Browsing by Subject "Frequency distributions"

Now showing 1 - 3 of 3

Open Access
Energy equipartition and frequency distribution in complex attachments
(Acoustical Society of America, 2009) Roveri, N.; Carcaterra, A.; Akay, A.
As reported in several recent publications, an undamped simple oscillator with a complex attachment that consists of a set of undamped parallel resonators can exhibit unusual energy sharing properties. The conservative set of oscillators of the attachment can absorb nearly all the impulsive energy applied to the primary oscillator to which it is connected. The key factor in the ability of the attachment to absorb energy with near irreversibility correlates with the natural frequency distribution of the resonators within it. The reported results also show that a family of optimal frequency distributions can be determined on the basis of a variational approach, minimizing a certain functional related to the system response. The present paper establishes a link between these optimal frequency distributions and the energy equipartition principle: optimal frequency distributions are those that spread the injected energy as uniformly as possible over the degrees of freedom or over the modes of the system. Theoretical as well as numerical results presented support this point of view. © 2009 Acoustical Society of America.
Open Access
Uncertainty and dissipation
(Katholieke Universiteit Leuven, 2012-09) Carcaterra, A.; Akay, Adnan
This paper discusses the question of the energy confinement in mechanical structures in the light of the uncertainties affecting the natural frequencies of the system. More precisely, recent studies have shown that energy can be introduced to a linear system with near irreversibility, or energy within a system can migrate to a subsystem nearly irreversibly, even in the absence of dissipation, provided that the system has a particular natural frequency distribution. In this paper, the case of uncertainties in the system's natural frequencies is discussed and a remarkable statistical property of the natural frequency is derived for permanent energy confinement within a part of the system. The results demonstrate the existence of a special class of linear non-dissipative dynamic systems that exhibit nearly-irreversible energy confinement (IEC) if they satisfy a minimum-variance-response (MIVAR) property. In this case, if the probability density function of the natural frequencies has a special distribution, the conservative system shows an unexpected decaying impulse response. © (2012) by the Katholieke Universiteit Leuven Department of Mechanical Engineering All rights reserved.
Open Access
Vibration absorption using non-dissipative complex attachments with impacts and parametric stiffness
(Acoustical Society of America, 2009) Roveri, N.; Carcaterra, A.; Akay, A.
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. © 2009 Acoustical Society of America.