The aim of this work has been to develop new knowledge about macromodelling of microsystems. Doing that, we have followed two different approaches for generating macromodels, namely model order reduction and lumped modelling. The latter is a rather mature method that has been widely recognized and used for a relatively long period of time. Model order reduction, on the other hand, is a relatively new area still in rapid development. Due to this, the parts considering reduced order modelling is strongly biased towards methodology and concepts, whereas parts on lumped modelling are biased towards systems and devices. In the first part of this thesis, we focus on model order reduction. We introduce some approaches for reducing model order for linear systems, and we give an example related to squeeze-film damping. We then move on to investigate model order reduction of nonlinear systems, where we present and use the concept of invariant manifolds. While the concept of invariant manifolds is general, we utilize it for reducing models. An obvious advantage of using invariant manifold theory is that it offers a conceptually clear understanding of effects and behaviour of nonlinear system. We exemplify and investigate the accuracy of one method for identifying invariant manifolds. The example is based on an industrialized dual-axis accelerometer. A new geometrical interpretation of external forcing, relating to invariant manifolds, is presented. We show how this can be utilized to deal with external forcing in a manner consistent with the invariance property of the manifold. The interpretation also aids in reducing errors for reduce models. We extend the asymptotic approach in a manner that makes it possible to create design-parameter sensitive models. We investigate an industrialized dual-axis accelerometer by means of the method and demonstrate capabilities of the method. We also discuss how manifolds for nonlinear dissipative systems can be found. Focusing on lumped modelling, we analyse a microresonator. We also discuss the two analogies that can be used to build electrical equivalents of mechanical systems. It is shown how the f → V analogy, linking velocity to voltage, is the natural choice. General properties of lumped modelling are investigated using models with varying degrees of freedom. Finally, we analyse an electromagnetic system, intended for levitating objects, and we demonstrate the scaling effects of the system. Furthermore, we prove the intrinsic stability of the system, although the floating disc will be slightly tilted. This is the first analysis done assessing the stability criterions of such a systems. The knowledge arising from the analysis gives strong indications on how such a system can be utilized, designed, and improved.

The purpose of this study is to investigate the hydrodynamic properties of an oyster floating raft system under environmental loadings. The floating raft system is an important facility for raising oyster in the near shore area of Tainan, Taiwan. The reasons for this kind of oyster culture being main income source for local fish farmers are as the following features: (1) low cost for the farming system, (2) easily to be installed in the field, and (3) easily to be harvested. Due to the raft structure could not withstand the impact of heavy storms; most of the oyster rafts are towed into harbor to avoid damage before the onset of typhoon. Since some unexpected violent sea states may occur and severely affect the integrity of raft system, the investigation of the hydrodynamic properties of a floating raft system is essential for oyster culture in the open sea. This study includes two parts: numerical simulation and physical modeling. In numerical simulation, a lumped mass method with a Morison type of relative motion equation are adopted to calculate the drag and inertial forces on raft components and then are equally divided to the associated nodes to form a system of motion equations based on Newton¡¦s second law. Through the fourth-order Runge-Kutta method, the dynamic performance of the oyster raft system can be obtained. To verify the numerical model, a physical model was carried out in a wave tank (35x1x1.2 m), and the results of dynamic performance of numerical model show good agreement with measurements. A case study of an in situ oyster farming system located near-shore of Tainan region is analyzed by the developed numerical model to investigate the maximum mooring tension, the optimal gap between rafts, and the required length of mooring line. These specifications are crucial to the shell fish farmers for their floating raft system to be survived in the strong currents and waves. The results showed that the optimum configuration for a raft system generated the lowest mooring tension is as the follows: the space between oyster rafts is about a length of oyster raft; the length of mooring line is three times of the water depth, which is consistent with the present practice of shell fish farmers adopting 3~4 times of water depth; the appropriate embedment anchor weight is 70 kg but the anchorage should be the type used by the farmers in Penghu county. Finally, this work intends to offer a guideline for the installation of oyster raft systems in the field, and anticipate minimizing the damage during the unexpected heavy sea states.

