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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
51

The effects of ambient temperature variations on structural dynamic characteristics

Woon, Christopher Earle 17 December 2008 (has links)
The precise and detailed characterization of the dynamic response of structures has become increasingly important in recent years. As a consequence, the accuracy of experimental data, which is often used to validate and update finite element models, has become extremely important. However, as researchers have attempted to identify and quantify sources of error in the experimental modal analysis (EMA) process, an important potential error source has been largely overlooked. Instabilities in the dynamic response of structures due to small variations in test environmental conditions may result in significant errors in experimental and analytical results, leading to erroneous and/or misleading conclusions. This thesis presents an experimental and analytical investigation of the effects of ambient temperature variations on the dynamic characteristics of a thin, square steel plate. The modal properties of the plate with two different boundary conditions and at temperatures above and below standard room temperature are examined. In addition, an analytical model is developed accounting for the effects of temperature-dependent material properties. Results indicate that natural frequencies and damping are significantly affected by changes in temperature. In the case of the natural frequency variations, the temperature-dependence of Young's modulus is the dominant factor, but boundary condition effects may also be important. Also, FRF magnitudes at spectral lines close to the resonances are very sensitive to temperature. Finally, only minor variations in the plate response shapes are observed, although significant changes in the imaginary component of the velocity field are evident. / Master of Science
52

Méthode d'identification d'un impact appliqué sur une structure admettant des modes de vibration basse fréquence faiblement amortis et bien séparés / Impact identification technique for a structure with weakly damped and well separated low frequency vibration modes

Goutaudier, Dimitri 03 April 2019 (has links)
La détection d'impacts est une préoccupation majeure pour suivre l'intégrité d'une structure évoluant dans un environnement comportant des risques de collision. Ce travail consiste à développer une méthode d’identification d'impact applicable à une structure composite de grandes dimensions qui soit à la fois robuste, peu coûteuse en temps de calcul, et qui nécessite peu de capteurs. Dans un premier temps, la démarche a été de décrire l'image du point d'impact dans la réponse vibratoire par un vecteur de participations modales. L'idée a ensuite été d'introduire l'hypothèse d'existence d'une famille de modes discriminants permettant d'établir le lien bijectif entre les participations modales et le point d'impact. Une procédure d'estimation de ces participations modales à partir d'un unique point de mesure a été proposée. Dans un second temps, la démarche a été d'étendre la procédure à l'identification d'une loi décrivant les paramètres principaux d'une force d'impact. Des conditions portant sur les paramètres de mesure et les propriétés modales de la structure sont déterminées pour garantir la précision et la robustesse de l'identification. Ce travail a permis de développer une approche en rupture par rapport à l'état de l'art, en ce sens qu'elle ne nécessite, en théorie, qu'un seul point de mesures vibratoires pour identifier un impact. Des essais expérimentaux sur un pavillon d'A350 ont permis de valider cette approche sur une structure composite de grandes dimensions. / Many industrial structures operate in an environment with a high risk of collision. The detection of impacts and the assessment of their severity is a major preoccupation in Structural Health Monitoring. This work deals with the development of an impact identification technique that is applicable to a large composite structure, numerically robust and time efficient, and that requires a low number of sensors. The first step was to describe the image of the impact point in the vibration response as a modal participation vector. The idea was to introduce the existence of a discriminating modes familly to make a bijective link between the modal participations and the impact point. A least-squares procedure is developed to estimate those modal participations by measuring the vibration response of a single point on the structure. The second step was to extend the procedure to the identification of a parametric law representing the impact load history. Some conditions on measurement parameters and modal properties of the structure are identified to guarantee both the accuracy and the robustness of the procedure. The approach developed in this work is new regarding the state of the art: only one measurement point is considered for identifying an impact event. An experimental validation on an A350 crown panel indicates that the methodology is valid for large composite structures.
53

Avaliação dos níveis de aceleração vertical e frequências de vibração no chassi de um implemento rodoviário considerando tipos de pavimento e condições de carga

