Dynamic response of spring mounted flexible platforms carring rotating machinery

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The development and stability analysis of a nonlinear growth model for microorganisms

A nonlinear dynamic model of microbial growth is established based on the theories of the diffusion response of thermodynamics and the chemotactic response of biology. Except for the two traditional variables, i.e. the density of bacteria and the concentration of attractant, the pH value, a crucial influencing factor to the microbial growth, is also considered in this model. The pH effect on the microbial growth is taken as a Gaussian function G0e-(f- fc)2/G1, where G0, G1 and fc are constants, f represents the pH value and fc represents the critical pH value that best fits for microbial growth. To study the effects of the reproduction rate of the bacteria and the pH value on the stability of the system, three parameters a, G0 and G1 are studied in detail, where a denotes the reproduction rate of the bacteria, G0 denotes the impacting intensity of the pH value to microbial growth and G1 denotes the bacterial adaptability to the pH value. When the effect of the pH value of the solution which microorganisms live in is ignored in the governing equations of the model, the microbial system is more stable with larger a. When the effect of the bacterial chemotaxis is ignored, the microbial system is more stable with the larger G1 and more unstable with the larger G0 for f0 > fc. However, the stability of the microbial system is almost unaffected by the variation G0 and G1 and it is always stable for f0 < fc under the assumed conditions in this paper. In the whole system model, it is more unstable with larger G1 and more stable with larger G0 for f0 < fc. The system is more stable with larger G1 and more unstable with larger G0 for f0 > fc. However, the system is more unstable with larger a for f0 < fc and the stability of the system is almost unaffected by a for f0 > fc. The results obtained in this study provide a biophysical insight into the understanding of the growth and stability behavior of microorganisms.

A study of the dynamic behaviour of a pulsed column solvent extraction plant

A study has been made of the dynamic behaviour of a nuclear fuel reprocessing plant utilising pulsed solvent extraction columns. A flowsheet is presented and the choice of an extraction device is discussed. The plant is described by a series of modules each module representing an item of equipment. Each module consists of a series of differential equations describing the dynamic behaviour of the equipment. The model is written in PMSP, a language developed for dynamic simulation models. The differential equations are solved to predict plant behaviour with time. The dynamic response of the plant to a range of disturbances has been assessed. The interactions between pulsed columns have been demonstrated and illustrated. The importance of auxillary items of equipment to plant performance is demonstrated. Control of the reprocessing plant is considered and the effect of control parameters on performance assessed.

Nonlinear signalling networks and cell-to-cell variability transform external signals into broadly distributed or bimodal responses

We show theoretically and experimentally a mechanismbehind the emergence of wide or bimodal protein distributions in biochemical networks with nonlinear input-output characteristics (the dose-response curve) and variability in protein abundance. Large cell-to-cell variation in the nonlinear dose-response characteristics can be beneficial to facilitate two distinct groups of response levels as opposed to a graded response. Under the circumstances that we quantify mathematically, the two distinct responses can coexist within a cellular population, leading to the emergence of a bimodal protein distribution. Using flow cytometry, we demonstrate the appearance of wide distributions in the hypoxia-inducible factor-mediated response network in HCT116 cells. With help of our theoretical framework, we perform a novel calculation of the magnitude of cell-to-cell heterogeneity in the dose-response obtained experimentally. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

A mathematical model of coal-fired fluidised bed boilers

A mathematical model of a large coal-fired fluidized bed boiler for power generation is synthesised. The effect of variations in the main parameters of the model on variables such as the background carbon concentrations in the bed, and the transient response of heat evolution are studied. The mechanisms of solids mixing within the bed, combustion and the flow of heat to the boiler tubes are shown to result in a characteristic dynamic response, knowledge of which is essential for the proper control and regulation of a practical system.

