Advanced Mathematical Methods for Scientists and Engineers

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The Shock and Vibration Digest

Research and applications of active bearings: A state-of-the-art review

Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences: 357 (1752)

Randomly Transitional Phenomena in the System Governed by Duffing′s Equation (乱流発生の機構に関する研究会報告)

Composite decision-making algorithms for optimisation of hybrid renewable energy systems: Port of Takoradi as a case study

Flexible rotor-bearing system stability is a very important subject impacting the design, control, maintenance and operating safety. As the rotor bearing-system dynamic nonlinearities are significantly more prominent at higher rotating speeds, the demand for better performance through higher speeds has rendered the use of linear approaches for analysis both inadequate and ineffective. To address this need, it becomes important that nonlinear rotor-dynamic responses indicative of the causes of nonlinearity, along with the bifurcated dynamic states of instabilities, be fully studied. The objectives of this research are to study rotor-dynamic instabilities induced by mass unbalance and to use smart materials to stabilise the performance of the flexible rotor-system. A comprehensive mathematical model incorporating translational and rotational inertia, bending stiffness and gyroscopic moment is developed. The dynamic end conditions of the rotor comprising of the active bearing-induced axial force is modelled, the equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. In this thesis the axial force terms included in the equations of motion provide a means for axially directed harmonic force to be introduced into the system. The Method of Multiple Scales is applied to study the nonlinear equations obtained and their stabilities. The Dynamics 2 software is used to numerically explore the inception and progression of bifurcations suggestive of the changing rotor-dynamic state and impending instability. 
In the context of active control of flexible rotors, smart materials particularly SMAs and piezoelectric stack actuators are introduced. The application of shape memory alloy (SMA) elements integrated within glass epoxy composite plates and shells has resulted in the design of a novel smart bearing based on the principle of antagonistic action in this thesis. Previous work has shown that a single SMA/composite active bearing can be very effective in both altering the natural frequency of the fundamental whirl mode as well as the modal amplitude. The drawback with that design has been the disparity in the time constant between the relatively fast heating phase and the much slower cooling phase which is reliant on forced air, or some other form of cooling. This thesis presents a modified design which removes the aforementioned existing shortcomings. This form of design means that the cooling phase of one half, still using forced air, is significantly assisted by switching the other half into its heating phase, and vice versa, thereby equalising the time constants, and giving a faster push-pull load on the centrally located bearing; a loading which is termed ‘antagonistic’ in this present dissertation. The piezoelectric stack actuator provides an account of an investigation into possible dynamic interactions between two nonlinear systems, each possessing nonlinear characteristics in the frequency domain. Parametric excitations are deliberately introduced into a second flexible rotor system by means of a piezoelectric exciter to moderate the response of the pre-existing mass-unbalance vibration inherent to the rotor. The intended application area for this SMA/composite and piezoelectric technologies are in industrial rotor systems, in particular very high-speed plant, such as small light pumps, motor generators, and engines for aerospace and automotive application.

Vibration analysis and intelligent control of flexible rotor systems using smart materials

Abstract Globally, reliable access to electricity improves people’s well-being, provides quality education, and promotes good health. Greenhouse gas emissions associated with fossil fuel combustion have incited an intense interest in low-carbon technologies for power generation. This study analyses the prospect of utilising a solar PV/biogas/battery hybrid energy system to provide electricity for Ghana’s remote communities. The study goal is to utilise locally available renewable energy resources to achieve a cost-effective levelized cost of electricity (LCOE) and mitigate greenhouse gas emissions. Hybrid Optimisation of Multiple Energy Resources (HOMER) software was employed to model and analyse the hybrid energy system’s technical, economic, and environmental aspects. The findings indicate that PV/biogas/battery system perform better than PV/diesel/battery and diesel-only systems in terms of cost and emissions reductions. Also, the LCOE generated from the PV/biogas/battery system is around 0.256 $/kWh. However, this LCOE is only about 64% higher than the LCOE for Ghana’s household residents. The sensitivity test indicates that the PV/biogas/battery system is sensitive to discount rates and capital subsidies, making it attractive for future development. This attests that Ghanaian rural communities without electricity access and with substantial biomass potential are likely to be electrified when given the necessary attention. Moreover, this project could be a viable alternative to rural electrification in Ghana with proper investment support.

https://www.tandfonline.com/doi/pdf/10.1080/23311916.2022.2034376?needAccess=true

Lawrence Atepor

Papers

Composite decision-making algorithms for optimisation of hybrid renewable energy systems: Port of Takoradi as a case study

Vibration analysis and intelligent control of flexible rotor systems using smart materials

Feasibility analysis of solar PV/biogas hybrid energy system for rural electrification in Ghana

A Multicriteria Decision Making Approach for Evaluating Crop Residues for Sustainable Briquette Production in Ghana

A Decision Support System for Evaluating Cooking Fuels for Sustainable Development in Ghana