A note on nonlinear oscillations at resonance

1987 ◽  
Vol 3 (4) ◽  
pp. 351-361 ◽  
Author(s):  
Pierpaolo Omari ◽  
Fabio Zanolin
Keyword(s):  
Nonlinear Oscillations ◽  
At Resonance

Nonlinear oscillations of aerosol in shock-wave flow in open tube

2012 ◽  
Vol 9 (1) ◽  
pp. 150-153
Author(s):  
L.A. Tkachenko
Keyword(s):  
Nonlinear Oscillations ◽  
Excitation Amplitude ◽  
Wave Mode ◽  
Wave Flow ◽  
Open Tube ◽  
At Resonance ◽  
Clearing Time ◽  
Surrounding Space ◽  
Greater Curvature ◽  
Numerical Concentration

Nonlinear oscillations of aerosol in open tube in shock-free wave mode at resonance at various amplitudes of excitation are experimentally investigated. Pressure diagrams are continuous. With an increase in the excitation amplitude, the amplitude of the pressure oscillations of the medium increases. At large amplitudes, the oscillation form is close to harmonic. The numerical concentration of aerosol droplets decreases monotonically with time. This is due to the coagulation of the aerosol, which consists in the coalescence of droplets and their sedimentation on the walls of the tube, as well as the emission of the aerosol into the surrounding space. With an increase in the excitation amplitude, the dependences acquire greater curvature and the aerosol clearing time decreases. At the same time, the aerosol clearing time is 5-10 times lower than in the case of natural sedimentation.

MULTIPLE-SCALE AND NUMERICAL ANALYSES FOR THE NONLINEAR OSCILLATIONS OF A GAS BUBBLE SURROUNDED BY A MAXWELL'S FLUID

2019 ◽  
Vol 46 (3) ◽  
pp. 261-275
Author(s):  
César Yepes ◽  
Jorge Naude ◽  
Federico Mendez ◽  
Margarita Navarrete ◽  
Fátima Moumtadi
Keyword(s):  
Nonlinear Oscillations ◽  
Multiple Scale ◽  
Numerical Analyses ◽  
Gas Bubble

On the solvability of the degenerate Noetherian difference-algebraic boundary value problem

2019 ◽  
Vol 33 ◽  
pp. 204-217
Author(s):  
Sergei Chuiko ◽  
Yaroslav Kalinichenko ◽  
Nikita Popov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Difference Equations ◽  
Nonlinear Oscillations ◽  
Bounded Operator ◽  
Boundary Value ◽  
Homogeneous Part ◽  
Solvability Conditions ◽  
Engineering Control ◽  
Generalized Green Operator

The original conditions of solvability and the scheme of finding solutions of a linear Noetherian difference-algebraic boundary-value problem are proposed in the article, while the technique of pseudoinversion of matrices by Moore-Penrose is substantially used. The problem posed in the article continues to study the conditions for solvability of linear Noetherian boundary value problems given in the monographs of A.M. Samoilenko, A.V. Azbelev, V.P. Maximov, L.F. Rakhmatullina and A.A. Boichuk. The study of differential-algebraic boundary-value problems is closely related to the investigation of boundary-value problems for difference equations, initiated in the works of A.A. Markov, S.N. Bernstein, Y.S. Bezikovych, O.O. Gelfond, S.L. Sobolev, V.S. Ryabenkyi, V.B. Demidovych, A. Halanai, G.I. Marchuk, A.A. Samarskyi, Yu.A. Mytropolskyi, D.I. Martyniuk, G.M. Vainiko, A.M. Samoilenko and A.A. Boichuk. On the other hand, the study of boundary-value problems for difference equations is related to the study of differential-algebraic boundary-value problems initiated in the papers of K. Weierstrass, N.N. Lusin and F.R. Gantmacher. Systematic study of differential-algebraic boundary value problems is devoted to the works of S. Campbell, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, N.A. Perestiyk, V.P. Yakovets, A.A. Boichuk, A. Ilchmann and T. Reis. The study of differential-algebraic boundary value problems is also associated with numerous applications of such problems in the theory of nonlinear oscillations, in mechanics, biology, radio engineering, control theory, motion stability theory. The general case of a linear bounded operator corresponding to the homogeneous part of a linear Noetherian difference-algebraic boundary value problem has no inverse is investigated. The generalized Green operator of a linear difference-algebraic boundary value problem is constructed in the article. The relevance of the study of solvability conditions, as well as finding solutions of linear Noetherian difference-algebraic boundary-value problems, is associated with the widespread use of difference-algebraic boundary-value problems obtained by linearizing nonlinear Noetherian boundary-value problems for systems of ordinary differential and difference equations. Solvability conditions are proposed, as well as the scheme of finding solutions of linear Noetherian difference-algebraic boundary value problems are illustrated in detail in the examples.

Nonlinear Oscillations of a Chain of Masses in a Liquid

2020 ◽  
Vol 65 (7) ◽  
pp. 238-241
Author(s):  
O. V. Rudenko
Keyword(s):  
Nonlinear Oscillations ◽  
A Chain

scholarly journals Simulation of 2-Coil and 4-Coil Magnetic Resonance Wearable WPT Systems

Proceedings ◽  
2021 ◽  
Vol 68 (1) ◽  
pp. 13
Author(s):  
Yixuan Sun ◽  
Stephen Beeby
Keyword(s):  
Power Efficiency ◽  
Power Transmission ◽  
Rotation Angle ◽  
Wireless Power ◽  
Peak Efficiency ◽  
Frequency Splitting ◽  
At Resonance ◽  
Higher Power ◽  
The Impact ◽  
Proper Frequency

This paper presents the COMSOL simulations of magnetically coupled resonant wireless power transfer (WPT), using simplified coil models for embroidered planar two-coil and four-coil systems. The power transmission of both systems is studied and compared by varying the separation, rotation angle and misalignment distance at resonance (5 MHz). The frequency splitting occurs at short separations from both the two-coil and four-coil systems, resulting in lower power transmission. Therefore, the systems are driven from 4 MHz to 6 MHz to analyze the impact of frequency splitting at close separations. The results show that both systems had a peak efficiency over 90% after tuning to the proper frequency to overcome the frequency splitting phenomenon at close separations below 10 cm. The four-coil design achieved higher power efficiency at separations over 10 cm. The power efficiency of both systems decreased linearly when the axial misalignment was over 4 cm or the misalignment angle between receiver and transmitter was over 45 degrees.

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