José, Gustavo de Godoy January 2017 (has links)
O desenvolvimento de componentes para veículos comerciais geralmente é uma tarefa bastante complexa, principalmente quando se trata de transporte pesado, considerando que são necessários uma série de simulações e diversos testes em campo, em vários tipos de pavimento e condição de carga, onde muitas vezes é necessário rodar milhares de quilômetros para validar um único componente ou subsistema. Este trabalho apresenta uma série de testes realizados com um implemento rodoviário em diferentes tipos de pavimento e condições de carga, bem como o tratamento e avaliação dos dados coletados, com o objetivo de caracterizar o comportamento do chassi do implemento rodoviário nas diferentes aplicações através de suas densidades espectrais. Através de uma avaliação de dados do transporte rodoviário nacional foi definida uma combinação veicular de carga (CVC) que, instrumentada em toda sua extensão longitudinal, foi submetida a uma série de pavimentos como estrada não pavimentada, rodovia pavimentada, pista de buracos, paralelepípedos, seixo rolado, costeletas, pista de torção e lombada, a fim de coletar os níveis de aceleração vertical e frequências de vibração aos quais a massa suspensa do implemento rodoviário é submetida. Para a aplicação em questão, foi definida a faixa de frequência de interesse entre zero e 30Hz. Os sinais foram tratados através de um filtro Butterworth passa-baixa com frequência ótima de corte igual a 45Hz e, por fim, foram geradas PSDs utilizando função janela de Hanning com sobreposição de 50%. Os resultados do trabalho permitiram a diferenciação das aplicações com maior clareza, com vibrações mais críticas na condição vazio entre 2,5Hz e 10Hz, para massa suspensa e na condição carregada entre 9Hz e 14Hz, para massa não suspensa. / Commercial vehicle parts development usually is a quite complex task, mainly for heavy cargo transportation, considering that are necessary several analysis and durability tests, in different roads and load conditions, that commonly requires thousands of kilometers to approve a single component or subsystem. This work presents a truck trailer test series using different pavement types and load conditions, as well as data processing and evaluation, aiming to describe the truck trailer chassis behavior on different applications through its spectral density. Based on the Brazilian road transport data, a load vehicle combination was chosen, instrumented throughout its length and submitted to different pavements as an offroad pavement, highway road pavement, pot holes, Belgian blocks, cobblestones, washboard, body twist track and a single bump track, seeking information regarding to the truck trailer sprung mass vertical acceleration and vibration frequencies. For the application studied, an interest frequency band was defined between zero and 30Hz. The acceleration data was processed using a Butterworth low pass filter with an optimal cutoff frequency at 45Hz and, finally, power spectral densities were created using Hanning window function and 50% as overlap value. The results allowed a clearer detailing of the application efforts, once the most critical sprung mass vibrations occurs at empty condition and are between 2,5Hz and 10Hz, and the most critical unsprung mass vibrations occurs at loaded condition and are between 9Hz and 14Hz.
54

Monitoring PC Hardware Sounds in Linux Systems Using the Daubechies D4 Wavelet.

Henry, Robert Karns 17 December 2005 (has links)
Users of high availability (HA) computing require systems that run continuously, with little or no downtime. Modern PCs address HA needs by monitoring operating system parameters such as voltage, temperature, and hard drive status in order to anticipate possible system failure. However, one modality for PC monitoring that has been underutilized is sound. The application described here uses wavelet theory to analyze sounds produced by PC hard drives during standard operation. When twenty-nine hard drives were tested with the application and the results compared with the drives' Self-Monitoring, Analysis, and Reporting Technology (S.M.A.R.T.) data, the binomial distribution's low p-value of 0.012 indicated better than chance agreement. While the concurrence between the two systems shows that sound is an effective tool in detecting hardware failures, the disagreements between the systems show that the application can complement S.M.A.R.T. in an HA system.
55

