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51.
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A cell mapping strategy based on Bellman'sPrinciple of optimality (BP) is proposed to solve the fixed final time optimalcontrol of strongly nonlinear systems with state and control bounds. Thefixed final time problem is transformed into a fixed final time-fixed finalstate optimal control problem by reversing the time. This transformationallows to solve the problem in the framework of the BP. Backward searchingalgorithms within the cell mapping context are used to obtain the solution ofthe new problem. This approach reduces considerably the computational effortrequired for the original problem when it is solved by a forward searchingapproach. The vibration control problem of damped and undamped variablestiffness oscillators with bounded stiffness tuning range is studied todemonstrate the effectiveness of the approach. A numerical study on theconvergence of the method is also presented. 相似文献
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54.
S. Natsiavas 《Nonlinear dynamics》1995,7(3):345-363
This work investigates nonlinear dynamic response of circular rings rotating with spin speed which involves small fluctuations from a constant average value. First, Hamilton's principle is applied and the equations of motion are expressed in terms of a single time coordinate, representing the amplitude of an in-plane bending mode. For nonresonant excitation or for slowly rotating rings, a complete analysis is presented by employing phase plane methodologies. For rapidly rotating rings, periodic spin speed variations give rise to terms leading to parametric excitation. In this case, the vibrations that occur under principal parametric resonance are analyzed by applying the method of multiple scales. The resulting modulation equations possess combinations of trivial and nontrivial constant steady state solutions. The existence and stability properties of these motions are first analyzed in detail. Also, analysis of the undamped slow-flow equations provides a global picture for the possible motions of the ring. In all cases, the analytical predictions are verified and complemented by numerical results. In addition to periodic response, these results reveal the existence of unbounded as well as transient chaotic response of the rotating ring. 相似文献
55.
本文详细地研究了厚度h=h_0ξ~的圆柱壳的轴对称弯曲问题.文中通过引入一个位移函数H(ξ),将该问题的方程组化成一个关于H(ξ)的6阶常微分方程,用广义超几何函数给出问题的精确解. 相似文献
56.
受模糊干扰的再生型颤振的模糊稳定性分析 总被引:3,自引:0,他引:3
首次在机床切削颤振分析中考虑了模糊不确定性因素的影响,利用模糊数学分析方法详细论述了受模糊干扰的再生型颤振的模糊稳定性分析问题,给出了模糊稳定性极限切削宽度集合的可能性分布及其置信区间表达式,最后依据所提出的理论分析方法,经计算编程绘制了模糊稳定性图。 相似文献
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非惯性系下柔性悬臂梁的振动主动控制 总被引:4,自引:2,他引:4
采用变结构控制方法对非惯性系下柔性悬臂梁的振动主动控制进行研究.重点通过算例揭示一次近似模型与传统的零次近似模型的巨大差异,以及变结构方法在控制非惯性系下柔性悬臂梁的稳态振动的有效性.结果表明,当大范围旋转运动角速度较大时,传统零次近似模型不能对动力系统进行正确的数学描述;变结构控制方法能够使得非惯性系下梁的稳态振动得到完全镇定,且该方法对转动角速度变化具有较好的鲁棒性;采用零次近似模型进行控制设计的控制效果将在某一临界角速度条件下出现失效,该临界角速度值大于静止悬臂梁的基频. 相似文献
60.
Variable Order and Distributed Order Fractional Operators 总被引:1,自引:0,他引:1
Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m
2) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m
2 memory may be chosen for a particular application. Memory retentiveness (m
2) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined. 相似文献