José Roberto França Arruda | Universidade Estadual de Campinas (original) (raw)
Papers by José Roberto França Arruda
In this work, the harmonic forced response of coupled mechanical systems composed of one-dimensio... more In this work, the harmonic forced response of coupled mechanical systems composed of one-dimensional periodic structures and elastic junctions are computed by means of the wave finite element (WFE) method. In the present study, the receptance matrices of the periodic structures are formulated on the basis of numerical wave modes. Also, the Craig-Bampton (CB) method, enhanced with a wave-based selection procedure of the fixed-interface modes, is used to derive the receptance matrices of the junctions. The assembly between the periodic structures and the junctions follows from a classic domain decomposition technique. The proposed WFE-based approach is validated through the analysis of a 3D aircraft fuselage involving stiffened cylindrical shells. The relevance of the WFE-based approach, in terms of accuracy and CPU time saving, is highlighted in comparison with the conventional FE and CB method.
Thermoacoustic core (TAC) is the element of a thermoacoustic system in which the temperature fiel... more Thermoacoustic core (TAC) is the element of a thermoacoustic system in which the temperature field is heterogeneous. It typically consists of a waveguide section enclosing an open porous material, a thermal buffer tube, and heat exchangers to establish the thermal gradient. The knowledge of its acoustic transfer matrix (T-matrix) allows predicting the performance of thermoacoustic engines. If the porous material inside the TAC is of simple geometry, one can obtain the T-matrix both theoretically and experimentally. On the other hand, in the case of complex geometry, the theoretical approach is restricted to the availability of geometrical parameters of equivalent simple materials. A reliable experimental approach is therefore of major interest in this case. Three experimental methods for the T-matrix evaluation are analyzed on their results for different porous materials inside the TAC, either of simple or complex geometry. Two of them are configurations of the classical two-load me...
Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and w... more Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and with the financial and infrastructural support from the Brazilian funding agency CAPES, from LAUM, and from UNICAMP, to which I am deeply grateful. I would like to thank M. Yves Aurégan, Research Director CNRS, and M. Joël Gilbert, Director of LAUM, for being welcome during the two years period that I lived in Le Mans as a Ph.D. Student. Writing this "Acknowledgments"essay is not a simple task. To accomplish this doctorate I depended on so many people, in so particularly different ways, that I can be sure that I will be unfair in my following words. But what I am indeed sure of is that I will do my best. What those forgotten or insufficiently acknowledged people can be sure of is that, even though not fairly mentioned here, they are imprinted in my heart.
The dynamic behavior of structural waveguides has attracted attention of many researchers that se... more The dynamic behavior of structural waveguides has attracted attention of many researchers that seek to develop new efficient methods taking advantage of the periodic characteristic of such struc-tures. This paper shows that it is possible to build the spectral dynamic matrix for a whole structure using the wavenumbers and the displacement and force wave vectors obtained by solving the eigen-value problem for the transfer matrix of a section of the waveguide. For this purpose, firstly, the procedure is demonstrated using a 1-D model. The analytical and numerical results are compared and are shown to agree well for a structural frame, which combines longitudinal, bending and shear effects. Then, the same methodology is applied to an elastic solid model. In this case, good results are obtained even including higher-order wave modes. This highlights the potential of this method as an efficient and easy way to compute the forced response of waveguides with arbitrary cross-sections. It al...
Special attention has been dedicated to the development of efficient numerical methods for comput... more Special attention has been dedicated to the development of efficient numerical methods for computation of the dynamic behavior of long structures. In this case, analyses via conventional finite element method (FEM) require high computational time as frequency rises. This happens because interpolation functions for finite elements yield parametric models in the time domain and harmonic analyses are performed in the frequency domain. The Spectral Element Model (SEM), as formalized by Doyle [1], is an alternative to FE analysis for these structures. It avoids the need of mesh refinement. Nevertheless, the method requires derivation of the equations of motion, which becomes cumbersome if higher-order effects should be taken into account. This work proposes a hybrid method which brings together the advantages of SEM and FEM in modeling complex, long structures, named here ”wave spectral finite element method” (WSFEM). Assuming the waveguide is periodic along one dimension, a thin slice o...
In this work, the harmonic forced response of coupled mechanical systems composed of one-dimensio... more In this work, the harmonic forced response of coupled mechanical systems composed of one-dimensional periodic structures and elastic junctions are computed by means of the wave finite element (WFE) method. In the present study, the receptance matrices of the periodic structures are formulated on the basis of numerical wave modes. Also, the Craig-Bampton (CB) method, enhanced with a wave-based selection procedure of the fixed-interface modes, is used to derive the receptance matrices of the junctions. The assembly between the periodic structures and the junctions follows from a classic domain decomposition technique. The proposed WFE-based approach is validated through the analysis of a 3D aircraft fuselage involving stiffened cylindrical shells. The relevance of the WFE-based approach, in terms of accuracy and CPU time saving, is highlighted in comparison with the conventional FE and CB method.