Vibration And Impact Induced Sound

Narla, Subrahmanya Prasad 07 1900 (has links)
Sound generated by impacting structures is of considerable importance in noise control. Sound is generated by a vibrating structure by inducing pressure fluctuations in the surrounding medium. Impact induced noise is the sound generated by a vibrating structure subjected to motion constraint. In such problems one has to study the vibration behavior of the oscillator, the impact mechanics, and the emanating acoustic field dynamics. A literature review carried out points to the fact that though there has been considerable work on vibration behavior of impact oscillators and the acoustics of impact of rigid masses, there is very little work reported on the sound generated due to vibration and impact. This thesis couples vibration analysis of oscillators undergoing impact with its acoustic behavior. The vibration behavior is nonlinear on account of the impact. Therefore the vibration analysis as well as the resulting acoustic field analysis has to be in the time-domain. This investigation is concerned with the effect of structural dynamics, impact dynamics, and acoustic field boundary conditions, on the sound pressure generated due to vibration and impact. We have considered a single degree of freedom as well as a flexible Euler-Bernoulli beam vibration model. The former is the simplest for studying vibro-acoustic response. The numerical model of the beam is derived using the finite element method resulting in a finite dimensional system with more than one degree of freedom. The dynamics of each degree of freedom are distinct in terms of amplitude and phase and are a function of the nature of linear dependence on other degrees of freedom and the nature of excitation. An impacting beam introduces interesting interactions between the dynamics of the degrees of freedom as a consequence of nonlinearity due to the motion constraint. The impact of the oscillator mass with a barrier is modeled using a simple coefficient of restitution model based on Hertzian contact theory. There is velocity reversal on contact with the barrier. The contact force is finite acting within a finite interval of time. The contact force is assumed to vary in time during the contact interval. This effectively models contact as linearly elastic. The pressure perturbation due to vibration of the oscillator mass is shown equivalent to the pressure perturbation due to an acoustic dipole. The acoustic dipole is placed at the equilibrium position of the vibrating mass. The dipole pressure is then a function of motion of the oscillator. In the case of a single degree of freedom oscillator the dipole axis is along the direction of motion. The sound pressure due to a vibrating beam is modeled as an array of acoustic dipoles placed at the finite element nodes of the beam and stationary at the beam's static equilibrium configuration. The dipole axis is once again aligned with the direction of vibration of the beam that is transverse to the beam neutral axis. Anechoic as well as perfectly reflecting acoustic boundary conditions are simulated in the time-domain. The resulting governing equation of motion of the single degree freedom oscillator as well as the beam are integrated numerically in time to compute its response. The acoustic pressure is shown to be critically dependent on the excitation frequency of the oscillator, dynamic properties of the oscillator, coefficient of restitution of impact and impact dynamics, and acoustic field boundary conditions.
56

Manutenção preditiva de um par engrenado através da análise de lubrificantes e da análise de vibrações utilizando a transformada de wavelet / Predictive maintenance of a gearbox through lubricant analysis and vibration analysis using the wavelet transform

Pereira, André Luis Vinagre 27 February 2018 (has links)
Submitted by ANDRÉ LUIS VINAGRE PEREIRA null (andreluisvp@gmail.com) on 2018-03-29T18:17:43Z No. of bitstreams: 1 Dissertação Mestrado Final.pdf: 7001331 bytes, checksum: 858704904256f11c8131d5f17bd44a78 (MD5) / Approved for entry into archive by Cristina Alexandra de Godoy null (cristina@adm.feis.unesp.br) on 2018-04-02T12:53:22Z (GMT) No. of bitstreams: 1 pereira_alv_me_ilha.pdf: 7001331 bytes, checksum: 858704904256f11c8131d5f17bd44a78 (MD5) / Made available in DSpace on 2018-04-02T12:53:22Z (GMT). No. of bitstreams: 1 pereira_alv_me_ilha.pdf: 7001331 bytes, checksum: 858704904256f11c8131d5f17bd44a78 (MD5) Previous issue date: 2018-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Na manutenção preditiva, as análises dos sinais de vibração e das partículas do óleo são frequentemente utilizadas para o diagnóstico de falhas em redutores, porque elas contêm informações das condições de seus elementos mecânicos. Os sinais de vibração de um redutor geralmente têm muito ruído e a relação sinal-ruído é tão baixa que a extração de informações dos componentes do sinal é muito difícil, especialmente em situações práticas. Uma das soluções para este problema é a aplicação de técnicas de processamento do sinal para facilitar a obtenção de informações. Neste trabalho, uma técnica de cancelamento de ruído, a média temporal síncrona (TSA), e outra técnica da transformada contínua de wavelet de Morlet foram desenvolvidas para extração de recursos e diagnóstico de diferentes tipos de danos locais da engrenagem. Estas técnicas são aplicadas em sinais medidos em uma bancada experimental, que consiste em um par engrenado acoplado a um motor e a um gerador. Outro método para monitorar o estado do sistema é pela análise de partículas presente no óleo provenientes do desgaste das engrenagens. Avaliando a quantidade, formato, tamanho e material das partículas é possível obter informações das condições do equipamento e do tipo de desgaste ocorrido. Neste trabalho, foram feitas a análise do óleo pelas técnicas da ferrografia e contagem de partículas. A parte experimental deste trabalho foi dividida em dois experimentos. No primeiro experimento as condições de um par engrenado durante toda a sua vida útil foi monitorada, enquanto que no segundo experimento, um entalhe foi feito na raiz do dente simulando uma trinca por fadiga. A análise das partículas de óleo mostrou quais tipos de desgastes estava ocorrendo e a técnica da transformada contínua de wavelet mostrou-se precisa na identificação de falhas em dentes de engrenagens, sendo possível indicar em qual dente a falha estava se desenvolvendo. / At the predictive maintenance, the vibration signals analysis and oil particles analysis are frequently used to diagnose failures in a gearbox, because they contain information about the condition of its mechanic’s elements. The vibration signals of a gearbox usually have a lot of noise and the ratio ‘signal-noise’ is very low, making the extraction of information from the signals component very hard, especially in a practical situation. One of the solutions to this problem is the application of technics of signal processing, to improve the collection of information. At this study, a technique of noise cancellation, Temporal Synchronous Average (TSA) and another technique called continuous transform with the Morlet wavelet were executed for the extraction of resources and diagnostics of different type of gears local damages. Those methods are applied to signals measured on an experimental test stand, consisting of a gearbox with an engine and a generator. Another method for monitoring system wear is by analyzing wear particles in the oil generated due to the wear on the gears. By evaluating the quantity, shape, size and material of the particles it is possible to obtain information about the conditions of the equipment and the type of wear that has occurred. During this work, it was done the analysis of the oil by the techniques of ferrography and particle counting. The experimental part of this study was divided into two experiments. On the first experiment was monitored the conditions of a couple meshed throughout its useful life and in the second was made a notch in the root of the tooth simulating a crack by fatigue. The analysis of the oil particles showed what types of wear was occurring and the technique of the continuous wavelet transform was accurate in the identification of defects in gear's teeth, and it was possible to indicate which tooth was failing.
57