Modelling and control of a hybrid stepping motor

The integration of a microprocessor and a medium power stepper motor in one control system brings together two quite different disciplines. Various methods of interfacing are examined and the problems involved in both hardware and software manipulation are investigated. Microprocessor open-loop control of the stepper motor is considered. The possible advantages of microprocessor closed-loop control are examined and the development of a system is detailed. The system uses position feedback to initiate each motor step. Results of the dynamic response of the system are presented and its performance discussed. Applications of the static torque characteristic of the stepper motor are considered followed by a review of methods of predicting the characteristic. This shows that accurate results are possible only when the effects of magnetic saturation are avoided or when the machine is available for magnetic circuit tests to be carried out. A new method of predicting the static torque characteristic is explained in detail. The method described uses the machine geometry and the magnetic characteristics of the iron types used in the machine. From this information the permeance of each iron component of the machine is calculated and by using the equivalent magnetic circuit of the machine, the total torque produced is predicted. It is shown how this new method is implemented on a digital computer and how the model may be used to investigate further aspects of the stepper motor in addition to the static torque.

Mathematical methods in power system stability studies

In this thesis various mathematical methods of studying the transient and dynamic stabiIity of practical power systems are presented. Certain long established methods are reviewed and refinements of some proposed. New methods are presented which remove some of the difficulties encountered in applying the powerful stability theories based on the concepts of Liapunov. Chapter 1 is concerned with numerical solution of the transient stability problem. Following a review and comparison of synchronous machine models the superiority of a particular model from the point of view of combined computing time and accuracy is demonstrated. A digital computer program incorporating all the synchronous machine models discussed, and an induction machine model, is described and results of a practical multi-machine transient stability study are presented. Chapter 2 reviews certain concepts and theorems due to Liapunov. In Chapter 3 transient stability regions of single, two and multi~machine systems are investigated through the use of energy type Liapunov functions. The treatment removes several mathematical difficulties encountered in earlier applications of the method. In Chapter 4 a simple criterion for the steady state stability of a multi-machine system is developed and compared with established criteria and a state space approach. In Chapters 5, 6 and 7 dynamic stability and small signal dynamic response are studied through a state space representation of the system. In Chapter 5 the state space equations are derived for single machine systems. An example is provided in which the dynamic stability limit curves are plotted for various synchronous machine representations. In Chapter 6 the state space approach is extended to multi~machine systems. To draw conclusions concerning dynamic stability or dynamic response the system eigenvalues must be properly interpreted, and a discussion concerning correct interpretation is included. Chapter 7 presents a discussion of the optimisation of power system small sjgnal performance through the use of Liapunov functions.

Variable impedance bearings for large rotating machinery

This thesis describes an investigation which was carried out under the Interdisciplinary Higher Degres (IHD) Scheme of The University of Aston in Birmingham. The investigation, which involved joint collaboration between the IHD scheme, the Department of Mechanical Engineering, and G.E.C. Turbine Generators Limited, was concerned with hydrostatic bearing characteristics and of how hydrostatic bearings could be used to enable turbine generator rotor support impedances to be controlled to give an improved rotor dynamic response. Turbine generator rotor critical speeds are determined not only by the mass and flexibility of the rotor itself, which are relatively easily predicted, but also by the dynamic characteristics of the bearing oil film, pedestal, and foundations. It is because of the difficulty in accurately predicting the rotor support characteristics that the designer has a problem in ensuring that a rotor's normal running speed is not close to one of its critical speeds. The consequence of this situation is that some rotors do have critical speeds close to their normal running speed and the resulting high levels of vibration cause noise, high rotor stresses, and a shortening of bearing life. A combined theoretical and experimental investigation of the effects of mounting the normal rotor journal bearing in a hydrostatic bearing was carried out. The purpose of the work was to show that by changing the oil flow resistance offered by capillaries connecting accumulators to the hydrostatic bearing, the overall rotor support characteristics could be tuned to enable rotor critical speeds to be moved at will. Testing of a combined journal and hydrostatic bearing has confirmed the theory of its operation and a theoretical study of a full size machine showed that its critical speed could be moved by over 350 rpm and that its rotor vibration at running speed could be reduced by 80%.

