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Advances in Applied Mathematics and Mechanics 2011年第6期3卷 689-701页

作者： Malik Mamode Department of Physics Laboratoire PIMENTEquipe MASCUniversity of La Reunion97400 Saint-DenisFrance

The exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential,is *** an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic *** result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

关键词： nonlinear oscillator exact period elliptic integral

Straightforward Method for nonlinear oscillators

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Journal of Donghua University(English Edition) 2023年第1期40卷 105-109页

作者：吕国娟何吉欢何春辉 SEDIGHI Hamid M School of Science Xi’an University of Architecture and TechnologyXi’an 710055China School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuo 454003China National Engineering Laboratory for Modern Silk College of Textile and ClothingEngineeringSoochow UniversitySuzhou 215021China School of Civil Engineering Xi’an University of Architecture and TechnologyXi’an 710055China Faculty of Engineering Shahid Chamran University of AhvazAhvaz61357-43337Iran

It is challenging to predict the frequency property of a nonlinear vibration system conveniently and ***,an invalid or physically irrelevant result might be obtained by some advanced ***,predicting the frequency lacks an expedient and efficient *** challenge is addressed by developing a straightforward and effective frequency formulation that reliably predicts the frequency-amplitude *** study provides a one-step approach which can fast determine the periodic properties of any conservative oscillators and also provides a reference for other similar studies.

关键词： He's frequency formulation Duffing oscillator nonlinear oscillator

nonlinear Electrostatic “Hesitant” oscillator

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American Journal of Computational Mathematics 2021年第1期11卷 42-52页

作者： Haiduke Sarafian The Pennsylvania State University University College York USA

In search of nonlinear oscillations, we envision a 3D elliptic curva-ture-dependent nonuniform charge distribution to creating an electric field along the symmetry axis causing a massive point-like charged particle placed on the symmetry axis to oscillate in a delayed/hesitant nonlinear mode. The charge distribution is a 3D twisted line creating nontrivial electric field causing an unexpected oscillation that is non-orthodox defying the common sense. Calculation of this research flavored investigation is entirely based on utilities accompanied with Computer Algebra Systems (CAS) especially Mathematic [1]. The characteristics of the delayed oscillations in addition to embodying classic graphics displaying the time-dependent kinematic quantities are augmented including various phase diagrams signifying the nonlinear oscillations. The output of our investigation is compared to nonlinear non-delayed oscillations revealing fresh insight. For comprehensive understanding of the hesitant oscillator a simulation program is crafted clarifying visually the scenario on hand.

关键词： nonlinear oscillator 3D Elliptic Curvature-Dependent Charge Distribution Computer Algebra System Mathematica

High frequency forcing on nonlinear systems

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Chinese Physics B 2013年第3期22卷 209-218页

作者：姚成贵何志威占萌 Department of Mathematics Shaoxing University Wuhan Center for Magnetic Resonance State Key Laboratory of Magnetic Resonance and Atomic and Molecular PhysicsWuhan Institute of Physics and MathematicsChinese Academy of Sciences University of the Chinese Academy of Sciences

High-frequency signals are pervasive in many science and engineering *** this work,the effect of high-frequency driving on general nonlinear systems is investigated,and an effective equation for slow motion is derived by extending the inertial approximation for the direct separation of fast and slow *** on this theory,a high-frequency force can induce various phase transitions of a system by changing its amplitude and *** simulations on several nonlinear oscillator systems show a very good agreement with the theoretic *** findings may shed light on our understanding of the dynamics of nonlinear systems subject to a periodic force.

关键词： high frequency nonlinear oscillator inertial approximation phase transitions

A Bionic Neural Network for Fish-Robot Locomotion

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Journal of Bionic Engineering 2006年第4期3卷 187-194页

作者： Dai-bing Zhang De-wen Hu Lin-cheng Shen Hai-bin Xie College of Mechatronic Engineering and Automation National University of Defense Technology Changsha 410073 P. R. China

A bionic neural network for fish-robot locomotion is presented. The bionic neural network inspired from fish neural net- work consists of one high level controller and one chain of central pattern generators （CPGs）. Each CPG contains a nonlinear neural Zhang oscillator which shows properties similar to sine-cosine model. Simulation re, suits show that the bionic neural network presents a good performance in controlling the fish-robot to execute various motions such as startup, stop, forward swimming, backward swimming, turn right and turn left.

关键词： neural network central pattern generators nonlinear oscillator swimming locomotion fish-robot

Modified variational iteration method for an El Nio Southern Oscillation delayed oscillator

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Chinese Physics B 2012年第2期21卷 51-55页

作者：曹小群宋君强朱小谦张理论张卫民赵军 School of Computer Science National University of Defense TechnologyChangsha 410073China

This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Nino Southern Oscillation. The approximate expansions of the delayed differential equation＇s solution are obtained successfully by the modified variational iteration method. The numerical results illustrate the effectiveness and correctness of the method by comparing with the exact solution of the reduced model.

关键词： air sea coupling nonlinear oscillator modified variational iteration method delayeddifferential equation

A simple analytical method for oscillators with strong nonlinear restoring force

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A simple analytical method for oscillators with strong nonli...

Numerical evolutions of information entropies in the nonlinear dynamical systems excited by Gaussian white noise

第十三届全国非线性振动暨第十届全国非线性动力学和运动稳...

作者：王士敏北京航空航天大学航空科学与工程学院

An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring *** from different points as the conventional methods,in this approach the nonlinear restoring force is written as a product of the displacement and the stiffness coefficient that is dependent on *** the stationary response,namely,the restoring force is formally written as That is,for given stationery vibration,the restoring force linearly varies along with the displacement within the amplitude,but the varying rate of the restoring force,so-called stiffness here referring to linear spring,is dependent on the vibration *** the stiffness is constructed according to the characters of the restoring force function;the characters of the restoring force are described with its averaged first and second derivatives respect to the *** this stiffness is used to calculate the frequency of free vibration and the amplitude frequency characteristics for forced *** examples show that this method can be applied to extensive oscillators with nonlinear restoring force,and that the solving process is extremely simple.

关键词： nonlinear oscillator analytical approximation method amplitude-frequency characteristics forced oscillator

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Numerical evolutions of information entropies in the nonline...