Manutenção preditiva de um par engrenado através da análise de lubrificantes e da análise de vibrações utilizando a transformada de wavelet /

Pereira, André Luis Vinagre. January 2018 (has links)
Orientador: Aparecido Carlos Gonçalves / Resumo: Na manutenção preditiva, as análises dos sinais de vibração e das partículas do óleo são frequentemente utilizadas para o diagnóstico de falhas em redutores, porque elas contêm informações das condições de seus elementos mecânicos. Os sinais de vibração de um redutor geralmente têm muito ruído e a relação sinal-ruído é tão baixa que a extração de informações dos componentes do sinal é muito difícil, especialmente em situações práticas. Uma das soluções para este problema é a aplicação de técnicas de processamento do sinal para facilitar a obtenção de informações. Neste trabalho, uma técnica de cancelamento de ruído, a média temporal síncrona (TSA), e outra técnica da transformada contínua de wavelet de Morlet foram desenvolvidas para extração de recursos e diagnóstico de diferentes tipos de danos locais da engrenagem. Estas técnicas são aplicadas em sinais medidos em uma bancada experimental, que consiste em um par engrenado acoplado a um motor e a um gerador. Outro método para monitorar o estado do sistema é pela análise de partículas presente no óleo provenientes do desgaste das engrenagens. Avaliando a quantidade, formato, tamanho e material das partículas é possível obter informações das condições do equipamento e do tipo de desgaste ocorrido. Neste trabalho, foram feitas a análise do óleo pelas técnicas da ferrografia e contagem de partículas. A parte experimental deste trabalho foi dividida em dois experimentos. No primeiro experimento as condições de um par engrenado d... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: At the predictive maintenance, the vibration signals analysis and oil particles analysis are frequently used to diagnose failures in a gearbox, because they contain information about the condition of its mechanic’s elements. The vibration signals of a gearbox usually have a lot of noise and the ratio ‘signal-noise’ is very low, making the extraction of information from the signals component very hard, especially in a practical situation. One of the solutions to this problem is the application of technics of signal processing, to improve the collection of information. At this study, a technique of noise cancellation, Temporal Synchronous Average (TSA) and another technique called continuous transform with the Morlet wavelet were executed for the extraction of resources and diagnostics of different type of gears local damages. Those methods are applied to signals measured on an experimental test stand, consisting of a gearbox with an engine and a generator. Another method for monitoring system wear is by analyzing wear particles in the oil generated due to the wear on the gears. By evaluating the quantity, shape, size and material of the particles it is possible to obtain information about the conditions of the equipment and the type of wear that has occurred. During this work, it was done the analysis of the oil by the techniques of ferrography and particle counting. The experimental part of this study was divided into two experiments. On the first experiment was monitored the... (Complete abstract click electronic access below) / Mestre
58