Applications of Reissner's principle to structural dynamics

The analysis and prediction of the dynamic behaviour of s7ructural components plays an important role in modern engineering design. :n this work, the so-called "mixed" finite element models based on Reissnen's variational principle are applied to the solution of free and forced vibration problems, for beam and :late structures. The mixed beam models are obtained by using elements of various shape functions ranging from simple linear to complex cubic and quadratic functions. The elements were in general capable of predicting the natural frequencies and dynamic responses with good accuracy. An isoparametric quadrilateral element with 8-nodes was developed for application to thin plate problems. The element has 32 degrees of freedom (one deflection, two bending and one twisting moment per node) which is suitable for discretization of plates with arbitrary geometry. A linear isoparametric element and two non-conforming displacement elements (4-node and 8-node quadrilateral) were extended to the solution of dynamic problems. An auto-mesh generation program was used to facilitate the preparation of input data required by the 8-node quadrilateral elements of mixed and displacement type. Numerical examples were solved using both the mixed beam and plate elements for predicting a structure's natural frequencies and dynamic response to a variety of forcing functions. The solutions were compared with the available analytical and displacement model solutions. The mixed elements developed have been found to have significant advantages over the conventional displacement elements in the solution of plate type problems. A dramatic saving in computational time is possible without any loss in solution accuracy. With beam type problems, there appears to be no significant advantages in using mixed models.

High-temperature sensitivity of long-period gratings in B-Ge codoped fiber

We report an investigation of thermal properties of long-period fiber gratings (LPFGs) of various periods fabricated in the conventional B-Ge codoped fiber. It has been found that the temperature sensitivity of the LPFGs produced in the B-Ge fiber can be significantly enhanced as compared with the standard telecom fiber. A total of 27.5-nm spectral shift was achieved from only 10 °C change in temperature for an LPFG with 240-μm period, demonstrating a first ever reported high sensitivity of 2.75 nm/°C. Such an LPFG may lead to high-efficiency and low-cost thermal/electrical tunable loss filters or sensors with extremely high-temperature resolution. The nonlinear thermal response of the supersensitive LPG was also reported and first explained.

Analysis and improvement of performance in LCL filter-based PWM rectifier/inverter application using hybrid damping approach

A hybrid passive-active damping solution with improved system stability margin and enhanced dynamic performance is proposed for high power grid interactive converters. In grid connected active rectifier/inverter application, line side LCL filter improves the high frequency attenuation and makes the converter compatible with the stringent grid power quality regulations. Passive damping though offers a simple and reliable solution but it reduces overall converter efficiency. Active damping solutions do not increase the system losses but can guarantee the stable operation up to a certain speed of dynamic response which is limited by the maximum bandwidth of the current controller. This paper examines this limit and introduces a concept of hybrid passive-active damping solution with improved stability margin and high dynamic performance for line side LCL filter based active rectifier/inverter applications. A detailed design, analysis of the hybrid approach and trade-off between system losses and dynamic performance in grid connected applications are reported. Simulation and experimental results from a 10 kVA prototype demonstrate the effectiveness of the proposed solution. An analytical study on system stability and dynamic response with the variations of various controller and passive filter parameters is presented.

Pabively Q-switched erbium-doped fiber laser using Fe3O4-nanoparticle saturable absorber

We experimentally demonstrate pabively Q-switched erbium-doped fiber laser (EDFL) operation using a saturable absorber (SA) based on Fe3O4 nanoparticles (FONPs). As a type of transition metal oxide, the FONPs have a large nonlinear optical response and fast response time. The FONPbased SA pobebes a modulation depth of 8.2% and nonsaturable absorption of 56.6%. Stable pabively Q-switched EDFL pulses with an output pulse energy of 23.76 nJ, a repetition rate of 33.3 kHz, and a pulse width of 3.2 μs were achieved when the input pump power was 110mW. The laser features a low threshold pump power of > 15mW.

Probability distribution modelling to improve stability in nonlinear MIMO control

We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

Amplitude response of a unilaterally constrained nonlinear micromechanical resonator

Dynamical systems that involve impacts frequently arise in engineering. This Letter reports a study of such a system at microscale that consists of a nonlinear resonator operating with an unilateral impact. The microresonators were fabricated on silicon-on-insulator wafers by using a one-mask process and then characterised by using the capacitively driving and sensing method. Numerical results concerning the dynamics of this vibro-impact system were verified by the experiments. Bifurcation analysis was used to provide a qualitative scenario of the system steady-state solutions as a function of both the amplitude and the frequency of the external driving sinusoidal voltage. The results show that the amplitude of resonant peak is levelled off owing to the impact effect and that the bandwidth of impacting is dependent upon the nonlinearity and the operating conditions.

Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.