Relevant bibliographies by topics / Duffing Oscillator

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  2. Dissertations / Theses
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Academic literature on the topic 'Duffing Oscillator'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 July 2024

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Journal articles on the topic "Duffing Oscillator"

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Fu, Yongqing, Yanan Li, Lin Zhang, and Xingyuan Li. "The DPSK Signal Noncoherent Demodulation Receiver Based on the Duffing Oscillators Array." International Journal of Bifurcation and Chaos 26, no. 13 (December 15, 2016): 1650216. http://dx.doi.org/10.1142/s0218127416502163.

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Chaotic communication requires the knowledge of corresponding phase relationship between the primary phase of Duffing oscillator’s internal driving force and the primary phase of the undetected signal. Currently, there is no method of noncoherent demodulation for DPSK (Differential Phase Shift Keying) signal and mobile communication signal by Duffing oscillator. To solve this problem, this study presents a noncoherent demodulation method based on the Duffing oscillators array and Duffing oscillator optimization. We first present the model of Duffing oscillator and its sensitivity to undetected signal primary phase. Then the zone partition is proposed to identify the Duffing oscillator’s phase trajectory, and subsequently, the mathematical model and implementation method of the Duffing oscillators array are outlined. Thirdly, the Duffing oscillator optimization and its adaptive strobe technique are proposed, also their application to DPSK signal noncoherent demodulation are discussed. Finally, the design of new concept DPSK chaotic digital receiver based on the Duffing oscillators array is presented, together with its simulation results obtained by using SystemView simulation platform. The simulation results suggest that the new concept receiver based on the Duffing oscillator optimization of Duffing oscillators array owns better SNR (signal-to-noise ratio) threshold property than typical existing receivers (chaotic or nonchaotic) in the AWGN (additive white Gaussian noise) channel and multipath Rayleigh fading channel. In addition, the new concept receiver may detect mobile communication signal.
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LUO, ALBERT C. J., and JIANZHE HUANG. "ASYMMETRIC PERIODIC MOTIONS WITH CHAOS IN A SOFTENING DUFFING OSCILLATOR." International Journal of Bifurcation and Chaos 23, no. 05 (May 2013): 1350086. http://dx.doi.org/10.1142/s0218127413500867.

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In this paper, asymmetric periodic motions in a periodically forced, softening Duffing oscillator are presented analytically through the generalized harmonic balance method. For the softening Duffing oscillator, the symmetric periodic motions with jumping phenomena were understood very well. However, asymmetric periodic motions in the softening Duffing oscillators are not investigated analytically yet, and such asymmetric periodic motions possess much richer dynamics than the symmetric motions in the softening Duffing oscillator. For asymmetric motions, the bifurcation tree from asymmetric period-1 motions to chaos is discussed comprehensively. The corresponding, unstable and stable, asymmetric and symmetric, periodic motions in the softening Duffing oscillator are presented, and numerical illustrations of stable and unstable periodic motions are completed. This investigation provides a better picture of complex motion in the softening Duffing oscillator.
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Cintra, Daniel, and Pierre Argoul. "Nonlinear argumental oscillators: A few examples of modulation via spatial position." Journal of Vibration and Control 23, no. 18 (January 22, 2016): 2888–911. http://dx.doi.org/10.1177/1077546315623888.

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Under certain conditions, an oscillator can enter a stable regime when submitted to an external harmonic force whose frequency is far from the natural frequency of the oscillator. This may happen when the external force acts on the oscillator in a way which depends on the oscillator's spatial position. This phenomenon is called “argumental oscillation”. In this paper, six argumental oscillators are described and modeled, and experimental results are given and compared to numerical simulations based on the models. A polar Van der Pol representation, with embedded time indications, is used to allow a precise comparison. The pendulums are modeled as Duffing oscillators. The six models are based on various pendulums excited by spatially localized magnetic-field sources consisting of wire coils. Each pendulum receives the excitation via a steel element, or a permanent magnet, fitted at the tip of the pendulum's rod. The spatial localization induces another nonlinearity besides the Duffing nonlinearity. A control system allowing a real-time Van der Pol representation of the motion is presented. Attractors are brought out from experimental results.
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Chen, Ting, Xiangyu Cao, and Dezhi Niu. "Model modification and feature study of Duffing oscillator." Journal of Low Frequency Noise, Vibration and Active Control 41, no. 1 (October 6, 2021): 230–43. http://dx.doi.org/10.1177/14613484211032760.

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With the development of chaos theory, Duffing oscillator has been extensively studied in many fields, especially in electronic signal processing. As a nonlinear oscillator, Duffing oscillator is more complicated in terms of equations or circuit analysis. In order to facilitate the analysis of its characteristics, the study analyzes the circuit from the perspective of vibrational science and energetics. The classic Holmes-Duffing model is first modified to make it more popular and concise, and then the model feasibility is confirmed by a series of rigorous derivations. According to experiments, the influence of driving force amplitude, frequency, and initial value on the system is finally explained by the basic theories of physics. Through this work, people can understand the mechanisms and characteristics of Duffing oscillator more intuitively and comprehensively. It provides a new idea for the study of Duffing oscillators and more.
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Kanamaru, Takashi. "Duffing oscillator." Scholarpedia 3, no. 3 (2008): 6327. http://dx.doi.org/10.4249/scholarpedia.6327.