The design of periodic layered structures with desired wave dispersion characteristics is a subje... more The design of periodic layered structures with desired wave dispersion characteristics is a subject of great potential use in vibration isolation. In this work, the modelling of a one-dimensional periodic layered structure is performed using the wave spectral finite element method (WSFEM). Wave spectral finite elements are developed based on post processing a short segment of the waveguide modelled with conventional structural finite elements. The dynamic stiffness spectral element matrices are developed for the different layered materials and applied to model the forced response of a finite periodic layered rod. The periodic rod is assumed to consist of a sequence of unit cells, each cell consisting of two layers of different materials with contrasting properties. The frequency spectrum of the periodic rod is deter-mined by the layered structure layout, so that the periodic rod structure can be designed to have the desired band gap by adjusting the thickness of each layer and total...
Journal of Sound and Vibration, 2007
Finite element models have been used by many authors to provide accurate estimations of coupling ... more Finite element models have been used by many authors to provide accurate estimations of coupling loss factors. Although much progress has been achieved in this area, little attention has been paid to the influence of uncertain parameters in the finite element model used to estimate these factors. It is well known that, in the mid-frequency range, uncertainty is a major issue. In this context, a spectral element method combined with a special implementation of a fuzzyset-based method, which is called the transformation method, is proposed as an alternative to compute coupling loss factors. The proposed technique is applied to a frame-type junction, which can consist of two beams connected at an arbitrary angle. In this context, two problems are investigated. In the first one, the influence of the confidence intervals of the coupling loss factors on the estimated energy envelopes assuming a unit power input is considered. In the other problem the influence of the envelope of the input power obtained considering the confidence intervals of the coupling loss factors is also taken into account. The estimates of the intervals are obtained by using the spectral element method combined with a fuzzy-set-based method. Results using a Monte Carlo analysis for the estimation of the coupling loss factors under the influence of uncertain parameters are shown for comparison and verification of the fuzzy method.
s.n., Feb 24, 2014
O projeto de um motor termoacustico (TA) se torna viabilizado a medida da confiabilidade de sua p... more O projeto de um motor termoacustico (TA) se torna viabilizado a medida da confiabilidade de sua previsao de desempenho. Uma tentativa para o exito nessa previsao vem do conhecimento da matriz de transferencia do nucleo termoacustico (NTA), que pode ser explorada em modelos analiticos para o motor considerado. A matriz de transferencia por si so pode ser obtida ou por modelagem analitica ou medicoes acusticas. As ultimas, no entanto, consistem em uma opcao interessante para se evitar consideracoes termo-fisicas ou geometricas de estruturas complexas, uma vez que o NTA e tratado como uma caixa preta. No entanto, antes de se prosseguir com a abordagem experimental, uma solucao analitica e apresentada, apenas para fins de comparacao, mas que contempla somente os casos de materiais de geometria simples, tal como um catalisador de cerâmica, por exemplo. Em relacao a abordagem experimental, tres diferentes metodos sao apresentados. Um metodo classico de duas cargas e aplicado em duas configuracoes distintas e, alem disso, um metodo alternativo com base em medicoes de impedância e aqui desenvolvido e aplicado. Uma comparacao entre estas tres abordagens e realizada por meio de uma avaliacao de performance experimental e tambem por uma analise de sensibilidade, de modo a se conhecer as perspectivas de viabilidade de cada metodo. Quatro diferentes materiais sao testados, cada um sendo usado como o elemento poroso colocado no interior do NTA, que e por sua vez submetido a diferentes regimes de gradiente de temperatura. Estes materiais sao escolhidos de tal maneira a cobrir uma vasta gama de porosidades compreendidas entre esperados stack puro e regenerador puro. O metodo alternativo foi bem sucedido no seu objectivo para todos os materiais, ao contrario do metodo classico de duas cargas. Desta forma, as matrizes de transferencia medidas sao aplicadas em uma modelagem dedicada a prever tanto a frequencia operacional como o ganho de amplificacao TA intrinseca. Tais parâmetros sao otimizados em simulacoes para dois modelos de motores TA basicos, um de onda estacionaria e outro progressiva, variando-se parâmetros geometricos dos componentes anexos ao NTA. Uma analise comparativa mostra em que condicoes o limiar TA e esperado ou nao para cada material, e tambem revela as limitacoes do aparato experimental no que se refere as dimensoes adequadas para melhor se ajustarem as investigacoes de desempenho. Abstract
Engineering Vibroacoustic Analysis, 2016
ABSTRACT Thermoacoustic refrigeration has been developed since the early eighties, mostly in the ... more ABSTRACT Thermoacoustic refrigeration has been developed since the early eighties, mostly in the United States, Europe and Japan. However, in the last decade, a few research groups have started preliminary investigations in Brazil. At Unicamp specifically, a demonstrative apparatus was built in order to reproduce the thermoacoustic effect, aiming at refrigeration or heat pumping applications. The construction elements involved were very simple, consisting basically of an acrylic tube, an automotive catalyser (stack) and a moveable piston directly connected to a small shaker. The purpose of the shaker is to provide mechanical power, acoustically, inside the tube filled with atmospheric air. As a consequence of this input power, acoustic waves cross the stack on its axial direction through its longitudinal holes. When this happens at a resonance frequency of the air inside the tube and a standing wave is formed, a gas parcel has its expansion and contraction at fixed spots, establishing therefore only one way of thermal interaction with the stack internal walls, so that a net heat is transferred from one end to another of the stack. The lenght of the tube must be chosen as a function of the first mode wavelength of the standing wave, which is a function of the stack hole dimensions, and the stack must be positioned in a suitable way with respect to the wave pattern. Measurements showed a consistent temperature difference of 2.2ºC between the stack ends, which demonstrated the presence of the thermoacoustic effect in this apparatus. Ongoing investigations aim at improving the insulation conditions, incrementing the gas pressure and specific power input, and also the installation of heat exchangers, according to proper analytical considerations. In this paper, the operative principle of a standing wave thermoacoustic refrigerator is reviwed and the preliminary results obtained with the demonstration apparatus are presented and discussed.
