of Nth gradient continua.Zeitschrift für angewandte Mathematik und Physik ZAMP 01/2012; 63(6). · 0.94 Impact Factor