Relevant bibliographies by topics / Mathieu stability diagram

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  1. Journal articles
  2. Dissertations / Theses
  3. Conference papers

Academic literature on the topic 'Mathieu stability diagram'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 February 2022

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Journal articles on the topic "Mathieu stability diagram"

1

Kidambi, R. "Inviscid Faraday waves in a brimful circular cylinder." Journal of Fluid Mechanics 724 (May 8, 2013): 671–94. http://dx.doi.org/10.1017/jfm.2013.178.

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AbstractWe study inviscid Faraday waves in a brimful circular cylinder with pinned contact line. The pinning leads to a coupling of the Bessel modes and leads to an infinite system of coupled Mathieu equations. For large Bond numbers, even though the stability diagrams and the subharmonic and harmonic resonances for the free and pinned contact lines are similar, the free surface shapes can be quite different. With decreasing Bond number, not only are the harmonic and subharmonic resonances very different from the free contact line case but also interesting changes in the stability diagram occu
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Azimi, Mohsen. "Parametric Frequency Analysis of Mathieu–Duffing Equation." International Journal of Bifurcation and Chaos 31, no. 12 (2021): 2150181. http://dx.doi.org/10.1142/s0218127421501819.

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The classic linear Mathieu equation is one of the archetypical differential equations which has been studied frequently by employing different analytical and numerical methods. The Mathieu equation with cubic nonlinear term, also known as Mathieu–Duffing equation, is one of the many extensions of the classic Mathieu equation. Nonlinear characteristics of such equation have been investigated in many papers. Specifically, the method of multiple scale has been used to demonstrate the pitchfork bifurcation associated with stability change around the first unstable tongue and Lie transform has been
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Butikov, Eugene I. "Analytical expressions for stability regions in the Ince–Strutt diagram of Mathieu equation." American Journal of Physics 86, no. 4 (2018): 257–67. http://dx.doi.org/10.1119/1.5021895.

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Orszaghova, J., H. Wolgamot, S. Draper, P. H. Taylor, and A. Rafiee. "Onset and limiting amplitude of yaw instability of a submerged three-tethered buoy." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2235 (2020): 20190762. http://dx.doi.org/10.1098/rspa.2019.0762.

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In this paper the dynamics of a submerged axi-symmetric wave energy converter are studied, through mathematical models and wave basin experiments. The device is disk-shaped and taut-moored via three inclined tethers which also act as a power take-off. We focus on parasitic yaw motion, which is excited parametrically due to coupling with heave. Assuming linear hydrodynamics throughout, but considering both linear and nonlinear tether geometry, governing equations are derived in 6 degrees of freedom (DOF). From the linearized equations, all motions, apart from yaw, are shown to be contributing t
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Li, Q. M., and M. X. Shi. "Intermittent transformation between radial breathing and flexural vibration modes in a single-walled carbon nanotube." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2096 (2008): 1941–53. http://dx.doi.org/10.1098/rspa.2007.0253.

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Based on an equivalent continuum cylindrical shell model, we have predicted the intermittent transformation between radial breathing and flexural vibration modes in a single-walled carbon nanotube. It is found that the radial breathing and flexural vibration modes may appear intermittently, in certain circumstances, when the dominant parameters of the problem are in the instable region of the Mathieu stability diagram. The coupled nonlinear differential equations of the radial breathing and the flexural vibration modes are presented to a fourth-order approximation, which is then solved using a
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Shi, M. X., Q. M. Li, and Y. Huang. "Internal resonance of vibrational modes in single-walled carbon nanotubes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2110 (2009): 3069–82. http://dx.doi.org/10.1098/rspa.2009.0147.

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We show, by molecular dynamics simulations, that 2:1 internal resonance may occur between a radial breathing mode (RBM) and a circumferential flexural mode (CFM) in single-walled carbon nanotubes (SWCNTs). When the RBM vibration amplitude is greater than a critical value, automatic transformations between the RBM and CFM with approximately half RBM-frequency are observed. This discovery in the discrete SWCNT atom assembly is similar to the 2:1 internal resonance mechanism observed in continuum shells. A non-local continuum shell model is employed to determine the critical conditions for the oc
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Orszaghova, J., H. Wolgamot, S. Draper, R. Eatock Taylor, P. H. Taylor, and and A. Rafiee. "Transverse motion instability of a submerged moored buoy." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2221 (2019): 20180459. http://dx.doi.org/10.1098/rspa.2018.0459.

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Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonline
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Hiroki, Seiji, Tetsuya Abe, and Yoshio Murakami. "Separation of helium and deuterium peaks with a quadrupole mass spectrometer by using the second stability zone in the Mathieu diagram." Review of Scientific Instruments 63, no. 8 (1992): 3874–76. http://dx.doi.org/10.1063/1.1143286.

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Белоусова, Елена Петровна. "OPTIMIZATION OF ULTRASOUND MEDICAL PARAMETERS TOOLS." СИСТЕМНЫЙ АНАЛИЗ И УПРАВЛЕНИЕ В БИОМЕДИЦИНСКИХ СИСТЕМАХ, no. 1 (April 19, 2021): 147–54. http://dx.doi.org/10.36622/vstu.2021.20.1.020.

