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: In this paper we examine the conditions that influence the return time, the time it takes before energy returns from a set of satellite oscillators attached to a primary structure. Two methods are presented to estimate the return time. One estimate is based on an analysis of the reaction force on a rigid base by a finite number of oscillators as compared with an infinite number of continuously distributed oscillators. The result gives a lower-bound estimate for the return time. A more accurate estimation results from considering the dynamic behavior of a set of oscillators as waves in a waveguide. Such an analogy explains energy flow between a primary structure and the oscillators in terms of pseudowaves and shows that a nonlinear frequency distribution of the oscillators leads to pseudodispersive waves. The resulting approximate expressions show the influence of the natural frequency distribution within the set of oscillators, and of their number, on the return time as compared with the asymptotic case of a continuous set with infinite oscillators. In the paper we also introduce a new method based on a Hilbert envelope to estimate the apparent damping loss factor of the primary structure during the return time considering transient energy flow from the primary structure before any energy reflects back from the attached oscillators. The expressions developed for return time and damping factor show close agreement with direct numerical simulations. The paper concludes with a discussion of the return time and its relation to apparent damping and optimum frequency distribution within a set of oscillators that maximize these quantities.The Journal of the Acoustical Society of America 03/2004; 115(2):683-96. · 1.65 Impact Factor
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ABSTRACT: Dissipation in solids describes conversion of kinetic energy to thermal energy. Heat capacity of a solid relates to the kinetic energy of the oscillations of its atoms with the assumption that they are in thermal equilibrium. Previous studies investigated criteria related to thermal relaxation, the process by which thermal equilibrium is established. They examined conditions for irreversible distribution of energy among the modes of a nonlinear periodic structure that represents atoms in a solid. These studies all point to the chaotic behavior of a freely vibrating nonlinear lattice as the kernel of the problem in addressing thermal relaxation. This paper extends the results of previous studies on thermalization to modeling of dissipation as energy absorption that takes place during forced vibration of particles in a nonlinear lattice. Results show that dissipation and chaotic behavior of the particles develop simultaneously. Such behavior develops when the forcing frequency falls within a resonance band. The results also support the argument that for a real solid, both in terms of size and complexity, resonance bands overlap significantly broadening the frequency range within which dissipation takes place.The Journal of the Acoustical Society of America 08/2000; 108(1):184-91. · 1.65 Impact Factor
- Journal of Vibration and Acoustics. 01/1995; 117.