Optimal control of nonholonomic motion planning for a flee-falling cat

The nonholonomic motion phnning of a free-falling cat is investigated.Nonholonomicity arises in a free-falling cat subject to nonintegrable angle velocity constraints or nonintegrable conservation laws.When the total angular momentum is zero,the motion equation of a free-falling cat is established based on the model of two symmetric rigid bodies and conservation of angular momentum.The control of system can be converted to the problem of nonholonomic motion planning for a free-falling cat.Based on Ritz approximation theory,the Gauss-Newton method for motion planning by a falling cat is proposed.The effectiveness of the numerical algorithm is demonstrated through simulation on model of a free-falling cat.     

Optimal control of nonholonomic motion planning for a free-falling cat

The nonholonomic motion planning of a free-falling cat is investigated. Non-holonomicity arises in a free-falling cat subject to nonintegrable angle velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the motion equation of a free-falling cat is established based on the model of two symmetric rigid bodies and conservation of angular momentum. The control of system can be converted to the problem of nonholonomic motion planning for a free-falling cat. Based on Ritz approximation theory, the Gauss-Newton method for motion planning by a falling cat is proposed. The effectiveness of the numerical algorithm is demonstrated through simulation on model of a free-falling cat.     

Wave motion in a thick cylindrical rod undergoing longitudinal impact

The paper presents a new formulation and the comprehensive analytical solution to longitudinal impact of thick elastic rods. In contrast to previously published works, the solution is derived based on the exact three-dimensional theory without using the classic Skalak’s decomposition. This new direct approach makes the analytical solution more transparent and much easier to obtain. The resulting formulas for basic mechanical quantities are derived using the residue theorem and their evaluation is made in such a way that the accuracy of presented results is significantly higher than those previously published. Based on these results, the transient wave phenomena occurring in the rods are discussed in detail. Additionally, the solution in time domain is obtained also by semi-analytical approach making use of numerical inverse Laplace transform. It is shown that the selected FFT based algorithm is accurate and robust enough, such that the analysis of wave motion in spatial and time domain can be done effectively preserving the results precision. Presented solution can be used as a benchmark for verification of numerical and experimental methods applied to elastodynamics problems.     

Correct modeling for gaussian distributed heat source on a finite thin rod

One of the main problems which arise during the computation of welding processes is the development of a proper mathematical model for the distribution of heat Power Density of a moving heat source. Though there has been an extensive research done following Pavelic who had proposed a formula of a Circular Source of Heat (see Fassani (J Brazilian Soc Mech Sci 25:302–305, 2003) in 1969 for the first time, no one has yet been able to give a crucial scientific idea for determining the heat source parameters of Gaussian distributed spatial heat source. Due to lack of clear mathematical modeling of Gaussian distributed heat Power Density, an accurate formula needs to be developed. In this paper, I have proposed a completely new idea to define Gaussian distributed spatial heat source for the one dimensional case. A simple and relevant method has been adopted to elucidate the new idea.     

Stability of a periodic motion of a rod suspended by an ideal thread

We consider the plane motion of a rod suspended by an ideal thread in a homogeneous field of gravity. We study the nonlinear orbital stability problem for the translational periodic motion of the rod along the vertical. Depending on two dimensionless parameters of the problem, we make conclusions on orbital instability, stability for a majority of initial conditions, or formal stability.     

漂浮基柔性两杆空间机械臂的关节运动鲁棒控制与柔性振动最优控制Robust joint motion control and vibration optimal control for a free-floating two-flexible-link space manipulator

讨论了载体位置、姿态均不受控情况下,具有有界干扰及有界未知参数的漂浮基柔性两杆空间机械臂的具有鲁棒性的关节运动控制与柔性振动最优控制算法设计问题。首先选择合理的联体坐标系,利用拉格朗日方程并结合动量守恒原理得到漂浮基柔性两杆空间机械臂系统的动力学方程。通过合理选择联体坐标系与利用奇异摄动理论,实现了两个柔性杆柔性振动之间、关节运动与两柔性杆柔性振动的解耦,得到了柔性两杆空间机械臂的慢变子系统与柔性臂快变子系统。针对两个子系统设计相应的控制规律,即增广鲁棒慢变子系统控制律与柔性臂快变子系统最优控制律,这两个相应的子系统控制规律综合到一起构成飘浮基柔性两杆空间机械臂总的关节运动与臂柔性振动控制的组合控制律。系统的数值仿真证实了方法的有效性。该控制方案不需要直接测量漂浮基的位置、移动速度和移动加速度。     

Homogenized equations of motion for rod bundles in fluid with periodic structure

Summary Homogenized or averaged equations of motion are deduced for linear dynamic fluid-structure interactions of rod bundles immersed in an acoustical fluid. The equations define an effective density tensor which couples the fluid and rod accelerations. In the pressure wave equation a sound speed tensor arises. The theory assumes that the bundle consists of a periodic lattice of cells with diameters which are very small in comparison to the bundle diameter and that cell averages are smooth functions in space and time. The derivation is based on Hamilton's principle. For the specific case of circular cylindrical rods in a square pattern the tensors are given numerically and the fluid-structure interaction effects are discussed.

