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Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control

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Chinese Physics B 2024年第6期33卷 142-154页

作者：黄美玲杨勇歌刘洋 School of Mathematics and Statistics Guangdong University of TechnologyGuangzhou 510520China State Key Laboratory for Strength and Vibration of Mechanical Structures Xi'an Jiaotong UniversityXi'an 710049China Exeter Small-Scale Robotics Laboratory Engineering DepartmentUniversity of ExeterNorth Park RoadExeter EX44QFUK

This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting efficiency. Firstly, to obtain the dimensionless governing equation of the system, the original bistable system is approximated as a system without viscoelastic term by using the stochastic averaging method of energy envelope, and then is further decoupled to derive an equivalent system. The credibility of the proposed method is validated by contrasting the consistency between the numerical and the analytical results of the equivalent system under different noise conditions. The influence of system parameters on average output power is analyzed, and the control effect of the time-delayed feedback control on system performance is compared. The output performance of the system is improved with the occurrence of stochastic resonance(SR). Therefore, the signal-to-noise ratio expression for measuring SR is derived, and the dependence of its SR behavior on different parameters is explored.

关键词： energy harvesting bistability stochastic averaging method stochastic resonance time-delayed feedback control

随机激励下Frenkel-Kontorova模型的纳米摩擦现象

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物理学报 2021年第9期70卷 220-225页

作者：李毅伟雷佑铭杨勇歌山西农业大学数学系晋中030801 西北工业大学应用数学系西安710129 广东工业大学应用数学学院广州510520

基于一维Frenkel-Kontorova (FK)模型,借助随机龙格库塔方法,在非公度(incommensurate)和公度(commensurate)两种情形下,分别研究了高斯白噪声激励下,随机FK模型的纳米摩擦现象(滞回和超滑)随噪声强度的变化而变化的规律.两种情形表明... 详细信息

基于一维Frenkel-Kontorova (FK)模型,借助随机龙格库塔方法,在非公度(incommensurate)和公度(commensurate)两种情形下,分别研究了高斯白噪声激励下,随机FK模型的纳米摩擦现象(滞回和超滑)随噪声强度的变化而变化的规律.两种情形表明随着噪声强度的增大,对减小系统滞回,产生超滑有积极的影响.另一方面,当系统机动性能(chain mobility)未达到饱和状态(B=1)时,噪声的引入,能加速原子的运动,使得原子更易脱离基底势的束缚而做运动,但是当系统达到饱和状态后,系统机动性能并不受噪声的影响.另外,两种情形的区别是,公度情形下,由于原子受到基底势更强烈的耦合作用,所以噪声对公度情形影响更为明显.

关键词： Frenkel-Kontorova模型高斯白噪声滞回超滑

Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation

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Chinese Physics B 2016年第2期25卷 13-21页

作者：杨勇歌徐伟孙亚辉谷旭东 Department of Applied Mathematics Northwestern Polytechnical University State Key Laboratory for Strength and Vibration of Mechanical Structures Xi'an Jiaotong University Department of Engineering Mechanics Northwestern Polytechnical University

This paper aims to investigate the stochastic response of the van der Pol （VDP） oscillator with two kinds of fractional derivatives under Gaussian white noise excitation. First, the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique. Then, the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution. Finally, the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator. The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order, the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator. An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary.

关键词： stochastic averaging method fractional derivative van der Pol equivalent stochastic system

随机激励下一类含分数阶阻尼的轮胎的振动响应

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应用数学和力学 2014年第12期35卷 1330-1340页

作者：范院琴徐伟韩群杨勇歌西北工业大学应用数学系西安710072

基于随机平均法研究了Kanai-Tajimi噪声激励下含分数阶阻尼的轮胎动力学系统的响应.首先将地震波近似为Kanai-Tajimi噪声,结合点接触模型和分数阶导数模型,建立轮胎的动力学方程,然后运用随机平均法求解振动位移的稳态概率密度函数的解... 详细信息