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Alhejaili, Weaam, Alvaro H. Salas, and Samir A. El-Tantawy. "Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators." Mathematics 11, no. 9 (April 24, 2023): 2007. http://dx.doi.org/10.3390/math11092007.

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In this study, both the ansatz and averaging methods are carried out for analyzing the complex Duffing oscillators including the undamped/conserved complex Duffing oscillator (CDO) and the damped/unconserved CDO to obtain some approximate analytical solutions. To analyze the conserved CDO, it is reduced to two decoupled conserved Duffing oscillators. After that, the exact solution of the conserved Duffing oscillator is employed to derive an approximation of the conserved CDO in terms of the Jacobi elliptic function. To analyze the damped CDO, two methodologies are considered. For the first methodology, the damped CDO is reduced to two decoupled damped Duffing oscillators, and the ansatz method is devoted to analyzing the damped Duffing oscillator. Accordingly, an approximation of the damped CDO in terms of trigonometric functions is obtained. In the second methodology, the averaging method is applied directly to the damped CDO to derive an approximation in terms of trigonometric functions. All the obtained solutions are compared with the fourth-order Runge–Kutta (RK4) numerical approximations. This study may help many researchers interested in the field of plasma physics to interpret their laboratory and observations results.
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Karimov, Timur, Olga Druzhina, Valerii Vatnik, Ekaterina Ivanova, Maksim Kulagin, Veronika Ponomareva, Anzhelika Voroshilova, and Vyacheslav Rybin. "Sensitivity Optimization and Experimental Study of the Long-Range Metal Detector Based on Chaotic Duffing Oscillator." Sensors 22, no. 14 (July 12, 2022): 5212. http://dx.doi.org/10.3390/s22145212.

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Sensors based on chaotic oscillators have a simple design, combined with high sensitivity and energy efficiency. Among many developed schemes of such sensors, the promising one is based on the Duffing oscillator, which possesses a remarkable property of demonstrating chaotic oscillations only in the presence of a weak sine wave at the input. The main goal of this research was to evaluate the maximal sensitivity of a practically implemented metal detector based on the Duffing oscillator and compare its sensitivity with conventional sensors. To achieve high efficiency of the Duffing-based design, we proposed an algorithm which performs a bifurcation analysis of any chaotic system, classifies the oscillation modes and determines the system sensitivity to a change in different parameters. We apply the developed algorithm to improve the sensitivity of the electronic circuit implementing the Duffing oscillator, serving as a key part of a three-coil metal detector. We show that the developed design allows detecting the presence of metal objects near the coils more reliably than the conventional signal analysis techniques, and the developed detector is capable of sensing a large metal plate at distances up to 2.8 of the coil diameter, which can be considered a state-of-the-art result.
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Kim, Valentine, and Roman Parovik. "Mathematical Model of Fractional Duffing Oscillator with Variable Memory." Mathematics 8, no. 11 (November 19, 2020): 2063. http://dx.doi.org/10.3390/math8112063.

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The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann–Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the fractional derivative of the Riemann–Liouville type by a discrete analog—the fractional derivative of Grunwald–Letnikov. The adequacy of the numerical scheme is verified using specific examples. Using a numerical algorithm, oscillograms and phase trajectories are constructed depending on the values of the model parameters. Chaotic regimes of the Duffing fractional oscillator are investigated using the Wolf–Bennetin algorithm. The forced oscillations of the Duffing fractional oscillator are investigated using the harmonic balance method. Analytical formulas for the amplitude-frequency, phase-frequency characteristics, and also the quality factor are obtained. It is shown that the fractional Duffing oscillator possesses different modes: regular, chaotic, multi-periodic. The relationship between the order of the fractional derivative and the quality factor of the oscillatory system is established.
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Wang, Ke, Xiaopeng Yan, Zhiqiang Zhu, Xinhong Hao, Ping Li, and Qian Yang. "Blind Estimation Methods for BPSK Signal Based on Duffing Oscillator." Sensors 20, no. 22 (November 10, 2020): 6412. http://dx.doi.org/10.3390/s20226412.

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To realize the blind estimation of binary phase shift keying (BPSK) signal, this paper describe a new relational expression among the state of Duffing oscillator excited by BPSK signal, the pseudo-random code of BPSK signal, and the difference frequency between the to-be-detect signal and internal drive force signal of Duffing oscillator. Two output characteristics of Duffing oscillators excited by BPSK signals named implied periodicity and pilot frequency array synchronization are presented according to the different chaotic states of Duffing oscillator. Then two blind estimation methods for the carrier frequency and pseudo-random sequence of the BPSK signal are proposed based on these two characteristics, respectively. These methods are shown to have a significant effect on the parameter estimation of BPSK signals with no prior knowledge, even at very low signal-to-noise ratios (SNRs).
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Krok, Kamila A., Artur P. Durajski, and Radosław Szczȩśniak. "The Abraham–Lorentz force and the time evolution of a chaotic system: The case of charged classical and quantum Duffing oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (July 2022): 073130. http://dx.doi.org/10.1063/5.0090477.