Avaliação dos níveis de aceleração vertical e frequências de vibração no chassi de um implemento rodoviário considerando tipos de pavimento e condições de carga

José, Gustavo de Godoy January 2017 (has links)
O desenvolvimento de componentes para veículos comerciais geralmente é uma tarefa bastante complexa, principalmente quando se trata de transporte pesado, considerando que são necessários uma série de simulações e diversos testes em campo, em vários tipos de pavimento e condição de carga, onde muitas vezes é necessário rodar milhares de quilômetros para validar um único componente ou subsistema. Este trabalho apresenta uma série de testes realizados com um implemento rodoviário em diferentes tipos de pavimento e condições de carga, bem como o tratamento e avaliação dos dados coletados, com o objetivo de caracterizar o comportamento do chassi do implemento rodoviário nas diferentes aplicações através de suas densidades espectrais. Através de uma avaliação de dados do transporte rodoviário nacional foi definida uma combinação veicular de carga (CVC) que, instrumentada em toda sua extensão longitudinal, foi submetida a uma série de pavimentos como estrada não pavimentada, rodovia pavimentada, pista de buracos, paralelepípedos, seixo rolado, costeletas, pista de torção e lombada, a fim de coletar os níveis de aceleração vertical e frequências de vibração aos quais a massa suspensa do implemento rodoviário é submetida. Para a aplicação em questão, foi definida a faixa de frequência de interesse entre zero e 30Hz. Os sinais foram tratados através de um filtro Butterworth passa-baixa com frequência ótima de corte igual a 45Hz e, por fim, foram geradas PSDs utilizando função janela de Hanning com sobreposição de 50%. Os resultados do trabalho permitiram a diferenciação das aplicações com maior clareza, com vibrações mais críticas na condição vazio entre 2,5Hz e 10Hz, para massa suspensa e na condição carregada entre 9Hz e 14Hz, para massa não suspensa. / Commercial vehicle parts development usually is a quite complex task, mainly for heavy cargo transportation, considering that are necessary several analysis and durability tests, in different roads and load conditions, that commonly requires thousands of kilometers to approve a single component or subsystem. This work presents a truck trailer test series using different pavement types and load conditions, as well as data processing and evaluation, aiming to describe the truck trailer chassis behavior on different applications through its spectral density. Based on the Brazilian road transport data, a load vehicle combination was chosen, instrumented throughout its length and submitted to different pavements as an offroad pavement, highway road pavement, pot holes, Belgian blocks, cobblestones, washboard, body twist track and a single bump track, seeking information regarding to the truck trailer sprung mass vertical acceleration and vibration frequencies. For the application studied, an interest frequency band was defined between zero and 30Hz. The acceleration data was processed using a Butterworth low pass filter with an optimal cutoff frequency at 45Hz and, finally, power spectral densities were created using Hanning window function and 50% as overlap value. The results allowed a clearer detailing of the application efforts, once the most critical sprung mass vibrations occurs at empty condition and are between 2,5Hz and 10Hz, and the most critical unsprung mass vibrations occurs at loaded condition and are between 9Hz and 14Hz.
59

Manutenção de redutores de velocidade pela integração das técnicas preditivas de análise de vibrações e análise de óleo lubrificante