基于随机平均法研究了Kanai-Tajimi噪声激励下含分数阶阻尼的轮胎动力学系统的响应.首先将地震波近似为Kanai-Tajimi噪声,结合点接触模型和分数阶导数模型,建立轮胎的动力学方程,然后运用随机平均法求解振动位移的稳态概率密度函数的解析解,最后通过Monte-Carlo数值模拟验证了该方法的有效性.利用振动位移的概率密度求解聚丁二烯橡胶、丁基B252橡胶轮胎振动位移的均值与方差,并以此为依据考察这两类橡胶的减振性能.研究结果表明,轮胎振动位移的均值和方差随橡胶的储能模量的增大而增大,随耗散模量的增大而减小,这说明减小橡胶的储能模量或增大耗散模量可有效改善轮胎的减振性能.所得结果可为轮胎的设计与制造提供一定的理论基础.

关键词：分数阶阻尼橡胶材料随机平均法粘弹材料

Sparse identification method of extracting hybrid energy harvesting system from observed data

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Chinese Physics B 2022年第12期31卷 28-39页

作者：孙亚辉曾远辉杨勇歌 School of Mathematics and Statistics Guangdong University of TechnologyGuangzhou 510520China State Key Laboratory for Strength and Vibration of Mechanical Structures Xi’an Jiaotong UniversityXi’an 710049China

Hybrid energy harvesters under external excitation have complex dynamical behavior and the superiority of promoting energy harvesting efficiency.Sometimes,it is difficult to model the governing equations of the hybrid energy harvesting system precisely,especially under external excitation.Accompanied with machine learning,data-driven methods play an important role in discovering the governing equations from massive datasets.Recently,there are many studies of datadriven models done in aspect of ordinary differential equations and stochastic differential equations(SDEs).However,few studies discover the governing equations for the hybrid energy harvesting system under harmonic excitation and Gaussian white noise(GWN).Thus,in this paper,a data-driven approach,with least square and sparse constraint,is devised to discover the governing equations of the systems from observed data.Firstly,the algorithm processing and pseudo code are given.Then,the effectiveness and accuracy of the method are verified by taking two examples with harmonic excitation and GWN,respectively.For harmonic excitation,all coefficients of the system can be simultaneously learned.For GWN,we approximate the drift term and diffusion term by using the Kramers-Moyal formulas,and separately learn the coefficients of the drift term and diffusion term.Cross-validation(CV)and mean-square error(MSE)are utilized to obtain the optimal number of iterations.Finally,the comparisons between true values and learned values are depicted to demonstrate that the approach is well utilized to obtain the governing equations for the hybrid energy harvester under harmonic excitation and GWN.

关键词： data-driven hybrid energy harvester harmonic excitation Gaussian white noise

Nano-friction phenomenon of Frenkel-Kontorova model under Gaussian colored noise

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Chinese Physics B 2022年第5期31卷 197-202页

作者：李毅伟许鹏飞杨勇歌 Department of Mathematics Shanxi Agricultural UniversityJinzhong 030801China School of Applied Mathematics Guangdong University of TechnologyGuangzhou 510520China

The nano-friction phenomenon in a one-dimensional Frenkel-Kontorova(FK)model under Gaussian colored noise is investigated by using the molecular dynamic simulation method.The role of colored noise is analyzed through the inclusion of a stochastic force via a Langevin molecular dynamics method.Via the stochastic Runge-Kutta algorithm,the relationship between different parameter values of the Gaussian colored noise(the noise intensity and the correlation time)and the nano-friction phenomena such as hysteresis,the maximum static friction force is separately studied here.Similar results are obtained from the two geometrically opposed ideal cases:incommensurate and commensurate interfaces.It was found that the noise strongly influences the hysteresis and maximum static friction force and with an appropriate external driving force,the introduction of noise can accelerate the motion of the system,making the atoms escape from the substrate potential well more easily.Interestingly,suitable correlation time and noise intensity give rise to super-lubricity.It is noteworthy that the difference between the two circumstances lies in the fact that the effect of the noise is much stronger on triggering the motion of the FK model for the commensurate interface than that for the incommensurate interface.