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This paper proves that the Abraham–Lorentz (AL) force can noticeably modify the trajectories of the charged Duffing oscillators over time. The influence of the reaction force on the oscillator evolution is strongly enhanced if the system is considered at the level of quantum mechanics. For example, the AL force examined within the scope of Newtonian description can change the trajectory of the Duffing oscillator only if it has the mass of an electron. However, we showed that when quantum corrections along with the nondeterministic contributions are taken into account, the reaction force of the electromagnetic field affects noticeably even the oscillator with a mass equal to the mass of the [Formula: see text] ion. The charged Duffing oscillators belong to the class of systems characterized by the chaotic nondeterministic dynamics. In classical terms, the nondeterministic behavior of the discussed systems results from the breaking of the causality principle by the AL force.
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Dissertations / Theses on the topic "Duffing Oscillator"

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Ivaschenko, M. "Noise-induced reentrant transition of the stochastic duffing oscillator." Thesis, Видавництво СумДУ, 2006. http://essuir.sumdu.edu.ua/handle/123456789/21639.

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Ma, Haolin. "Periodic Motions and Bifurcation Trees in a Parametric Duffing Oscillator." Thesis, Southern Illinois University at Edwardsville, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10242344.

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This thesis is a study of bifurcation trees of periodic motions in a parametric Duffing oscillator. The bifurcation trees from period-1 to period-4 motions are investigated by a semi-analytic method. For the semi-analytic method, the discretization of differential equations of nonlinear dynamical systems is obtained to attain the implicit mapping structure. Following the development of implicit mapping structure, the periodic nodes of periodic motions are computed. The stability and bifurcation conditions are carried out by the eigenvalue analysis. For a better understanding of nonlinear behaviors of periodic motions, the harmonic frequency-amplitude characteristics are presented by the finite Fourier series. Numerical simulations are illustrated to verify the analytical predictions. Based on the comparison of numerical and analytical result, the trajectory, time history, harmonic amplitude and harmonic phase plots of period-1 to period-4 motions are completed.

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Gargouri, Ameni. "On the perturbations theory of the Duffing oscillator in a complex domain." Thesis, Toulouse 3, 2015. http://www.theses.fr/2015TOU30243/document.

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La thèse concerne l'étude des cycles limites d'une équation différentielle sur le plan (la deuxième partie du 16ème problème de Hilbert). La notion de "cycle limite" a une grande importance dans la théorie de la stabilité, elle est introduite par Poincaré vers la fin du 19ème siècle et désigne une orbite périodique isolée. Le but de cette thèse est : d'établir l'existence d'une borne supérieure finie, pour le nombre de cycle limites d'une équation quadratique dans le plan. Ce problème est aussi appelé 16ème problème d' Hilbert infinitésimal. Probablement, l'outil le plus fondamental pour l'étude de la stabilité et les bifurcations des orbites périodiques est l'application de Poincaré, défini par Henri Poincaré en 1881. Cependant, la méthode de Melnikov nous donne une excellente procédure pour déterminer le nombre de cycles limites dans une bande continue de cycles qui sont préservés sous perturbation. En effet, le nombre, les positions et les multiplicités des équations différentielles planes perturbées avec une petite perturbation non nulle sont déterminées par le nombre, les positions et les multiplicités des zéros des fonctions génératrices. La fonction de Melnikov est plus précisément, appelé la fonction de Melnikov de premier- ordre. Si cette fonction est identiquement nulle à travers la bande continue de cycles, on calcule ce qu'on appelle " la fonction de Melnikov d'ordre supérieure ". Ensuite, une analyse d'ordre supérieure est nécessaire, ce qui peut être fait par " l'algorithme de Françoise. Les discussions et les calculs présentés dans notre travail sont limités non seulement à la fonction de Melnikov de premier ordre, mais aussi pour les fonctions de Melnikov de deuxième -ordre. Ces outils seront utiles pour résoudre notre problématique. Les activités de recherche menées dans le cadre de cette recherche sont divisées en quatre parties : La première partie de cette thèse, traite les systèmes dynamiques plans et l'existence de cycles limites. Nous souhaitons après résoudre le problème suivant: Calculer la cyclicité de l'oscillateur asymétrique perturbé de Duffing. Dans la deuxième partie, nous sommes intéressés de la cyclicité à l'extérieur de l'anneau périodique de l'oscillateur de Duffing pour une perturbation particulière, puis, nous fournissons un diagramme de bifurcation complet pour le nombre de zéros de la fonction de Melnikov associée dans un domaine complexe approprié en se basant sur le principe de l'argument. Le nombre de cette cyclicité est égal à trois. Dans la troisième partie, nous étudions la cyclicité à l'intérieur ainsi que à l'extérieur de double boucle homocline pour une perturbation cubique arbitraire de l'oscillateur de Duffing en utilisant les mêmes techniques de Iliev et Gavrilov dans le cas d'un Hamiltonien asymétrique de degré quatre. Notre principal résultat est que deux au plus cycle limite peuvent bifurquer de la double homocline. D'autre part, il est représenté, qu'après bifurcation de eight-loop un cycle limite étranger est née, qui ne soit pas contrôlée par un zéro lié par les intégrales Abéliennes, ce cycle supplémentaire est appelé " Alien "
This thesis concerns the study of limit cycles of a differential equation in the plane (The second part of the 16th Hilbert problem). The concept of "limit cycle" has a great importance in the theory of stability; Poincaré introduces this notion at the end of the 19th century and denotes an isolated periodic orbit. The purpose of this thesis: Find an upper bound finite to the number of limit cycles of a quadratic equation in the plane. This problem is so- called the infinitesimal Hilbert 16th problem. Probably, the most basic tool for studying the stability and bifurcations of periodic orbits is the Poincaré, defined by Henri Poincaré in 1881. However, Melnikov's method gives us an excellent method for determining the number of limit Cycles in a continuous band of cycles that are preserved under perturbation. In fact, the number, positions and multiplicities of perturbed planar differential equations for a small nonzero parameters, are determined by the number, positions and multiplicities of the zeros of the generating functions. The Melnikov function is more precisely, called the first-order Melnikov function. If this function is identically equal zero across the continuous band of cycles, one computes the so-called "Higher order Melnikov function". Then, a higher order analysis is necessary which can be done by making use of the so called "the algorithm of Françoise". The discussions and computation presented in this thesis are restricted not only to the first order Melnikov function, but also to the second-order Melnikov functions. These tools will be useful to resolve the question problem. The research activities in the framework of this thesis are divided into four parts: The first part of this thesis, discusses planar dynamical systems and the existence of limit cycles. We wish to solve the following problem: Calculate the cyclicity of the perturbed asymmetric oscillator Duffing. In the second part, we are interested of the cyclicity of the exterior period annulus of the asymmetrically perturbed Duffing oscillator for a particular perturbation, then, we provide a complete bifurcation diagram for the number of zeros of the associated Melnikov function in a suitable complex domain based on the argument principle. The number of this cyclicity is equal to three. In the third part, we study the cyclicity of the interior and exterior eight-loop especially for arbitrary cubic perturbations by using the same techniques of Iliev and Gavrilov in the case of an asymmetric Hamiltonian of degree four. Our main result is that at most two limit cycles can bifurcate from double homoclinic loop. On the other hand, it is appears after bifurcation of eight-loop an "Alien" limit was born, which is not covered by a zero of the related Abelian integrals
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O'Day, Joseph Patrick. "Investigation of a coupled Duffing oscillator system in a varying potential field /." Online version of thesis, 2005. https://ritdml.rit.edu/dspace/handle/1850/1212.

