Relevant bibliographies by topics / Nonlinear sonic vacuum

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Academic literature on the topic 'Nonlinear sonic vacuum'

Author: Grafiati
Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Nonlinear sonic vacuum"

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Sminrov, V. V., and L. I. Manevitch. "Forced oscillations of the string under conditions of ‘sonic vacuum’." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2127 (July 23, 2018): 20170135. http://dx.doi.org/10.1098/rsta.2017.0135.

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We present the results of analytical study of the significant regularities which are inherent to forced nonlinear oscillations of a string with uniformly distributed discrete masses, without its preliminary stretching. It was found recently that a corresponding autonomous system admits a series of nonlinear normal modes with a lot of possible intermodal resonances and that similar synchronized solutions can exist in the presence of a periodic external field also. The paper is devoted to theoretical explanation of numerical data relating to one of possible scenarios of intermodal interaction which was numerically revealed earlier. This is unidirectional energy flow from unstable nonlinear normal mode to nonlinear normal modes with higher wavenumbers under the conditions of sonic vacuum. The mechanism of such a scenario has not yet been clarified contrary to alternative mechanisms consisting in almost simultaneous energy flow to all nonlinear normal modes with breaking the above-mentioned conditions of sonic vacuum. We begin with a description of single-mode manifolds and then show that consideration of arbitrary double mode manifolds is sufficient for solution of the problem. Because of this, the two-modal equations of motion can be reduced to a linear equation which describes a perturbation of initially excited nonlinear normal mode of the forced system in the conditions of sonic vacuum. We have found analytical representation (in the parametric space) of the thresholds for all possible energy transfers corresponding to unidirectional energy flow from unstable nonlinear normal modes. The analytical results are in a good agreement with previous numerical calculations.This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.
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Nesterenko, Vitali F. "Waves in strongly nonlinear discrete systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2127 (July 23, 2018): 20170130. http://dx.doi.org/10.1098/rsta.2017.0130.

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The paper presents the main steps in the development of the strongly nonlinear wave dynamics of discrete systems. The initial motivation was prompted by the challenges in the design of barriers to mitigate high-amplitude compression pulses caused by impact or explosion. But this area poses a fundamental mathematical and physical problem and should be considered as a natural step in developing strongly nonlinear wave dynamics. Strong nonlinearity results in a highly tunable behaviour and allows design of systems with properties ranging from a weakly nonlinear regime, similar to the classical case of the Fermi–Pasta–Ulam lattice, or to a non-classical case of sonic vacuum. Strongly nonlinear systems support periodic waves and one of the fascinating results was a discovery of a strongly nonlinear solitary wave in sonic vacuum (a limiting case of a periodic wave) with properties very different from the Korteweg de Vries solitary wave. Shock-like oscillating and monotonous stationary stress waves can also be supported if the system is dissipative. The paper discusses the main theoretical and experimental results, focusing on travelling waves and possible future developments in the area of strongly nonlinear metamaterials. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.
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Koroleva (Kikot), I. P., L. I. Manevitch, and Alexander F. Vakakis. "Non-stationary resonance dynamics of a nonlinear sonic vacuum with grounding supports." Journal of Sound and Vibration 357 (November 2015): 349–64. http://dx.doi.org/10.1016/j.jsv.2015.07.026.

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Cooke, D. H. "On Prediction of Off-Design Multistage Turbine Pressures by Stodola’s Ellipse." Journal of Engineering for Gas Turbines and Power 107, no. 3 (July 1, 1985): 596–606. http://dx.doi.org/10.1115/1.3239778.