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Übersicht Es werden homogenisierte oder gemittelte Bewegungs-Gleichungen für lineare, dynamische Fluid-Struktur-Wechselwirkungen von Stabbündeln in einem akustischen Fluid abgeleitet. Die Gleichungen definieren einen Tensor der effektiven Dichten, der die Fluid- und Stabbeschleunigungen koppelt. In der Wellengleichung für das Druckfeld tritt ein Schallgeschwindigkeits-Tensor auf. Die Theorie unterstellt, daß das Bündel aus einem periodischen Gitter von Zellen besteht, deren Abmaße sehr klein sind im Vergleich zum Bündeldurchmesser und daß Zellen-Mittelwerte glatte Funktionen in Raum und Zeit sind. Die Ableitungen gehen aus vom Hamiltonschen Prinzip. Für den Sonderfall von kreisförmigen, zylindrischen Stäben in quadratischer Anordnung werden die Tensoren zahlenmäßig angegeben und die Effekte der Fluid-Struktur-Wechselwirkungen diskutiert.

     

Experimental study on convective heat transfer coefficient around a vertical hexagonal rod bundle

Research on convective heat transfer coefficient around a rod bundle has many diverse applications in industry. So far, many studies have been conducted in correlations related to internal and turbulent fully-developed flow. Comparison shows that Dittus-Boelter, Sieder-Tate and Petukhov have so far been the most practical correlations in fully-developed turbulent fluid flow heat transfer. The present study conducts an experimental examination of the validity of these frequently-applied correlations and introduces a manufactured test facility as well. Due to its generalizibility, the unique geometry of this test facility (hexagonal arranged, 7 vertical rods in a hexagonal tube) can fulfil extensive applications. The paper also studies the major deviation sources in data measurements, calibrations and turbulence of fluid flow in this. Finally, regarding to sufficient number of experiments in a vast fluid mean velocity range (3,800?<?Re?<?40,000), a new curve and correlation are presented and the results are compared with the above mentioned commonly-applied correlations.     

一类多体系统非完整运动最优规划的拟牛顿算法

研究带有非完整约束的一类多体系统运动规划问题。多体系统中的非完整约束通常是由不可积的速度约束或不可积的守恒律引起。在系统动量和动量矩守恒情况下,动力学方程降阶为非完整形式约束方程,系统的控制问题可转化为无漂移系统的非完整运动规划问题。文中首先导出具有多体开链系统的非完整运动模型。利用最优控制理论和最优化技术,采用输入参数化的方法将连续的最优控制问题转化为离散的最优控制问题,提出一种非完整多体系统运动规划的拟牛顿算法。最后将该方法用于自由漂浮的空间三连杆机构,仿真结果验证了该方法的有效性。     

Incremental deformation model for a rod

A nonlinear deformation model for a rod with rigid cross sections is proposed. A complete system of local incremental equations, a variational equation equivalent to this system, and an equation of virtual work are formulated. Numerical analysis of the deformation of a ring transmission is performed. Institute of Computer Modeling, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 229–235, July–August, 1999.     

Transient heat conduction from a vertical rod buried in a semi-infinite medium with variable heating strength

In this paper, a variable heating strength model (VHS model) is developed to predict transient heat conduction from a vertical rod buried in a semi-infinite medium. Unlike past studies, the current VHS model permits a VHS along the rod. Both axial heat conduction through the rod and lateral heat conduction to the surrounding ground are modeled. A derived distribution of axial heating strength is then applied to a finite line heat source model to predict transient temperature changes in the surrounding medium. The predicted results show how the rod’s radius and ground’s thermal conductivity affect the vertical variation of heating strength and temperature response. Additional simulations predict the long-term temperature increase in the ground, due to a power transmission tower installed in a region of initially frozen ground.     

采用包络-准则法优化考虑瞬态传热的薄板结构

刚度和强度是薄板结构的两个主要性能。在瞬态传热过程中,考虑热-力耦合,随时间和空间变化的非均匀温度场在结构中会引起热变形和热应力,温度场随时间变化的规律和空间分布依赖于板的厚度变化,进而影响板的刚度和强度。因此,考虑瞬态传热的薄板优化问题具有更强的非线性,更加难以求解。本文给出一种包络-准则方法处理这类结构优化问题。首先,针对外力荷载,进行一个结构柔顺性的优化设计;以这一设计为基础,通过瞬态热-力耦合分析及优化准则,计算多个时刻的优化设计变量并取其包络,对上述优化结果进行迭代修正,以消除瞬态温度场作用下较高的局部应力。优化算例表明,该方法对于考虑瞬态传热薄板优化问题有效。     

A numerical study of EGS heat extraction process based on a thermal non-equilibrium model for heat transfer in subsurface porous heat reservoir

With a previously developed numerical model, we perform a detailed study of the heat extraction process in enhanced or engineered geothermal system (EGS). This model takes the EGS subsurface heat reservoir as an equivalent porous medium while it considers local thermal non-equilibrium between the rock matrix and the fluid flowing in the fractured rock mass. The application of local thermal non-equilibrium model highlights the temperature-difference heat exchange process occurring in EGS reservoirs, enabling a better understanding of the involved heat extraction process. The simulation results unravel the mechanism of preferential flow or short-circuit flow forming in homogeneously fractured reservoirs of different permeability values. EGS performance, e.g. production temperature and lifetime, is found to be tightly related to the flow pattern in the reservoir. Thermal compensation from rocks surrounding the reservoir contributes little heat to the heat transmission fluid if the operation time of an EGS is shorter than 15 years. We find as well the local thermal equilibrium model generally overestimates EGS performance and for an EGS with better heat exchange conditions in the heat reservoir, the heat extraction process acts more like the local thermal equilibrium process.     

Variational principle for a special Cosserat rod

In this paper, we describe the nonlinear models of a rod in three-dimensional space based on the Cosserat theory. Using the pseudo-rigid body method and variational principle, we obtain the motion equations of a Cosserat rod including shear deformations.