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Jin, Hanxiang. "Periodic Motions and Bifurcation Tree in a Periodically Excited Duffing Oscillator with Time-delay." Thesis, Southern Illinois University at Edwardsville, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1567592.

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Analytical solutions of periodic motions in a periodically excited, Duffing oscillator with a time-delayed displacement are developed through the Fourier series, and the stability and bifurcation of such periodic motions are discussed through eigenvalue analysis. The analytical bifurcation trees of period-1 motions to chaos in the time-delayed Duffing oscillator is presented through asymmetric period-1 to period-4 motions. Four independent symmetric period-3 motions were obtained. Two independent symmetric period-3 motions are not relative to chaos, while the other two includes bifurcation trees of period-3 motion to chaos, which are presented through period-3 to period-6 motions. Stable periodic motions are illustrated from numerical and analytical solutions. The appropriate initial history functions for periodic motions are analytically computed from the analytical solutions of periodic motions. Without the appropriate initial history functions, such a time-delayed system cannot yield periodic motions directly.

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Xing, Siyuan. "Periodic Motions and Bifurcation Trees in a Periodically Excited Duffing Oscillator with Time-delay." Thesis, Southern Illinois University at Edwardsville, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10147051.

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In this paper, bifurcation trees of periodic motions in a periodically forced, time-delayed, hardening Duffing oscillator are analytically predicted by a semi-analytical method. Such a semi-analytical method is based on the differential equation discretization of the time-delayed, non-linear dynamical system. Bifurcation trees for the stable and unstable solutions of periodic motions to chaos in such a time-delayed, Duffing oscillator are achieved analytically. From the finite discrete Fourier series, harmonic frequency-amplitude curves for stable and unstable solutions of period-1 to period-4 motions are developed for a better understanding of quantity levels, singularity and catastrophes of harmonic amplitudes in the frequency domain. From the analytical prediction, numerical results of periodic motions in the time-delayed, hardening Duffing oscillator are completed. Through the numerical illustrations, the complexity and asymmetry of period-1 motions to chaos in nonlinear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes. With the quantity level increases of specific harmonic amplitudes, effects of the corresponding harmonics on the periodic motions become strong, and the certain complexity and asymmetry of periodic motion and chaos can be identified through harmonic amplitudes with higher quantity levels.

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Manzione, Piergiuseppe. "Nonlinear transverse vibrations of centrally clamped rotating circular disks." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/31524.

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A study is presented of the instability mechanisms of a damped axisymmetric circular disk of uniform thickness rotating about its axis with constant angular velocity and subjected to various transverse space-fixed loading systems. The natural frequencies of spinning floppy disks are obtained for various nodal diameters and nodal circles with a numerical and an approximate method. Exploiting the fact that in most physical applications the thickness of the disk is small compared with its outer radius, we use their ratio to define a small parameter. Because the nonlinearities appearing in the governing partial-differential equations are cubic, we use the Galerkin procedure to reduce the problem into a finite number of coupled weakly nonlinear second-order equations. The coefficients of the nonlinear terms in the reduced equations are calculated for a wide range of the lowest modes and for different rotational speeds. We have studied the primary resonance of a pair of orthogonal modes under a space-fixed constant loading, the principal parametric resonance of a pair of orthogonal modes when the disk is subject to a massive loading system, and the combination parametric resonance of two pairs of orthogonal modes when the excitation is a linear spring. Considering the case of a spring moving periodically along the radius of the disk, we show how its frequency can be coupled to the rotational speed of the disk and lead to a principal parametric resonance. In each of these cases, we have used the method of multiple scales to determine the equations governing the modulation of the amplitudes and phases of the interacting modes. The equilibrium solutions of the modulation equations are determined and their stability is studied.
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Švihálková, Kateřina. "Stabilizace chaosu: metody a aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2016. http://www.nusl.cz/ntk/nusl-254422.