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The variation of extraction pressures with flow to the following stage for high backpressure, multistage turbine designs is highly nonlinear in typical cogeneration applications where the turbine nozzles are not choked. Consequently, the linear method based on Constant Flow Coefficient, which is applicable for uncontrolled expansion with high vacuum exhaust, as is common in utility power cycles, cannot be used to predict extraction pressures at off-design loads. The paper presents schematic examples and brief descriptions of cogeneration designs, with background and theoretical derivation of a more generalized “nozzle analogy” which is applicable in these cases. This method is known as the Law of the Ellipse. It was originally developed experimentally by Stodola and published in English in 1927. The paper shows that the Constant Flow Coefficient method is really a special case of the more generalized Law of the Ellipse. Graphic interpretation of the Law of the Ellipse for controlled and uncontrolled expansions, and variations for sonic choking and reduced number of stages (including single stage) are presented. The derived relations are given in computer codable form, and methods of solution integral with overall heat balance iteration schemes are suggested, with successful practical experience. The pressures predicted by the relations compare favorably with manufacturers’ data on four high-backpressure, cogeneration cycle turbines and three large utility low-pressure ends.
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Pozharskiy, D., Y. Zhang, M. O. Williams, D. M. McFarland, P. G. Kevrekidis, A. F. Vakakis, and I. G. Kevrekidis. "Nonlinear resonances and antiresonances of a forced sonic vacuum." Physical Review E 92, no. 6 (December 23, 2015). http://dx.doi.org/10.1103/physreve.92.063203.

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Kevorkov, S. S., I. P. Koroleva, V. V. Smirnov, and L. I. Manevitch. "Forced Oscillations of the Discrete Membrane Under Conditions of “Sonic Vacuum”." Journal of Applied Mechanics 87, no. 11 (July 27, 2020). http://dx.doi.org/10.1115/1.4047812.

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Abstract This study presents a new analytical model for nonlinear dynamics of a discrete rectangular membrane that is subjected to external harmonic force. It has recently been shown that the corresponding autonomous system admits a series of nonlinear normal modes. In this paper, we describe stationary and non-stationary dynamics on a single mode manifold. We suggest a simple formula for the amplitude-frequency response in both conservative and non-conservative cases and present an analytical expression (in parametric space) for thresholds for all possible bifurcations. Theoretical results obtained through asymptotic approach are confirmed by the experimental data. Experiments on the shaking table show that amplitude-frequency response to external force in a real system matches our theory. Substantial hysteresis is observed in the regimes with increasing and decreasing frequency of external force. The obtained results may be used in designing nonlinear energy sinks.
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Gendelman, O. V., V. Zolotarevskiy, A. V. Savin, L. A. Bergman, and A. F. Vakakis. "Accelerating oscillatory fronts in a nonlinear sonic vacuum with strong nonlocal effects." Physical Review E 93, no. 3 (March 15, 2016). http://dx.doi.org/10.1103/physreve.93.032216.

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Starosvetsky, Y., and Y. Ben-Meir. "Nonstationary regimes of homogeneous Hamiltonian systems in the state of sonic vacuum." Physical Review E 87, no. 6 (June 26, 2013). http://dx.doi.org/10.1103/physreve.87.062919.

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Dissertations / Theses on the topic "Nonlinear sonic vacuum"

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Vakakis, Alexander. "Nonlinear Sonic Vacua." Thesis, NTU "KhPI", 2016. http://repository.kpi.kharkov.ua/handle/KhPI-Press/24954.

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We will present recent results on a special class of dynamical systems designated as nonlinear sonic vacua. These systems are non-linearizable, and have zero speed of sound (in the sense of classical acoustics). Accordingly, their dynamics and acoustics are highly degenerate and tunable with energy, enabling new and highly complex nonlinear phenomena. Two examples of sonic vacua will be discussed. The first is uncompressed ordered granular media, which, depending on their local state, behave either as strongly nonlinear and non-smooth dynamical systems (in the absence of strong local compression), or as almost linear coupled oscillators (under strong local compression, e.g., in the primary fronts of propagating solitary pulses) [1,2]. The second example concerns a spring-mass lattice in the plane. In the small energy limit this seemingly simple system is 'transformed' by geometric nonlinearity to a nonlinear sonic vacuum with surprising properties, such as strong nonlocality (despite o f only next-neighbor interactions in the lattice!), orthogonal nonlinear normal modes, and accelerating propagating fronts [3,4]. Interesting applications of nonlinear sonic vacua will be discussed, including intense energy cascading from low-to-high frequencies and long-to-short wavelengths, resembling “mechanical turbulence ”. We will discuss the implications of these findings on the design of dynamical systems for predictive passive energy management.
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