There are four types of oyster aquaculture such as oyster plug rod, horizontal hanging scaffold, pontoon-style longline, and floating raft system. This study is to investigate the mooring tension of an oyster floating raft system under environmental loadings. According to the hydrodynamic experimental test, the horizontal fluid velocity has a retarded phenomenon when encountering the front part of structure, and then gradually reduces to a stable situation after the second floating rod. The phenomenon is identified as shielding effect for the raft system and has been used as a shielding coefficient to modify the fluid velocity in the computation program. The dynamic analysis of floating raft system under random wave interaction is investigated numerically and experimentally. The lumped mass method is applied to divide the structure into many nodes and elements. A modified Morison equation dealing with moving structure components is used to calculate the environmental forces on the elements. Further, the forces on elements are divided equally into neighboring nodes to form the equation of motion based on Newton¡¦s second law. Finally, the 4th-order Runge-Kutta (RK4) method is used as a time marching scheme to predict the displacement and velocity of nodes for the next time step. The results of time series and spectrum analysis of mooring tension show good agreement between numerical predictions and experimental data. This paper has further expanded to predict the field oyster raft system in an open sea, and offers some useful information to the oyster farmers in terms of improving the structure safety.

Offshore culture becomes the most attractive industry in last decades because of overfishing and excessively pumping groundwater causing land subsidence social problems. Oyster culture is one of offshore culture with several advantages such as easy set-up and without feeding cost. In this study, we focus on a longline-style oyster aquaculture system because it is recyclable, high growing efficiency and advanced technique against traditional tidal flat culture. This study establishes a numerical model through a lumped mass method, then employs fourth order Runge-Kutta method to solve the system of motion equations and evaluates the tension on the anchor rope. The results show the discrepancy between the numerical model and experimental data is lower than 4% in current-only situation, and similarly in wave-only situation the discrepancy is lower than 6%. The comparison results indicate that the numerical model is capable to predict the environmental loadings on longline-style oyster culture system. An in-situ case study of a longline-style oyster aquaculture system via regular and random waves, located in the Penghu Bay, is investigated based on the sea-state, Chebi Typhoon occurred in June, 2001, causing a catastrophic damage to the cage aquaculture. The conclusions of dynamic responses of the case study may be utilized as guidance for the local oyster farmers to build and protect their oyster culture system in the Bay.

Developing full-wave simulators for high-frequency circuit simulation is a topic many researchers have investigated. Generally speaking, methods invoking analytic pre-processing of the device¡¦s V-I relations (admittance or impedance) are computationally more efficient than methods employing numerical procedure to iteratively process the device at each time step. For circuits providing complex functionality, two-port or possibly multi-port devices whether passive or active, are sure to appear in the circuits. Therefore, extensions to currently available full-wave methods for handling one-port devices to process multi-port devices would be useful for hybrid microwave circuit designs. In this dissertation, an efficient scheme for processing arbitrary multi-port devices in the finite-difference time-domain (FDTD) method is proposed. The device¡¦s admittance is analytically pre-processed and fitted into one grid cell. With an improved time-stepping expression, the computation efficiency is further increased. Multi-port devices in the circuit can be systematically incorporated and analyzed in a full-wave manner. The accuracy of the proposed method is verified by comparison with results from the equivalent current-source method and is numerically stable.

FDTD is a numerical method that uses the second-order central-difference method to discrete the Maxwell¡¦s equations in differential form, and positioning electromagnetic field in space grids and time grids. It is applied to analyze many electromagnetic problems in time domain. In this report the FDTD method is extended to include lumped-elements (as resistor, inductor, capacity),and nonlinear elements(as diode, transistor) to combine the circuit elements and electromagnetic fields, it¡¦s so called LE-FDTD algorithm. The first, we will introduce the theory derivations and simulate some circuit structures in 2D, and then in order to simulate the real circuits, we will extend this algorithm in 3D to make full-wave analysis.

The purpose of this study is improve the cage net volume deformation during typhoon attacking. A special bottom collar system is to substitute the sinkers system. The Research contents include the numerical development and the hydrodynamic physical model test in a wave tank. The numerical model is based on the lumped mass method to set up the equation of motion of the whole cage net system; meanwhile the solutions of equation have been solved through the Runge-Kutta fifth order method. The hydrodynamic physical model tests have been carried out to verify the goodness of the numerical model. The research results are as follows. The sinker system¡¦s numerical model simulation indicates that the error of the maximum tension at anchor is about 4.54% higher than the physical model results, and the error of net deformation rate is about 8.04% higher. While the bottom collar system¡¦s numerical model simulation indicates that the error of the maximum tension at anchor is 6.34% lower than physical model results, and the error of net deformation rate is 3.82% lower. The physical model show that the minimum side projection area deformation rates of net in the bottom collar system is about 4~6% higher than the sinker system¡¦s. According to the conclusions of this study, the presented numerical model is capable to predict the whole cage net system performance and indicates that the bottom collar system is practically feasible in improving the cage net volume deformation.

