Singular Trajectories in Multi-Input Time-Optimal Problems: Application to Controlled Mechanical Systems

This paper deals with the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems have certain special properties. These properties are explored and used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated by an application to a time-optimal problem for a class of underwater vehicles.     

灰铸铁石墨形态的研究

文本研究了化学成份与冷却速度及孕育处理对灰铸铁石、墨形态的影响．并对形成的地B、C、D、E、F等六种衣铸铁石墨形态的形成条件作了讨论．     

Investigation of a miniature centrifugal fan

A centrifugal fan was designed with a matching centrifugal volute flow channel in order to investigate a numerical simulation with prototype manufacturing, and to compare with experimental results. The fan configuration was developed according to a fan-design theorem. A model P-60 turbojet engine compressor blade design was adopted for the fan aerodynamic analysis and design. The results were verified using the STAR-CD code. Also, based on the findings, a miniature centrifugal fan was designed and manufactured using a CNC five axes machine. The P–Q performance curves were tested using an AMCA standard 210-85 test chamber apparatus. From the numerical analysis results, the pressure on the suction and pressure surfaces will increase gradually from the inlet to one-half the distance of the hub’s camber line, however, it will increase more rapidly afterwards. In addition, stress-concentration phenomenon occurred at the tip of the suction and pressure surfaces. In other words, the tip was more prone to damage when the fan was operated. Experiments show that the designed fan maximum flow rate Q and static pressure P were 32% and 59%, respectively, which were lower than the commercial fan data at 2000 rpm rotational speed. However, when the rotational speed was increased to 4000 rpm, the maximum flow rate Q and static pressure P were increased to 38% and 82%. This study concluded that a centrifugal fan’s static pressure at high rotational speed is higher than that of an axial-flow fan. Therefore, a centrifugal fan should be chosen if high static pressure cooling or blowing is required. This advanced research investigation is to build up the capabilities of design, analysis, manufacturing, and measurement of a centrifugal fan with an outer diameter smaller than 10 cm.     

Reductive acid leaching of manganese dioxide with glucose: Identification of oxidation derivatives of glucose

The oxidation of glucose during the reductive leaching of pure MnO₂ and manganese ore in sulphuric acid at 90 °C MnO₂ was investigated. The aim was to identify the derivatives and the chemical pathway of glucose oxidation. Organic derivatives were monitored by HPLC using an Aminex HPX-78H column and UV detection. Chromatographic patterns of leaching solutions showed that major compound formed was formic acid. Minor quantities of glycolic, glyceric and traces of gluconic acids were identified. Results suggest that during the leaching reaction, the carbon chain of glucose is shortened by detachment of one carbon atom as formic acid.     

Quasiperiodic forced vibrations of a beam interacting with a nonlinear spring

Summary A simply supported beam with fixed ends and an attached strongly nonlinear spring is considered. As the forced bending vibrations of the beam have moderate amplitudes, the stretching force is a nonlinear function of the deflection. The vibrations are presented as a series with respect to the modes of the beam without attachment. Applying the Bubnov-Galerkin procedure, an infinite system of ordinary differential equations is derived. Using the multiple scales method, the quasiperiodic vibrations in the region of the combination resonance are analyzed in the paper. The system vibrations, when the nonlinear spring is attached in different points, are analyzed. Applicability of the nonlinear spring for mitigation of a combination resonance is discussed.     

Numerical thermo-elastic analysis of singularities in two-dimensions

Linear elastic two-dimensional problems with singular points subjected to steady-state temperature distribution are considered. The stress tensor in the vicinity of the singular points exhibits singular behavior characterized by the strength of the singularity and the associated thermal stress intensity factors (TSIFs). It is shown that the TSIFs and the strength of the stress singularity can be obtained using the principle of complementary energy together with the modified Steklov method and the p-version of the finite element method. Importantly, the proposed method is applicable not only to singularities associated with crack tips, but also to multi-material interfaces and non-homogeneous materials. Numerical results of crack-tip singularities in a rectangular plate and singular points associated with a two-material inclusion are presented.Research performed while the author served as a visiting assistant professor at the Center for Computational Mechanics, Washington University, St. Louis, Missouri 63130, USA.     

Dynamics of cracked hollow beams

The finite element method with normal quadrilateral plate elements is used for the determination of the bending compliance of orthogonal full and open hollow section beams with transverse cracks. Computed results are compared with those from theory for the full rectangular sections and with experiments performed with rectangular hollow sections. The effect of such cracks on the dynamic response of channel-section beams is investigated. Such analysis is of importance for the identification of cracks in steel structures.     

Small volume PCR in PDMS biochips with integrated fluid control and vapour barrier

In this paper we demonstrate a new method for microfabricating PDMS devices that controls vapour diffusion, thereby reducing water loss at elevated temperatures and greatly increasing the reliability of the PCR. In the past, the vapour and liquid diffusion properties of the PDMS material in microfluidic devices have impaired performance. We show that this water loss is primarily due to vapour diffusion from the PDMS biochip and by implanting a polyethylene vapour barrier layer in the PDMS, the overall fluid loss was almost eliminated (reduced by a factor of 3). We have also developed a procedure to ensure irreversible bonding between the PDMS and the implant. With this improved microfabrication method we demonstrate the feasibility and advantages of performing small volume PCR genetic amplification (i.e. with less than 2 μl of PCR sample) within a PDMS–glass hybrid biochip. Diaphragm pumps and pinch-off valves were integrated in the system and these enabled fluid retention during the amplification stage and will facilitate higher levels of on-chip automation.     

Procedures for analysis of strain transfer in the acetabular region in vitro

The failure of acetabular cups via loosening, migration or fracture is partially related to the stress distribution existing in the acetabular region. The complexity of the investigation of these stresses demands the application of a variety of model testing techniques involving combined embedded strain gauging, finite element analysis, transmission and reflective photoelasticity and crack propagation studies. The application of these procedures are described and the difficulties of obtaining representative loadings and restraints are commented upon.