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The diploma thesis is focused on the use of heuristic and metaheuristic methods to stabilization and controlling the selected systems distinguished by the deterministic chaos behavior. There are discussed parameterization of chosen optimization methods, which are the genetic algorithm, simulated annealing and pattern search. The thesis also introduced the suitable controlling methods and the definition of the objective function. In the theoretical part of the thesis there is a brief introduction to the deterministic chaos theory. The next chapters describes the most common and deployed methods in~the~control theory, especially OGY and Pyragas methods. The practical part of the thesis is divided into two chapters. The first one describes the~stabilization of the artifical chaotic systems with the time delayed Pyragas method - TDAS and its modification ETDAS. The second chapter shows the real chaotic system control. The Duffing oscillator system was chosen to serve this purpose.
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Hem, Sopheasith. "Nonlinear epitaxial functional oxide-based resonant sensors." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPAST220.

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La détection de signaux magnétiques faibles a suscité une attention considérable en raison de ses applications potentielles dans des domaines tels que la médecine et la nanotechnologie. Diverses méthodes ont été employées pour améliorer la détection de signaux faibles, notamment les dispositifs SQUID, les capteurs diamant et les résonateurs magnétoélectriques (ME). Le choix de la méthode dépend de facteurs tels que le contexte d'application, le coût et les exigences de sensibilité. Parmi ces méthodes, les résonateurs MEMS-ME ont retenu l'attention en raison de leur flexibilité de conception, de leur compacité et compatibilité avec les circuits intégrés. Dans ces résonateurs à microéchelle, l'interaction entre films magnétostrictifs et piézoélectriques permet d'obtenir des effets de contrainte à l'échelle-micrométrique, offrant ainsi une grande précision et une résolution spatiotemporelle élevée. Cette thèse explore le régime nonlinéaire du fonctionnement des résonateurs, caractérisé par des formes asymétriques, des bifurcations et des résonances nonlinéaires. Le régime nonlinéaire permettre des modes de fonctionnement analogiques, qui sont obtenus en balayant la fréquence d'excitation jusqu'au point de bifurcation. Malgré les défis liés au comportement nonmonotonique, le régime nonlinéaire se révèle être une méthode précieuse pour détecter les signaux faibles. La bistabilité, courante dans les résonateurs fonctionnant de manière nonlinéaire, n'est pas largement utilisée dans les configurations piézoélectriques. Cette thèse explore le potentiel du régime de bifurcation dans les résonateurs actionnés piézoélectriquement et présente dispositif de preuve-de-concept pour quantifier les changements du signal en mesurant la fréquence. Mathématiquement, les équations différentielles sont transformées en équations de Duffing normalisées à l'aide de la méthode de Galerkin, permettant ainsi aux comportements dynamiques de se manifester à travers les coefficients Duffing. Différents modèles ont été développés pour répondre à différentes conditions et hypothèses, révélant des liens entre les paramètres mécaniques. Combler l'écart entre les modèles basés sur l'amplitude des vibrations et les données d'impédance s'est avéré complexe mais réalisable. Grâce à des expériences et à l'affinement itératif du modèle, le modèle basé sur l'amplitude des vibrations a fourni des informations sur les réponses en fréquence, bien qu'il ne prédise pas directement l'ampleur et la phase de l'impédance. La recherche a reconnu les limitations liées à l'emplacement de l'axe neutre dans les films minces monocouches, suggérant de réévaluer les hypothèses, de tenir compte des effets multicouches et d'effectuer des simulations numériques pour obtenir des représentations plus précises. Le concept d'axe neutre relatif a été introduit, reconnaissant les écarts par rapport aux prédictions du modèle monocouche. Cette approche a été justifiée de manière transparente et alignée sur le comportement expérimental observé. Parallèlement, la fabrication de microcantilevers à base de PZT, composants essentiels du capteur résonant, a subi de multiples itérations pour relever les défis. Ces améliorations itératives ont abouti à un processus de fabrication plus robuste et fiable. En conclusion, cette étude a fait progresser la compréhension des résonateurs actionnés piézoélectriquement et de leur potentiel dans la détection de signaux faibles. Les améliorations itératives de la fabrication et les modèles mathématiques ont contribué au développement de dispositifs de détection multifonctionnels. Elle a mis en lumière l'interaction complexe entre la nonlinéarité et la résonance dans les systèmes de résonateurs, fournissant informations pour des recherches futures et des applications pratiques
The detection of weak magnetic field signals has gained significant attention for its potential applications in fields such as medicine, geophysics, and nanotechnology. Various methods, including Superconducting Quantum Interference Devices (SQUIDs), optically pumped magnetometers (diamond sensors), and magnetoelectric (ME) resonators, have been used to enhance the detection of these weak signals. The choice of detection method depends on factors such as application context, available resources, cost, and sensitivity requirements. Among these methods, MEMS ME resonator-based sensors have garnered attention due to their design flexibility, compactness, and compatibility with integrated circuits. In these microscale resonators, the interaction between magnetostrictive and piezoelectric thin films enables a strain-mediated effect at micro- and nano-scales, resulting in high precision and spatial-temporal resolution. The thesis delves into the nonlinear regime in resonator operation, characterized by nonlinearity in vibrational responses, including asymmetrical peak shapes, multivalued responses, bifurcations, and nonlinear resonances. The nonlinear regime, particularly bifurcation, promises enhanced sensing capabilities and analog operation modes by sweeping the excitation frequency. Despite challenges like noise-activated stochastic switching, the nonlinear regime is valuable for detecting weak signals. Bistability in resonators within the nonlinear regime, underutilized in piezoelectric configurations, is explored. A proof-of-concept device quantifies signal changes through jumping frequency. Mathematically, differential equations are transformed into normalized Duffing equations using Galerkin's method, enabling dynamic behaviors to manifest through coefficients. Distinct models accommodate various conditions and assumptions, revealing connections between mechanical parameters and normalized coefficients in linear and nonlinear regimes. Bridging the gap between vibrational amplitude-based models and impedance data is complex but achievable. Experiments and iterative model refinement provide insights into frequency responses. Limitations regarding the neutral axis in monolayer thin films are acknowledged, with suggestions to reevaluate assumptions, consider multilayer effects, and employ numerical simulations. A relative neutral axis concept is introduced, transparently justified, and aligned with observed experimental behavior. The nonlinear regime widens resonance peaks, enhancing sensitivity in magnetic field detection. Parameters like piezoelectric and dielectric coefficients influence the transition to the nonlinear regime. The research extends beyond ideal scenarios, requiring further investigation to replicate the bifurcation regime under different conditions. In parallel, the fabrication of PZT-based microcantilevers, vital components of the resonant sensor, underwent multiple iterations to address challenges. These iterative improvements resulted in a more robust and reliable fabrication process. In conclusion, this study advanced the understanding of piezoelectrically actuated resonators and their potential applications in weak signal detection. The iterative fabrication enhancements and mathematical models contributed to the development of multifunctional sensing devices. The research also emphasized the importance of bridging the gap between vibrational amplitude-based models and impedance data. Finally, it shed light on the intricate interplay of nonlinearity and resonance in resonator systems, providing insights for future investigations and practical applications
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SANTOS, Desiane Maiara Gomes dos. "Amplificação de pequenos sinais em osciladores parametricamente forçados." Universidade Federal de Campina Grande, 2015. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1578.