The finite-Difference Time Domain method (FDTD) derives the discrete form of the Maxwell¡¦s equations with second-order central difference with the electromagnetic distribution of the Yee space lattice, and computes the value of the electric field and magnetic field in the simulation space using leapfrog for time derivatives. This method is different from the frequency domain method which needs to analyze its value individually (ex. Finite Element method). The frequency domain method needs to take a long time for analyzing the response on each spectrum point when the bandwidth is very wide. The advantage of time domain analysis is to obtain the complete frequency response from the simulation value through Fourier Transform method. It¡¦s difficult to combine the electromagnetic analysis with the lumped circuit simulation in current simulation CAD. Thereby the performance of the simulation result and the practical implementation always causes error. The FDTD method is the full-wave algorithm which can also simulate the lump element, nonlinear element or active element in simulation space by linking to SPICE or S-parameter. In this dissertation, an efficient scheme for processing arbitrary one-port devices in the finite-difference time-domain (FDTD) method is proposed. Generally speaking, methods invoking analytic pre-processing of the device¡¦s V-I relations (admittance or impedance) are computationally more efficient than methods employing numerical procedure to iteratively process the device at each time step. The accuracy of the proposed method is verified by comparison with results from the equivalent current-source method and is numerically stable.

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Thermal modelling is of great importance in all electric machines but especially in permanent magnet synchronous machines (PMSMs). The thermally fragile permanent magnets (PMs) can more easily be demagnetized at high temperatures. When high speed machines are considered, heat extraction surfaces are small due to the higher energy density. This thesis focuses on the thermal modelling of a high speed slotless PMSM using analytical techniques. From literature it is clear that analytical distributed models have not reached its full potential in thermal modelling of electric machines. Thermal experiments on high speed electric machine, including rotor PM temperature measurements are not commonly found in literature. The thermal behaviour of each component of the machine is influenced by the overall temperature distribution. The widely used lumped parameter (LP) cylindrical component model derived by Mellor et al. is used to derive a LP model of the entire machine. A two dimensional (2-D) analytical distributed model is derived for the rotor PM using the separation of variables method. Three of the boundaries are assumed to be of the convection type and the fourth of constant heat flow type. Different convection coefficients are assumed to exist in the radial and axial directions. The distributed model is verified using COMSOL R and good correlation is shown. The distributed model is used to determine the temperature distribution in the PM and the convection heat flow in the axial direction. Loss calculation is an integral part of thermal modelling. Temperature changes in an electric machine is due to the interaction between the heat generation (losses) and heat removal. The losses found in a high speed slotless PMSM are investigated. A 2-D analytical magnetic model is used to determine the stator lamination loss as well as the stator winding eddy current loss. A simple LP model is derived for the rotor eddy current loss. Due to the relatively large resistivity of the shielding cylinder and PM material, the rotor eddy current loss is a significant part of the total machine loss. The tangential current width is determined empirically in this thesis but a 3-D distributed model which includes end space effects and skin depth could also be used. A large part of thermal modelling is empirically based. The convection and interface resistances are determined through a set of experiments in this thesis. The measured and calculated convection coefficients correlated well for both forced and natural convection cooling. A large temperature increase found during the no-load test can be attributed to large bearing loss, possibly due to axial loading. The LP model is modified to include the phenomena found during the experiments. The thermal model is used to predict the temperatures of a high speed PMSM at rated load and speed. Although the PM is not heated above the Curie temperature, demagnetization is still possible. According to the model, the machine will not be able to operate at full load and speed for extensive periods due to mechanical stress limits being exceeded. The temperature distribution of the PM could not be verified since the temperatures in the air gap and end space could not be measured. It is expected that axial heat flow will be larger than what is currently predicted by the distributed model. A sensitivity analysis was used to investigate the influence of the thermal resistances and losses on the machine temperatures. Methods for reducing the rotor eddy current loss and interface resistances are also discussed. The first contribution of this thesis is the 2-D analytical distributed model for the PM of a high speed PMSM. Hot spots and 2-D heat flow can be analysed using this model. Combining the LP and 2-D analytical distributed models is another contribution. This combines the simplicity and fast solution times of the LP model with the 2-D thermal distribution of the analytical distributed model. The systematic experimental investigation of the thermal behaviour of a high speed PMSM is a further contribution. / Thesis (Ph.D. (Electrical Engineering))--North-West University, Potchefstroom Campus, 2011.