Results 11 to 20 of about 3,607 (229)
An instrumental insight for a periodic solution of a fractal Mathieu–Duffing equation
Journal of Low Frequency Noise, Vibration and Active Control, 2023 The primary goal of the present study is to investigate how to obtain a periodic solution for a fractal Mathieu–Duffing oscillator. To achieve this, the fractal oscillator in the fractal space has been transformed into a damping Mathieu–Duffing equation ...
Yusry O El-Dib +2 more
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Computable solution of fractional kinetic equations using Mathieu-type series
Advances in Difference Equations, 2019 The Mathieu series appeared in the study of elasticity of solid bodies in the work of Émile Leonard Mathieu. Since then numerous authors have studied various problems arising from the Mathieu series in several diverse ways.
Owais Khan +3 more
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CHARTS STRUTT-INCE FOR GENERALIZED MATHIEU EQUATION [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2012 We have investigated the solution of the generalized Mathieu equation. With the aid of diagrams Stratton-Ince built the instability region, the condition can occur when the parametric resonance.
R.I. Parovik
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On the solutions of the Mathieu’s equation [PDF]
Vietnam Journal of Mechanics, 2008 As shown in [1] solutions of the Mathieu’s equation were classified on three fundamental kinds depending mainly on its parameters. These solutions were constructed in the form of infinite series. This paper presents a new approach in which approximated analytical solutions of the Mathieu’s equation are constructed in the finite form.
Dao Huy Bich +2 more
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On a fine localization of the Mathieu azimuthal numbers by Cassini ovals
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 The study is devoted to numerical and analytical problems concerning generating periodic and antiperiodic solutions of the angular (circumferential) Mathieu equation obtained for the circumferential harmonics of an elliptic cylinder.
Yuri Nikolaevich Radayev +1 more
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Numerical solution of fractional Mathieu equations by using block-pulse wavelets
Journal of Ocean Engineering and Science, 2019 In this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases.
P. Pirmohabbati +3 more
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WKB and resurgence in the Mathieu equation [PDF]
, 2017 In this paper, based on lectures by the authors at the May 2015 workshop {\it Resurgence, Physics and Numbers}, at the Centro di Ricerca Matematica Ennio De Giorgio of the Scuola Normale Superiore in Pisa, we explain the origin of resurgent trans-series in the Mathieu equation spectral problem, using uniform WKB and all-orders (exact) WKB.
Dunne, Gerald V., Unsal, Mithat
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The damped Mathieu equation [PDF]
Quarterly of Applied Mathematics, 1993 We establish an asymptotic lower bound for the minimum excitation needed to cause instability for the damped Mathieu equation. The methods used are Floquet theory and Liapunov-Schmidt, and we use a fact about the width of the instability interval for the undamped Mathieu equation. Our results are compared with published numerical data.
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Sensors, 2017 Vibration frequencies and modes for the thickness-shear vibrations of infinite partially-electroded circular AT-cut quartz plates are obtained by solving the two-dimensional (2D) scalar differential equation derived by Tiersten and Smythe.
Bin Wang +3 more
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Transverse oscillation of particles in the vicinity of resonances for a cyclotron
Physical Review Accelerators and Beams, 2019 Transverse oscillation is an important issue in beam dynamics of cyclotrons and can be described by the Mathieu equation. We review the standard form of the Mathieu equation, d^{2}u/dθ^{2}+(δ+ϵ·cos2θ)u=0, and propose a modification of the method of ...
Kai Zhou +4 more
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