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Nesta dissertação, analisamos a dinâmica de osciladores parametricamente forçados, com enfoque na amplificação de pequenos sinais. Iniciamos por uma revisão da ressonância paramétrica e da amplificação paramétrica em um oscilador linear parametricamente excitado. Em seguida, estudamos dois tipos de osciladores não-lineares parametricamente forçados e concluímos a dissertação com a análise de um dímero parametricamente excitado. Basicamente, analisamos os fenômenos de ressonância paramétrica e de amplificação paramétrica, comparando os resultados obtidos analiticamente (via métodos da média ou do balanço harmônico) com os obtidos via integração numérica das equações do movimento. Em todos os casos, obtivemos a linha de transição para a instabilidade paramétrica do oscilador paramétrico. Nós excitamos os amplificador paramétrico com e sem dessintonia entre entre o bombeamento e o sinal externo ac. Verificamos que o ganho da amplificação paramétrica depende da sensitivamente na fase do sinal externo ac e na amplitude do bombeamento. Mostramos que tais sistemas podem ser facilmente utilizados para recepção e decodificação de sinais com modulação de fase. Além disso, obtivemos séries temporais, envelopes e transformadas de Fourier para a resposta da amplificação paramétrica de pequenos sinais ac. Especificamente nos casos dos osciladores de Duffing parametricamente forçados, obtivemos e analisamos linhas de bifurcação e a amplitude dos ciclos limites como função da frequência e da amplitude de bombeamento. Adicionalmente, conseguimos obter uma relação analítica para os ganhos do sinal e do idler dos osciladores não-lineares parametricamente forçados pelo método do balanço harmônico. Os resultados obtidos implicam que os amplificadores paramétricos não-lineares podem ser excelentes detectores, especialmente em pontos próximos a bifurcações para instabilidade, em que apresentam altos ganhos e largura de banda bem estreitas. Por último, investigamos também o comportamento de dois osciladores lineares acoplados e parametricamente estimulados, com e sem força externa ac. Tais sistemas são muito sensíveis à fase do sinal a ser amplificado e podem ser utilizados para criar amplificadores sintonizáveis em função do parâmetro de acoplamento.
In this dissertation, we studied the dynamics of parametrically-driven oscillators, with a focus on the amplification of small signals. We begin with a revision of parametric resonance and parametric amplification in a linear oscillator parametrically excited. Next, we studied two types of nonlinear parametrically-driven oscillators and finished the dissertation with an analysis of a parametric dimer. Basically, we analyzed the phenomena of parametric resonance and parametric amplification by comparing the results obtained analytically (via the averaging or harmonic balance methods) with those of numerical integration of the equations of motion. In all cases, we obtained the transition line to parametric instability of the parametric oscillator. We excited the parametric amplifier with and without detuning between the pump and the external signal. We found that the parametric amplification depends sensitively on the phase of the external ac signal and on the internal pump amplitude. We showed that such amplifiers can be easily used for the reception and decoding of signals with phase modulation. Furthermore, we obtained time series, envelopes, and Fourier transforms of the response of the parametric amplifier to small external ac signals. Specifically in the cases of the parametrically-driven Duffing oscillators, we obtained and analysed the bifurcation lines and the amplitude of limit cycles as function of the pump amplitude and frequency. In addition, we derived an expression for the signal and idler gains of the nonlinear parametrically-driven oscillators with the harmonic balance method. The results imply that the nonlinear parametric amplifiers can be excellent detectors, specially near bifurcations to instability, due to their high gains and narrow bandwidths. Finally, we studied the dynamics of two linear oscillators coupled and parametrically excited, with and without external ac driving. We found that such systems have a wealth of dynamical responses. They present parametric amplification that is dependent on the coupling parameter and on the phases of the external ac signals. Such systems may be used as tunable amplifiers.
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Books on the topic "Duffing Oscillator"