Lago, Daniel Fabiano [UNESP] 13 November 2007 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:27:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-11-13Bitstream added on 2014-06-13T19:55:36Z : No. of bitstreams: 1 lago_df_me_ilha.pdf: 2600686 bytes, checksum: 82a754d34e90e3dd82ddaab84ab68958 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Todo sistema ou equipamento mecânico está sujeito a processos de deterioração. Esta deterioração leva ao aparecimento de defeitos que podem atrapalhar a continuidade e qualidade do serviço (produção). Uma quebra não prevista traduz-se por uma parada brusca, levando geralmente a grandes prejuízos e a perda de tempo de produção. Para evitar paradas inesperadas eficientemente e reduzir os custo de manutenção são utilizadas técnicas de manutenção preditiva. Entre todas as técnicas existentes, as mais importantes na manutenção de redutores são a análise de vibrações e a análise de partículas de desgaste. A determinação da severidade, modos e tipos de desgaste em máquinas pode ser feita pela identificação da morfologia, acabamento superficial, coloração, natureza, quantidade e tamanho das partículas encontradas em amostras de óleo ou graxas. Pela análise do sinal vibratório é possível tomar decisões de intervir ou não na operação da máquina, aumentando a disponibilidade e confiabilidade da mesma. A integração destas técnicas tem o potencial para revolucionar práticas industriais e proporcionar para as companhias um significante alívio econômico. Para estudo destas duas técnicas, neste trabalho foi construída uma bancada experimental com o propósito de se realizar a manutenção preditiva em um redutor de velocidades. O Sistema foi posto para funcionar até o limite de utilização. Foram utilizados lubrificantes recomendados pelo fabricante do redutor, lubrificantes com contaminação líquida em várias porcentagens e lubrificantes com contaminação sólida em duas porcentagens. Foram observadas que para baixas rotações a análise de partículas foi vantajosa em relação à análise de vibrações e que a contaminação por água, embora tenha ocasionado uma maior oxidação do sistema, proporcionou menor desgaste do que o lubrificante sem contaminação. / Every system or mechanical equipment is subject to deterioration processes. This deterioration takes to the apparition of defects that can disturb the continuity and quality of the service (production). One break not foreseen translates for an abrupt stop, usually taking to great damages and waste of time of production. For avoid unexpected stops efficiently and reduce the cost, predictive maintenance techniques are used. Among all the existent techniques, the most important in the maintenance of reducers are vibration analysis and wear particle analysis. The determination of the severity, wear modes and types in machines can be done through the identification of the morphology, surface finishing, coloration, nature, quantity and size of the particles found in oil samples or lubricating greases. Vibration Analysis is one of the oldest techniques in the maintenance. By vibration sign analysis it is possible to make decisions of intervening or not in the machine operation, improving its availability and reliability. The integration of these techniques has the potential to revolutionize industry practices and provide a significant industrial economic relief. For the study of these two techniques, in this work, an experimental bench was built with the purpose of doing the predictive maintenance in a reducer. The System was put to work until the limit. It was observed that for low rotations the wear particle analysis were advantageous in relation to the vibration analysis and for oil with water contamination, although causing a larger oxidation in the system, a smaller wear than the lubricant without contamination was provided.
60

A simplified analysis of the vibration of variable length blade as might be used in wind turbine systems

Tartibu, Kwanda January 2008 (has links)
Vibration is an inherent phenomenon in dynamic mechanical systems. The work undertaken in this thesis is to identify natural frequencies of a variable length blade. Therefore designers can ensure that natural frequencies will not be close to the frequency (or integer multiples) of the main excitation forces in order to avoid resonance. For a wind turbine blade, the frequency range between 0.5 Hz and 30 Hz is relevant. The turbine blade is approximated by a cantilever, therefore, it is fully constrained where attached to a turbine shaft/hub. Flap-wise, edge-wise and torsional natural frequencies are calculated. The MATLAB program “BEAMANALYSIS.m” has been developed for the finite element analysis of a one dimensional model of the beam. Similarly, a three dimensional model of the beam has been developed in a finite element program Unigraphics NX5. The results found using the MATLAB program are compared with those found with NX5. Satisfactory agreement between the results is found for frequencies up to almost 500 Hz. Additionally, the frequencies one might expect in an experiment are identified. Experimental modal analysis has been performed on a uniform and stepped beam made of mild steel to extract the first five flap-wise natural frequencies. The results found have been compared to numerical results and the exact solution of an Euler-Bernoulli beam. Concurrence is found for the frequency range of interest. Although, some discrepancies exist at higher frequencies (above 500 Hz), finite element analysis proves to be reliable for calculating natural frequencies. Finally, the fixed portion and moveable portion of the variable length blade are approximated respectively by a hollow and a solid beam which can be slid in and out. Ten different configurations of the variable length blade, representing ten different positions of the moveable portion are investigated. A MATLAB program named VARIBLADEANALYSIS.m was developed to predict natural frequencies. Similarly three dimensional models of the variable length blade have been developed in the finite element program Unigraphics NX5. / This work was supported by the Research office of CPUT.

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