Forced vibrations of a turbine blade undergoing regularized unilateral contact conditions through the wavelet balance method

The method of weighted residuals can efficiently enforce time‐periodic solutions of flexible structures experiencing unilateral contact. The harmonic balance method (HBM) based on Fourier expansion of the sought solution is a common formulation, although wavelet bases that can sparsely define nonsmooth solutions may be superior. This hypothesis is investigated using a full three‐dimensional blade with unilateral contact conditions on a set of N_c discrete contact points located at its tip. The unilateral contact conditions are first regularized, and a distributional formulation in time is introduced, allowing trial functions to properly approximate in the time domain the solution to the governing equations. The mixed wavelet Petrov–Galerkin solutions are found to yield consistent or better results than HBM, with higher convergence rates and seemingly more accurate contact force prediction. Copyright © 2014 John Wiley & Sons, Ltd.     

一种基于GNC和增广拉格朗日对偶的非凸非光滑图像恢复方法

逐步非凸方法（GNC）和增广拉格朗日对偶在非凸非光滑图像恢复中有较高的恢复性能.然而分别使用这两种方法时GNC不能够保证全局收敛,增广拉格朗日对偶不能获得有效的初始值.为克服上述缺陷,本文通过转换原始问题为等式约束优化问题推出了一种基于GNC和增广拉格朗日对偶的组合图像恢复方法,并对其收敛性严格证明.该方法不仅可以获得有效的初始值,同时不要求问题具有凸性和光滑性.更多地,一个自适应能量函数通过对偶迭代而得到.实验结果表明推出的方法可以有效地提高图像恢复质量和算法效率.     

On the Control of a One Degree-of-Freedom Juggling Robot

This paper is devoted to the feedback control of a one degree-of-freedom (dof) juggling robot, considered as a subclass of mechanical systems subject to a unilateral constraint. The proposed approach takes into account the whole dynamics of the system, and focuses on the design of a force input. It consists of a family of hybrid feedback control laws, that allow to stabilize the object around some desired (periodic or not) trajectory. The closed-loop behavior in presence of various disturbances is studied. Despite good robustness properties, the importance of good knowledge of the system parameters, like the restitution coefficient, is highlighted. Besides its theoretical interest concerning the control of a class of mechanical systems subject to unilateral constraints, this study has potential applications in non-prehensile manipulation, extending pushing robotic tasks to striking-and-pushing tasks. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solving a continuous nonlinear problem of optimal set partition with arrangement of subset centers in the case of a convex objective functional

A continuous nonlinear single-commodity problem of optimal partition of a set Ω in an n-measurable Euclidean space into disjoint subsets with arrangement of their centers is analyzed using equality and inequality constraints in the case of a convex objective functional. A method and algorithm are proposed to solve this problem. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 134–152, March–April 2008.     

Complementary finite-element method for finite deformation nonsmooth mechanics

The complementary finite-element programming method and algorithm for solving finite deformation problems in nonsmooth mechanics are presented. This method provides a dual approach for the numerical solutions of the mixed boundary-value problem governed by nonsmooth physical laws. Application to non-smooth plastic flow is illustrated.     

非线性梯度下降算法理论及其对Hopfield网络稳定性的分析

讨论目标函数可分解为凸函数和一个广义可微函数之差的优化问题,对于可微函数利用线性函数进行局部逼近，从而求得目标函数的一个凸函数逼近,然后求解凸优化问题得到最优解的一个更好近似；重复这个过程直到结束，利用广义梯度和凸函数的性质，证明得到的优化算法为全局收敛的下降算法。它所求解的优化问题可以具有光滑或非光滑的目标函数,同时可以利用它的全局收敛性分析Hopfield网络的稳定性。     

一类非线性控制系统可生存性的判别

讨论了一类微分包含可生存性的判别问题. 基于非光滑分析理论，通过判别一个线性不等式组的相容性,或等价地求解一个辅助的线性规划问题,来判别此微分包含在一点处是否满足可生存性条件.     

非光滑广义凸多目标规划的一般对偶理论

对一大类非光滑函数提出了几种很弱的广义凸条件,然后将Mond和Weir关于光滑数学规划的一般对偶理论推广到非光滑广义凸多目标规划的情形。     

土壤与非光滑表面减粘降阻界面动力学模型

根据土壤车辆系统力学的理论，对具有普遍意义的波纹非光滑形态建立了波纹形仿生推土板切削粘性土壤时的切削阻力力学模型，并进行了实验验证，计算值与实测值吻合很好，同时进行了非光滑表面减粘降阻机理分析。