1

Aguirre, L. A. Controlling regular and chaotic dynamics in the Duffing-Ueda oscillator. Sheffield: University of Sheffield, Dept. of Automatic Control and Systems Engineering, 1993.

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2

The Duffing equation: Nonlinear oscillators and their phenomena. Chichester, West Sussex, U.K: Wiley, 2011.

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3

Ueda, Yoshisuke. The road to chaos. Santa Cruz, CA: Aerial Press, 1992.

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Yoshisuke, Ueda. The road to chaos. Santa Cruz, CA: Aerial Press, 1992.

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Yoshisuke, Ueda. The road to chaos-II. 2nd ed. Santa Cruz, CA: Aerial Press, 1992.

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Hassan, Ameer. On the periodic and chaotic responses of Duffing's oscillator. 1989.

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Brennan, Michael J., and Ivana Kovacic. Duffing Equation: Nonlinear Oscillators and Their Behaviour. Wiley & Sons, Limited, John, 2011.

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Brennan, Michael J., and Ivana Kovacic. Duffing Equation: Nonlinear Oscillators and Their Behaviour. Wiley & Sons, Incorporated, John, 2011.

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Brennan, Michael J., and Ivana Kovacic. Duffing Equation: Nonlinear Oscillators and Their Behaviour. Wiley & Sons, Incorporated, John, 2011.

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Brennan, Michael J., and Ivana Kovacic. Duffing Equation: Nonlinear Oscillators and Their Behaviour. Wiley & Sons, Incorporated, John, 2011.

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Book chapters on the topic "Duffing Oscillator"

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Korsch, H. J., and H. J. Jodl. "The Duffing Oscillator." In Chaos, 157–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03866-6_8.

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Chakraverty, Snehashish, and Susmita Mall. "Duffing Oscillator Equations." In Artificial Neural Networks for Engineers and Scientists, 117–32. Boca Raton : CRC Press, 2017.: CRC Press, 2017. http://dx.doi.org/10.1201/9781315155265-9.

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Korsch, H. J., and H. J. Jodl. "The Duffing Oscillator." In Chaos, 157–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-662-02991-6_8.

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Luo, Albert C. J. "Time-Delayed Duffing Oscillator." In Nonlinear Systems and Complexity, 271–96. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42778-2_5.

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Kovacic, Ivana, and Michael J. Brennan. "Forced Harmonic Vibration of an Asymmetric Duffing Oscillator." In The Duffing Equation, 277–322. Chichester, UK: John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9780470977859.ch8.

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Yabuno, Hiroshi. "Free Vibration of a Duffing Oscillator with Viscous Damping." In The Duffing Equation, 55–80. Chichester, UK: John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9780470977859.ch3.

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Kalmár-Nagy, Tamás, and Balakumar Balachandran. "Forced Harmonic Vibration of a Duffing Oscillator with Linear Viscous Damping." In The Duffing Equation, 139–74. Chichester, UK: John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9780470977859.ch5.

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Mallik, Asok Kumar. "Forced Harmonic Vibration of a Duffing Oscillator with Different Damping Mechanisms." In The Duffing Equation, 175–217. Chichester, UK: John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9780470977859.ch6.

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Lenci, Stefano, and Giuseppe Rega. "Forced Harmonic Vibration in a Duffing Oscillator with Negative Linear Stiffness and Linear Viscous Damping." In The Duffing Equation, 219–76. Chichester, UK: John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9780470977859.ch7.

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Aldridge, Sequoyah. "The Duffing Oscillator for Nanoelectromechanical Systems." In Nonlinear Dynamics of Nanosystems, 203–19. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA, 2010. http://dx.doi.org/10.1002/9783527629374.ch7.

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Conference papers on the topic "Duffing Oscillator"

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Agarwal, Vipin, and Balakumar Balachandran. "Noise-Influenced Response of Duffing Oscillator." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51620.

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Noise is unavoidable and present in a range of engineering systems, and it can play a significant role in influencing system dynamics. In the present study, a combination of experimental and numerical studies are undertaken to understand the responses of Duffing oscillators with hardening and softening spring characteristics. To serve as a prototype for hardening type and softening type oscillators, a cantilever structure with a magnet at the free end is considered. This tip magnet is located in the magnetic field of another magnet that is fixed in position. In the presence of harmonic excitations, the complex motions of this system are examined through experimental and numerical means. The influence of noise on the system response is studied, and it is shown that with an appropriate level of noise, the chaotic behavior of a harmonically forced oscillator can be significantly influenced. The present work provides a glimpse into the possibilities for noise-influenced responses.
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Chen, Yonghe, Zhenbiao Wei, Zhanjun Niu, and Baozhan Qin. "Behavior Evolution of Duffing Oscillator." In 2015 7th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC). IEEE, 2015. http://dx.doi.org/10.1109/ihmsc.2015.139.

