Solutions to physical problems described by Differential Equationson complex domains are in except for special cases almost impossibleto find. This turns our interest toward numerical approaches. Sincethe size of the numerical models tends to be very large when handlingcomplex problems, the area of model reduction is always a hot topic. Inthis report we look into a model reduction method called ComponentMode Synthesis. This can be described as dividing a large and complexdomain into smaller and more manageable ones. On each of thesesubdomains, we solve an eigenvalue problem and use the eigenvectorsas a reduced basis. Depending on the required accuracy we mightwant to use many or few modes in each subdomain, this opens for anadaptive selection of which subdomains that affects the solution most.We cover two numerical examples where we solve Helmholtz equationin a linear elastic problem. The first example is a truss and the othera gear wheel. In both examples we use an adaptive algorithm to refinethe reduced basis and compare the results with a uniform refinementand with a classic model reduction method called Modal Analysis. Wealso introduce a new approach when computing the coupling modesonly on the adjacent subdomains.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis (M. Eng. Sc.)--University of Queensland, 2002. / Includes bibliographical references.

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Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references. Also available via the Internet.

abstract: Flow measurement has always been one of the most critical processes in many industrial and clinical applications. The dynamic behavior of flow helps to define the state of a process. An industrial example would be that in an aircraft, where the rate of airflow passing the aircraft is used to determine the speed of the plane. A clinical example would be that the flow of a patient's breath which could help determine the state of the patient's lungs. This project is focused on the flow-meter that are used for airflow measurement in human lungs. In order to do these measurements, resistive-type flow-meters are commonly used in respiratory measurement systems. This method consists of passing the respiratory flow through a fluid resistive component, while measuring the resulting pressure drop, which is linearly related to volumetric flow rate. These types of flow-meters typically have a low frequency response but are adequate for most applications, including spirometry and respiration monitoring. In the case of lung parameter estimation methods, such as the Quick Obstruction Method, it becomes important to have a higher frequency response in the flow-meter so that the high frequency components in the flow are measurable. The following three types of flow-meters were: a. Capillary type b. Screen Pneumotach type c. Square Edge orifice type To measure the frequency response, a sinusoidal flow is generated with a small speaker and passed through the flow-meter that is connected to a large, rigid container. True flow is proportional to the derivative of the pressure inside the container. True flow is then compared with the measured flow, which is proportional to the pressure drop across the flow-meter. In order to do the characterization, two LabVIEW data acquisition programs have been developed, one for transducer calibration, and another one that records flow and pressure data for frequency response testing of the flow-meter. In addition, a model that explains the behavior exhibited by the flow-meter has been proposed and simulated. This model contains a fluid resistor and inductor in series. The final step in this project was to approximate the frequency response data to the developed model expressed as a transfer function. / Dissertation/Thesis / M.S.Tech Electrical Engineering 2013

Vibration measurement and analysis has been an accepted method since decades to meet a number of objectives - machinery condition monitoring, dynamic qualification of any designed structural components, prediction of faults and structural aging-related problems, and several other structural dynamics studies and diagnosis. However, the requirement of the vibration measurement at number of locations in structures, machines and/or equipments makes the vibration measurement exorbitant if conventional piezoelectric accelerometers are used. Hence, there is a need for cheaper and reliable alternative for the conventional accelerometers. The Micro-Electro-Mechanical Systems (MEMS) accelerometers are one such cheap alternative. However, a significant deviation in the performance of the MEMS accelerometers has been observed in earlier research studies and also confirmed by this presented study when compared with well known conventional accelerometer. Therefore, two methods have been suggested to improve the performance of the existing MEMS accelerometers; one for correction in time domain and other in frequency domain. Both methods are based on the generation of a characteristic function (CF) for the MEMS accelerometer using well known reference accelerometer in laboratory tests. The procedures of both methods have been discussed and validations of these methods have been presented through experimental examples. In addition, a Finite Element (FE) model of a typical MEMS accelerometer has been developed and modal analysis has been carried out to understand the dynamics of capacitive type MEMS accelerometer and to identify the source of errors. It has been observed that the moving fingers behave like a cantilever beam while the fixed fingers showed rigid body motion. This cantilever type of motion seems to be causing non-parallel plates effect in the formed capacitors between moving and fixed fingers which results in errors in the vibration measurement. Hence, design modifications on finger shape have been suggested to remove the cantilever motion and results showed remarkable improvement. Moreover, the effect of using synchronous amplitude modulation and demodulation in the readout circuit has been studied. The experimental study showed that this circuit also introduces errors in amplitude and phase of the output signal compared with the input signal. Thus, in the new design of MEMS accelerometers, improvements in both mechanical design and electronic circuit are required.