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

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.

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

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.

空间解析几何教学改革初探与实践

空间解析几何是大学数学类专业的一门重要基础课,也是数学专业学生深入学习几何学专业知识的基础课程。本文通过在课堂中引入雨课堂、数学史和MATLAB,提高了学生的学习效率。

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

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.

空间解析几何教学改革初探与实践

空间解析几何是大学数学类专业一门重要的基础课,也是数学专业学生深入学习几何学专业知识的基础课程。通过在课堂中引入雨课堂、数学史和MATLAB,提高学生的学习效率。

随机激励下一类含分数阶阻尼的轮胎的振动响应

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.

随机激励下Frenkel-Kontorova模型的纳米摩擦现象

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.

MATLAB在常微分方程教学中的应用

常微分方程是大学数学类专业的核心课程,有着深刻而又生动的实际背景。在常微分方程教学过程中引入软件MATLAB,加深了学生对知识的理解,提高了学生解决问题的能力。

线性代数案例式教学的研究与思考

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。

非高斯过程下混合式能量采集系统的方程识别

混合式能量采集系统由于提高采集效率的优点被广泛地应用于许多领域.在实际环境中,许多表现为跳跃、飞行、罕见跃迁以及间歇性特征的现象能够被非高斯Lévy过程所描述.但有时候精确地建立复杂条件下的混合式能量采集系统方程是较为困难的,尤其是由非高斯Lévy噪声驱动的系统.近年来,随着仿真能力和观测技术的发展,大量的噪声测量数据以及仿真数据能够被收集,并且已有许多研究致力于从大量数据中提取控制法则.本文采用数据驱动的方法,从受非高斯Lévy噪声影响的观测数据中提取系统方程.利用Fokker-Planck方程和非局部Kramers-Moyal公式,获得漂移项、扩散项和Lévy参数的近似表达式,并利用稀疏回归方法识别近似表达式中的系数.本文给出了三个算例,验证了该方法的有效性.结果表明,该方法不仅适用于高斯布朗过程下的混合能量收集系统,也适用于非高斯Lévy过程下的混合能量收集系统.此外,还分析了不同时间步长下区间划分参数与指标Ratio的关系.结果表明,该指标可以作为选择合适的划分参数的标准.

数控加工刀具运动的优化控制

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.