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Guo, Yu, Zeltzin Reyes, Abigail Reyes, and Albert C. J. Luo. "An Experimental Study of Periodic Motions in a Duffing Oscillator." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86833.

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In this paper, the experimental dynamics of a Duffing oscillatory system are studied for periodic motions. A Duffing oscillatory circuit is developed for the experimental study of periodic motions on the bifurcation trees. The coexisting asymmetric periodic motions are obtained experimentally. The analytical periodic motions in the Duffing oscillator are presented for comparison with experimental results. Because of hardware and data leakage of experimental instruments, the experimental result accuracy is much lower than the analytical results of periodic motions. To improve the experimental results accuracy, the high quality hardware and instruments should be adopted and the high resolution data acquisition systems should be adopted.
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Hao, Long, Dan Liu, Fei Liu, QingXin Wang, Lin Liang, and GuangHua Xu. "Research on the Weak Signal Detection of Bearing Fault Based on Duffing Oscillator." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86892.

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In this paper, chaotic system is applied to identify and extract the weak signals of bearing early fault which are often submerged in strong background noise. Chaotic system is an effective method in weak signal detection because of its properties of noise immunity and sensitivity to the weak periodic signal. However, chaotic system is not completely immune to noise in critical chaotic state. Aiming at this problem, four indicators are used to evaluate the detection performance of Duffing oscillators. Then, the influence of Duffing oscillator parameters on the four indicators is studied in detail and a new method is proposed to improve the detection performance of Duffing oscillator. The simulation and experimental results show that the proposed method can accurately obtain the characteristic signals of early bearing fault in a lower signal-to-noise ratio (SNR) situation.
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Folley, Christopher, and Anil K. Bajaj. "The Dynamics of a Cyclic Ring of Coupled Duffing Oscillators." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85108.

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The dynamics of a planar ring of N coupled identical, damped Duffing oscillators with external excitation is considered. Each oscillator is in 1:1 resonance with all other oscillators. The external forcing is a mono-frequency excitation near primary resonance with each oscillator and the analysis is considered in the context of weakly nonlinear systems. The symmetry of the system is exploited to determine, for an arbitrary number of oscillators, all possible classes of periodic solutions at the excitation frequency. These are fixed-point solutions for the system and are determined by the averaged equations. These solutions are classified into standing waves, traveling waves, and motions in-phase with the external forcing. Linear stability analysis is described for each solution class containing the highest degree of symmetry. To continue the study to motions with smaller degrees of symmetry, numerical simulations using the bifurcation analysis and branch continuation software AUTO 97 are utilized. The study presents the specific example of the dynamics of three Duffing oscillators.
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Ahmed, Syed Hassaan, Sajjad Hussain, Saad Rehman, Syed Kashif Abbas, and Shahzad Amin Sheikh. "Stability analysis of forced duffing oscillator (FDO)." In 2016 19th International Conference on Computer and Information Technology (ICCIT). IEEE, 2016. http://dx.doi.org/10.1109/iccitechn.2016.7860185.

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Li-xin, Ma. "Weak Signal Detection Based on Duffing Oscillator." In 2008 International Conference on Information Management, Innovation Management and Industrial Engineering (ICIII). IEEE, 2008. http://dx.doi.org/10.1109/iciii.2008.226.

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Bermudez-Gomez, Carlos R., Rogerio Enriquez-Caldera, and Jorge Martinez-Carballido. "Chirp signal detection using the Duffing oscillator." In 2012 22nd International Conference on Electrical Communications and Computers (CONIELECOMP). IEEE, 2012. http://dx.doi.org/10.1109/conielecomp.2012.6189936.

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Xu, Yeyin, and Albert C. J. Luo. "Periodic Motions in a Coupled Van Der Pol-Duffing Oscillator." 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/detc2017-67563.

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In this paper, periodic motions of a periodically forced, coupled van der Pol-Duffing oscillator are predicted analytically. The coupled van der Pol-Duffing oscillator is discretized for the discrete mapping. The periodic motions in such a coupled van der Pol-Duffing oscillator are obtained from specified mapping structures, and the corresponding stability and bifurcation analysis are carried out by eigenvalue analysis. Based on the analytical prediction, the initial conditions of periodic motions are used for numerical simulations.
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Luo, Albert C. J., and Jianzhe Huang. "Analytical Periodic Motions in a Periodically Forced, Damped Duffing Oscillator." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-86077.

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The analytical solutions of the period-1 motions for a hardening Duffing oscillator are presented through the generalized harmonic balance method. The conditions of stability and bifurcation of the approximate solutions in the oscillator are discussed. Numerical simulations for period-1 motions for the damped Duffing oscillator are carried out.
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Reports on the topic "Duffing Oscillator"

1

Sen, T., J. Ellison, and S. Kauffmann. Collective behavior of an ensemble of forced duffing oscillators near the 1{vert_ellipsis}1 resonance. Revision 1. Office of Scientific and Technical Information (OSTI), July 1994. http://dx.doi.org/10.2172/71686.

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