共查询到19条相似文献,搜索用时 62 毫秒
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本文研究了基础激励下含分数阶阻尼的线性系统的响应特性. 当基础激励为简谐激励时, 通过待定系数方法求得系统的动力传递系数; 当基础激励为非简谐周期激励时, 首先将激励展开成傅里叶级数, 然后根据线性系统的叠加原理求得激励中各阶频率成分所引起的动力传递系数, 并根据展开的傅里叶级数解决了数值运算中的不可导问题. 用数值仿真的方法对解析结果进行了验证, 两者符合良好, 证明了解析分析的正确性. 研究表明, 基础激励引起的动力传递系数依赖于分数阶阻尼阶数的值, 通过调节阻尼阶数可以控制动力传递系数的大小. 对于基础激励为非简谐的周期激励情况, 当激励频率一定时, 激励中的高阶频率成分引起的动力传递系数可能大于激励中的低阶频率成分引起的动力传递系数. 因此, 激励中的高阶频率成分所起的作用是不可忽略的. 相似文献
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赵晓龙 《原子与分子物理学报》2014,31(6)
基于分数阶微积分理论和介电分数单元,建立了分数Poynting-Thomson模型,给出了复介电常数的表达式.利用遗传算法结合共轭梯度法,分别求得复介电常数实部和虚部的最优参数,并对E7(主要是氰基联苯化合物)复介电常数实部和虚部的实验数据进行拟合.结果表明能对E7的复介电常数给出很好的描述.另外,由于该法对研究聚合物的复介电常数有广泛的适用性,故该法对研究与E7性质相差很大的聚合物同样适用. 相似文献
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基于分数阶微积分理论和介电分数单元,建立了分数Poynting-Thomson模型,给出了复介电常数的表达式.利用遗传算法结合共轭梯度法,分别求得复介电常数实部和虚部的最优参数,并对E7(主要是氰基联苯化合物)复介电常数实部和虚部的实验数据进行拟合.结果表明能对E7的复介电常数给出很好的描述.另外,由于该法对研究聚合物的复介电常数有广泛的适用性,故该法对研究与E7性质相差很大的聚合物同样适用. 相似文献
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根据分数阶微分定义,采用Adomian分解算法,研究了分数阶简化Lorenz系统的数值解.研究发现,该算法与预估-校正算法相比,求解结果更准确,所耗计算资源和内存资源更少,求解整数阶系统时较Runge-Kutta算法更准确;利用Adomian算法得到的分数阶简化Lorenz系统出现混沌的最小阶数为1.35,比利用预估-校正算法得到的最小阶2.79更小.采用相图、分岔图分析了该系统的动力学特性,基于谱熵算法(SE)和C0算法分析了该系统的复杂度.结果表明,复杂度结果和分岔图一致,说明系统的复杂度同样能反映出系统动力学特性;复杂度随阶数q的增加呈总体减小的趋势,而混沌态时系统参数c变化对系统复杂度影响不大.为分数阶混沌系统应用于信息加密、保密通信领域提供了理论与实验依据. 相似文献
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研究了Caputo导数定义下带有分数阶热流条件的一维时间分数阶热波方程及其参数估计问题.首先,对正问题给出了解析解;其次,基于参数敏感性分析,利用最小二乘算法同时对分数阶阶数α和热松弛时间τ进行参数估计;最后对不同的热流分布函数所构成的两个初边值问题,分别进行参数估计仿真实验,分析温度真实值和估计值的拟合程度.实验结果表明,最小二乘算法在求解时间分数阶热波方程的两参数估计问题中是有效的.本文为分数阶热波模型的参数估计提供了一种有效的方法. 相似文献
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本文通过设计一个新型的含分数阶滑模面的滑模控制器,应用主动控制原理和滑模控制原理,实现了一个新分数阶超混沌系统和分数阶超混沌Chen系统的投影同步.应用Lyapunov理论,分数阶系统稳定理论和分数阶非线性系统性质定理对该控制器的存在性和稳定性分别进行了分析,并得到了异结构分数阶超混沌系统达到投影同步的稳定性判据.数值仿真采用分数阶超混沌Chen 系统和一个新分数阶超混沌系统的投影同步,仿真结果验证了方法的有效性.
关键词:
分数阶滑模面滑模控制器
稳定性分析
分数阶超混沌系统
投影同步 相似文献
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We introduce conformable fractional Nikiforov-Uvarov (NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schrödinger equation (SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods-Saxon potential, and Hulthen potential. 相似文献
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Fractional calculus (FC) is the area of calculus that generalizes the operations of differentiation and integration. FC operators are non-local and capture the history of dynamical effects present in many natural and artificial phenomena. Entropy is a measure of uncertainty, diversity and randomness often adopted for characterizing complex dynamical systems. Stemming from the synergies between the two areas, this paper reviews the concept of entropy in the framework of FC. Several new entropy definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. However, FC is not yet well disseminated in the community of entropy. Therefore, new definitions based on FC can generalize both concepts in the theoretical and applied points of view. The time to come will prove to what extend the new formulations will be useful. 相似文献
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CHEN Yong AN Hong-Li 《理论物理通讯》2008,49(4):839-844
In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the fractional derivative that satisfies the Caputo's definition, we directly extend the applications of the Adomian decomposition method to the new system. As a result, with the aid of Maple, the realistic and convergent rapidly series solutions are obtained with easily computable components. Two famous fractional coupled examples: KdV and mKdV equations, are used to illustrate the efficiency and accuracy of the proposed method. 相似文献
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An approach based on the fractional Fourier transform is proposed for both analysis and synthesis of fiber Bragg gratings. The method is shown to be simple and accurate. A comparison is made with the results of the numerical integration of the full Riccati equation, which are valid for arbitrary reflectivities. The method being very efficient, processing times can be short enough for a real-time control of the writing process, during grating manufacturing. The effects of profile random irregularities on FBG performance are studied, and several examples, useful for design purposes, are given. 相似文献
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Malik Bataineh Mohammad Alaroud Shrideh Al-Omari Praveen Agarwal 《Entropy (Basel, Switzerland)》2021,23(12)
Fuzzy differential equations provide a crucial tool for modeling numerous phenomena and uncertainties that potentially arise in various applications across physics, applied sciences and engineering. Reliable and effective analytical methods are necessary to obtain the required solutions, as it is very difficult to obtain accurate solutions for certain fuzzy differential equations. In this paper, certain fuzzy approximate solutions are constructed and analyzed by means of a residual power series (RPS) technique involving some class of fuzzy fractional differential equations. The considered methodology for finding the fuzzy solutions relies on converting the target equations into two fractional crisp systems in terms of ρ-cut representations. The residual power series therefore gives solutions for the converted systems by combining fractional residual functions and fractional Taylor expansions to obtain values of the coefficients of the fractional power series. To validate the efficiency and the applicability of our proposed approach we derive solutions of the fuzzy fractional initial value problem by testing two attractive applications. The compatibility of the behavior of the solutions is determined via some graphical and numerical analysis of the proposed results. Moreover, the comparative results point out that the proposed method is more accurate compared to the other existing methods. Finally, the results attained in this article emphasize that the residual power series technique is easy, efficient, and fast for predicting solutions of the uncertain models arising in real physical phenomena. 相似文献
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The Hamiltonian formulation for mechanical systems containing Riemman-Liouville fractional derivatives are investigated in
fractional time. The fractional Hamilton’s equations are obtained and two examples are investigated in detail.
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