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Для многих видов медицинских вмешательств требуется применение ультразвуковых инструментов с различными характеристиками. Используются инструменты, совершающие продольные колебания, значительно реже - инструменты с изгибами и крутильными колебаниями, либо достаточно длинные ультразвуковые медицинские инструменты, либо короткие, но тонкие. В таких инструментах часто наблюдается так называемая динамическая потеря устойчивости, когда прямолинейный инструмент, совершающий продольные колебания, внезапно начинает совершать изгибные колебания, амплитуда которых бывает настолько высока, что приводит к
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WRIGHT, JEFF, STEVE YON, and C. POZRIKIDIS. "Numerical studies of two-dimensional Faraday oscillations of inviscid fluids." Journal of Fluid Mechanics 402 (January 10, 2000): 1–32. http://dx.doi.org/10.1017/s0022112099006631.

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The dynamics of two-dimensional standing periodic waves at the interface between two inviscid fluids with different densities, subject to monochromatic oscillations normal to the unperturbed interface, is studied under normal- and low-gravity conditions. The motion is simulated over an extended period of time, or up to the point where the interface intersects itself or the curvature becomes very large, using two numerical methods: a boundary-integral method that is applicable when the density of one fluid is negligible compared to that of the other, and a vortex-sheet method that is applicable
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Dissertations / Theses on the topic "Mathieu stability diagram"

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Pothula, Sunil George. "Dynamic Response of Composite Cylindrical Shells Under External Impulsive Loads." University of Akron / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1248097987.

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Vernier, Arnaud. "Développement instrumental en spectrométrie de masse pour le diagnostic in vitro en microbiologie clinique." Phd thesis, Université Claude Bernard - Lyon I, 2014. http://tel.archives-ouvertes.fr/tel-00986856.

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La spectrométrie de masse, en particulier le couplage HPLC/MRM3, est un outil bien adapté au diagnostic in vitro, particulièrement en microbiologie clinique. L'utilisation en routine de cette technologie est cependant tributaire de sa sensibilité et de sa spécificité. Ce travail de thèse a pour objectif d'étudier la possibilité d'éjecter et de détecter simultanément et de façon sélective des ions de ratio masse/charge donnés, ceux-ci étant confinés dans un piège ionique quadrupolaire. Cette approche permet de supprimer les étapes de balayage en masse et d'intégration mathématique du signal en
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Conference papers on the topic "Mathieu stability diagram"

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Mamontov, Eugenie V., Roman N. Dyatlov, Alexander A. Dvagilev, and Olga V. Melnik. "The Modeling of Ion Oscillations in Rapidly Oscillating Quadrupole Fields when Crossing the Mathieu Diagram Stability Boundaries." In 2021 10th Mediterranean Conference on Embedded Computing (MECO). IEEE, 2021. http://dx.doi.org/10.1109/meco52532.2021.9460205.

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Osada, Reiko, and Chikara Sato. "Stabilization of Inverted Coupled Pendula Using Parametric Excitation." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4008.

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Abstract Parametric stabilization of a single inverted pendulum has been extensively studied using the Mathieu equation and its corresponding stability diagram. The inverted single pendulum may be stabilized using parametric excitation at a specified frequency and amplitude given by a narrow stable region in the Mathieu diagram. Coupled pendula with parametric excitation or corresponding resonant systems have been studied from mathematical view point (Cesari, 1959; Gambill, 1955; Richards, 1983), from electrical view point (Sato, 1962a; Sato, 1962b; Sato, 1971; Sato, 1975) and from mechanical
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Tweten, Dennis J., Genevieve M. Lipp, Firas A. Khasawneh, and Brian P. Mann. "Comparative Study of Semi-Analytical Methods for the Stability Analysis of Delay Differential Equations." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47519.

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This paper describes and compares the zeroth-order semi-discretization, spectral element, and Legendre collocation methods. Each method is a technique for solving delay differential equations (DDEs) as well as determining regions of stability in the DDE parameter space. We present the necessary concepts, assumptions, and equations required to implement each method. To compare the relative performance between the methods, the convergence rate achieved and computing time required by each method are determined in two numerical studies consisting of a ship stability example and the delayed damped
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4

Sharma, Ashu, and Subhash C. Sinha. "An Approximate Analysis of Quasi-Periodic Systems via Floquét Theory." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-68041.

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Parametrically excited systems are generally represented by a set of linear/nonlinear ordinary differential equations with time varying coefficients. In most cases, the linear systems have been modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquét theory. However, in many cases the parametric excitation is not periodic but consists of frequencies that are incommensurate, making them quasi-periodic. Unfortunately, there is no complete theory for linear dynamic systems with quasi-periodic coefficients. Motivated by this fac
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Gavassoni, Elvidio, Paulo Batista Gonçalves, and Deane M. Roehl. "Nonlinear Dynamics of a Spar Platform." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70384.

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Spar floating platforms have been largely used for deep water drilling, oil and natural gas production and storage of these fluids. In extreme weather conditions such structures may exhibit a highly nonlinear dynamic behavior. In this paper a 2-DOF model is used to study the heave and pitch coupled response in free and forced vibration. Special attention is given to the determination of the nonlinear vibration modes (NNMs). Non-similar and similar NNMs are obtained analytically by direct application of asymptotic methods and the results show important NNM features such as instability and multi
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