关键词： Frenkel-Kontorova model Gaussian colored noise hysteresis super-lubricity

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数控加工刀具运动的优化控制

数学的实践与认识 2016年第15期46卷 57-64页

作者：都琳杨富强王茁茁杨勇歌西北工业大学应用数学系陕西西安710072 西北工业大学现代设计与集成制造技术教育部重点实验室陕西西安710072 西北工业大学航海学院陕西西安710072

数控加工的精准性与高速性主要体现在加工路径的插补与加工过程中刀具的速度控制.首先针对数控加工过程中常见的折线轨迹进行分析,提出了折线加工转角处的速度平滑过渡方案,保证加工精度的同时提高加工效率.进一步,得出了转角处的最大... 详细信息

数控加工的精准性与高速性主要体现在加工路径的插补与加工过程中刀具的速度控制.首先针对数控加工过程中常见的折线轨迹进行分析,提出了折线加工转角处的速度平滑过渡方案,保证加工精度的同时提高加工效率.进一步,得出了转角处的最大加工速度与加工误差关系.针对圆弧类曲线插补问题,在折线模型的基础上拓展了内接和外切两种插补方案.计算结果表明,采用折线平滑过渡时,外切插补方案可以保证更高的精度.

关键词：数控加工高速平滑过渡圆弧插补优化控制

Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise

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中国物理B:英文版 2023年第9期32卷 108-115页

作者：杨勇歌孟运曾远辉孙亚辉 School of Mathematics and Statistics Guangdong University of TechnologyGuangzhou 510520China State Key Laboratory for Strength and Vibration of Mechanical Structures Xi'an Jiaotong UniversityXi'an 710049China

Because of the increasing demand for electrical energy,vibration energy harvesters(VEHs)that convert vibratory energy into electrical energy are a promising technology.In order to improve the efficiency of harvesting energy from environmental vibration,here we investigate a hybrid VEH.Unlike previous studies,this article analyzes the stochastic responses of the hybrid piezoelectric and electromagnetic energy harvesting system with viscoelastic material under narrow-band(colored)noise.Firstly,a mass-spring-damping system model coupled with piezoelectric and electromagnetic circuits under fundamental acceleration excitation is established,and analytical solutions to the dimensionless equations are derived.Then,the formula of the amplitude-frequency responses in the deterministic case and the first-order and secondorder steady-state moments of the amplitude in the stochastic case are obtained by using the multi-scales method.The amplitude-frequency analytical solutions are in good agreement with the numerical solutions obtained by the Monte Carlo method.Furthermore,the stochastic bifurcation diagram is plotted for the first-order steady-state moment of the amplitude with respect to the detuning frequency and viscoelastic parameter.Eventually,the influence of system parameters on mean-square electric voltage,mean-square electric current and mean output power is discussed.Results show that the electromechanical coupling coefficients,random excitation and viscoelastic parameter have a positive effect on the output power of the system.

关键词： hybrid vibration energy harvesting narrow-band random excitation multi-scales method viscoelastic material stochastic bifurcation

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线性代数案例式教学的研究与思考

中国科技经济新闻数据库教育 2021年第2期 127-127,150页

作者：吴先萍杨勇歌刘冬冬广东工业大学应用数学学院广东广州510520

线性代数是大学本科的一门重要的公共基础课,具有概念多、定理多、性质多等特点,其理论与方法在社会科学、工程技术、人工智能等众多科学领域中具有广泛的应用。本文遵循以学生为中心的理念,结合传统的教学方法与现代教育技术,研究线性... 详细信息

线性代数是大学本科的一门重要的公共基础课,具有概念多、定理多、性质多等特点,其理论与方法在社会科学、工程技术、人工智能等众多科学领域中具有广泛的应用。本文遵循以学生为中心的理念,结合传统的教学方法与现代教育技术,研究线性代数课程案例式教学的实践。力求激发教师的教学热情,提高学生的学习兴趣,以达到最好的教学效果。

关键词：线性代数案例教学法问题驱动实际应用