On one boundary problem for nonlinear stationary controlled system

The object of study is nonlinear stationary controlled system of ordinary differential equations with constant disturbance in the right part. The problem of constructing the synthesising control function providing the transfer of this system from the initial state to the origin is considered. The sufficiently simple for numerical implementation algorithm of solution of the above-mentioned problem is obtained. It is shown that for local null controllability of the considered system, it is sufficient that the conditions of the Kalman's type were satisfied. In addition, the estimates restricting the choice of initial conditions and external disturbances under which the transfer is guaranteed are obtained. The main idea of the method of construction of the desired control function consists in reducing the original problem to stabilisation of a special kind linear non-stationary system and solving the Cauchy problem for an auxiliary system of ordinary differential equations closed by stabilising control. The simplicity of the realisation of this algorithm is determined by the construction of the auxiliary system and its stabilisation that could be obtained by analytical methods. The effectiveness of the method is illustrated by solving the problem of crane control and its numerical simulation.     

Assessment of spray quality from an external mix nozzle and its impact on SQL grinding performance

Spray quality is the critical factor which decides the efficacy of Small Quantity Lubrication (SQL) technology in a high specific energy involved machining process like grinding. Yet, the understanding about spray quality, the actual process mechanics and its effect on machining performance is inadequate. The present work is an attempt to establish a correlation between the spray input variables, quality of the spray and machining performance of SQL grinding through modelling and experiments. Using computational fluid dynamic techniques, the variation of droplet size, droplet velocity, number of droplets and heat transfer coefficient have been analysed at different input parameters and the computed trends have been verified and validated. CFD modelling of spray indicates that it is possible to produce aerosol medium with high heat dissipation ability at moderately high air pressure and low flow rate. It also shows that any increase in atomising air pressure favourably leads to notable increase in wetting area and also results in substantial enhancement in heat dissipation ability. Reduction of residual stress is thus remarkably good. On the other hand, grinding fluid flow rate, if increased, offers significantly better lubricity and reduces the grinding force which also reduces tensile residual stress. Short spell grinding test results are found to be in good agreement with CFD results.     

An overlapping domain decomposition dual reciprocity method

We present a domain decomposition boundary integral equation method for two-dimensional partial differential equations. The overlapping Schwarz method is employed to improve the dual reciprocity boundary element method. The resulting algorithm turns out to be more accurate than a non-overlapping approach previously proposed. Some numerical results showing the improved accuracy and efficiency of the methods are given.     

Stabilization of uncertain boundary control systems

We consider a class of linear infinite-dimensional systems subject to boundary uncertainties, which are linear and time-invariant. Using a deterministic approach to the design of stabilizing feedback controls, uniform exponential stability of the zero state is achieved. Lyapunov techniques are combined with Datko or Ichikawa theory. Three illustrative examples are presented.     

腈纶纤维上油率的稳定控制

从油剂泵、皮辊和钢罗拉等设备构件运行状态考虑，探讨了腈纶纤维上油率的稳定控制问题。     

A note on the satisfaction of the boundary conditions for Chebyshev collocation methods in rectangular domains

The way boundary conditions are imposed when applying Chebyshev collocation methods to Poisson and biharmonic-type problems in rectangular domains is investigated. It is shown that careful selection of the number of collocation points leads to a linear system ofn linearly independent equations inn unknowns.     

Breakdown of oil films and formation of residual films

The breakdown processes of oil films under quasi-static loading have been investigated by using a newly developed steel-oil-mercury system. The relationship between the thickness and breakdown ratio of a hexadecane film is represented by a single master curve independently of the indentation speed, indentation load, and temperature. The master curve shows that the breakdown process of hexadecane includes two stages; one is the decrement of the thickness without breakdown and the other is the decrement of the thickness with a drastic progress of breakdown. By solving a small amount of fatty acid in hexadecane, the thickness increases and the breakdown ratio decreases noticeably; a multilayer residual film supporting normal load is formed between two metal surfaces. Experiments at different temperatures reveal a negative relationship between the temperature and thickness of residual film, which indicates that the residual film is organized by physical interaction rather than chemical interaction. At least under a lower concentration, the residual film appears to consist of not only fatty acid molecules but also hexadecane molecules.     

Three dimensional boundary element analysis of internal cracks under sliding contact load with a spherical indenter

Using boundary element based three dimensional modelling for linear fracture mechanics, we present an analysis of cracking in a homogeneous medium subject to contact load. The proposed iterative solution procedure allows a simultaneous treatment of a reasonable number of partially closed cracks. It is shown that the most probable direction of propagation of a vertical internal crack is strongly dependent on its size compared to the contact radius and its location with respect to the axis of maximum normal load.     

Numerical simulation of flying phenomena of the running tape on rotating drum

This paper analyzes the running mechanism of flexible and thin tape above rotating protrusion through a numerical simulation. The scope of analysis is confined to the phenomena of elastohydrodynamic lubrication between the rotating drum with a protrusion and the running tape. This model is based on the modified Reynolds equation and the equation of plate considering the effect of geometric nonlinearity and geometry of protrusion. Finite element method of Bubnov-Galerkin type is adopted as a numerical simulation technique to solve the above two coupled nonlinear equations. In numerical simulation, the influences of tape tension and protrusion velocity are evaluated in simple model. In complex models, the reciprocal action of two protrusions is simulated.     

Displacement Discontinuity Method for Fracture Mechanics Analysis of Reissner Plates: Static and Dynamic

This paper is concerned with the displacement discontinuity method applied to the shear deformable plates (Reissner’s and Mindlin’s theories) with cracks subjected to static and dynamic loads. Fundamental solutions of dislocation are derived using the Fourier transform method and the Laplace transformation technique. Boundary integral equations are presented in terms of rotations/displacement on the crack surfaces. The Chebyshev polynomials of the second kind are used to evaluate the integral equations with hypersingular kernels on the crack boundaries and determine the stress intensity factors at the crack tips. Comparisons are made with other numerical solutions to demonstrate the proposed method is accurate both for static and dynamic problems.