Characterisation of Young's modulus and loss factor of damping materials
- Authors: Nortemann, Markus
- Date: 2014
- Subjects: Elasticity , Simulation methods , Damping (Mechanics)
- Language: English
- Type: Thesis , Masters , MEngineering (Mechatronics)
- Identifier: vital:9662 , http://hdl.handle.net/10948/d1021036
- Description: Given the importance of simulation techniques in automotive engineering, there is a lack of implementation regarding these techniques in the acoustics of damping materials for air-borne sound. Biot’s calculations have proven its abilities to simulate the acoustic characteristics of these damping materials. However, the characterisation of essential structural parameters, such as Young’s modulus and loss factor, in order to conduct Biot’s calculations have been inconclusive. Thus, the primary research objective of this study is to propose a new measurement system for the structural Biot parameters. After a comprehensive literature review has been undertaken on damping materials, as well as measurement apparatuses for Young’s modulus and loss factor of damping materials, two causes of measurement errors have been identified. Unknown stresses in measurement apparatuses and inhomogeneous, polytrophic and viscoelastic behaviour of specimens. A new measurement system that does not affect the specimens with unknown stresses and accounts for their complex behaviour required investigation. Non-contact ultrasound had been selected as a solution to determine the aforementioned parameters, since these methods do not necessarily touch or compress the specimen, which led to unknown stresses and neglection of the complex specimen behaviour with the aforementioned techniques. Although ultrasound had been used to determine structural parameters on various types of materials, it has never been used to measure soft porous damping materials. In order to find possible solutions, various sources using ultrasonics to investigate struc- tural parameters had been reviewed. In order to calculate structural parameters, the longitudinal and transversal wave velocity inside the specimen had to be determined. The main findings showed that non-contact ultrasound will be able to evaluate the Young’s modulus, loss factor as well as Poisson’s ratio. Consequently, it was shown that longitudinal velocity measurements could be conducted using well known transmission measurements. However, well known approaches would not be sufficient measuring the transversal wave velocity in soft damping materials. This problem was addressed with a special gas to be used, with lower sound speed velocity in the fluid than in the solid. Moreso, a new method determining the transversal wave velocity had been found, as it would enable the use of an even larger range of damping materials, especially ones with heavy frames and lower porosity. It will use refracted waves inside the specimen and the determination of the convertion position of the transversal to the longitudinal wave at the rear specimen surface. At the end of the study, hardware components were selected and a test rig was constructed, which should be able to prove that a determination of structural Biot parameters with non-contact ultrasound is possible with less errors instead of using mechanical transfer function systems. The development of measurement software as well as the testing of the measurement system and its validation was not under investigation in this dissertation. This study has expanded on the body of literature knowledge regarding non-contact ultrasound. Furthermore, a significant contribution has been made towards a new measurement system measuring Young’s modulus and loss factor which circumvents errors in mechanical transfer function systems. This will contribute to more precise simulations of damping materials and damped enclosures, which may ultimately result in enhanced efficiency of damping materials as well as the acoustic packaging of cars.
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- Date Issued: 2014
Pricing exotic options using C++
- Authors: Nhongo, Tawuya D R
- Date: 2007
- Subjects: C++ (Computer program language) , Monte Carlo method , Simulation methods , Options (Finance) -- Mathematical models , Pricing -- Mathematical models
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5577 , http://hdl.handle.net/10962/d1008373 , C++ (Computer program language) , Monte Carlo method , Simulation methods , Options (Finance) -- Mathematical models , Pricing -- Mathematical models
- Description: This document demonstrates the use of the C++ programming language as a simulation tool in the efficient pricing of exotic European options. Extensions to the basic problem of simulation pricing are undertaken including variance reduction by conditional expectation, control and antithetic variates. Ultimately we were able to produce a modularized, easily extend-able program which effectively makes use of Monte Carlo simulation techniques to price lookback, Asian and barrier exotic options. Theories of variance reduction were validated except in cases where we used control variates in combination with the other variance reduction techniques in which case we observed increased variance. Again, the main aim of this half thesis was to produce a C++ program which would produce stable pricings of exotic options.
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- Date Issued: 2007