Shock and Vibration, 2013
Structural spectral elements are formulated using the analytical solution of the applicable elast... more Structural spectral elements are formulated using the analytical solution of the applicable elastodynamic equations and, therefore, mesh refinement is not needed to analyze high frequency behavior provided the elastodynamic equations used remain valid. However, for modeling complex structures, standard spectral elements require long and cumbersome analytical formulation. In this work, a method to build spectral finite elements from a finite element model of a slice of a structural waveguide (a structure with one dimension much larger than the other two) is proposed. First, the transfer matrix of the structural waveguide is obtained from the finite element model of a thin slice. Then, the wavenumbers and wave propagation modes are obtained from the transfer matrix and used to build the spectral element matrix. These spectral elements can be used to model homogeneous waveguides with constant cross section over long spans without the need of refining the finite element mesh along the w...
Journal of Sound and Vibration, 2012
A large number of inverse problems in acoustics consist of a reverse propagation of the acoustic ... more A large number of inverse problems in acoustics consist of a reverse propagation of the acoustic pressure measured with an array of microphones. The goal is usually to identify the acoustic source location and strength or the surface velocity of a vibrating structure. The quality of the results obtained depends on the propagation model, on the accuracy of the pressure measurements and, finally, on the inverse problem conditioning. How to quantify this quality is the issue addressed in this paper. For this purpose, a geometrical interpretation of the inverse acoustic problem is proposed. The main application will, eventually, be nearfield acoustic holography (NAH), but it is expected that the proposed approach will also apply to other types of inverse acoustic problems. First, the geometrical representation of the inverse problem is proposed. The inverse problem is stated from a direct linear problem in the frequency domain. For each frequency, an overdetermined system of linear complex algebraic equations must be inverted. The concept of quality is discussed and a quality index is proposed based upon the residue of the inverse problem, solved in a mean square sense. Then, a simple one-dimensional (plane wave) acoustic example consisting of a source and two pressure measurements is used to illustrate the proposed geometrical representation of the inverse problem and the quality criterion inspired by it. In the simple example, the propagation model can be improved by searching for a reflection coefficient at the origin of the simulated hologram. This reflection coefficient is used to simulate the presence of a hidden source placed behind the source. An artificial attenuation is introduced to simulate the effect of geometrical attenuation present in real NAH problems. Again, using the geometrical representation, it is shown how, from an improved propagation model together with a given measurement noise level in the hologram, one can guarantee a certain quality level of the inverse procedure. Finally, numerical results show, in a preliminary way, how the identified source strength converges towards the exact velocity when the estimated propagation model tends to the exact propagation model.
Journal of Sound and Vibration, 2002
This paper discusses the well-known, but often misunderstood, concept of complex modes of dynamic... more This paper discusses the well-known, but often misunderstood, concept of complex modes of dynamic structures. It shows how complex modes can be interpreted in terms of wave propagation phenomena caused by either localized damping or propagation to the surrounding media. Numerical simulation results are presented for di!erent kinds of structures exhibiting modal and wave propagation characteristics: straight beams, an L-shaped beam, and a three-dimensional frame structure. The input/output transfer relations of these structures are obtained using a spectral formulation known as the spectral element method (SEM). With this method, it is straightforward to use in"nite elements, usually known as throw-o! elements, to represent the propagation to in"nity, which is a possible cause of modal complexity. With the SEM model, the exact dynamic behavior of structures can be investigated. The mode complexity of these structures is investigated. It is shown that mode complexity characterizes a behavior that is halfway between purely modal and purely propagative. A coe$cient for quantifying mode complexity is introduced. The mode complexity coe$cient consists of the correlation coe$cient between the real and imaginary parts of the eigenvector, or of the operational de#ection shape (ODS). It is shown that, far from discontinuities, this coe$cient is zero in the case of pure wave propagation in which case the plot of the ODS in the complex plane is a perfect circle. In the other extreme situation, a "nite structure without damping (or with proportional damping), where the mode shape (or the ODS) is a straight line on the complex plane, has a unitary complexity coe$cient. For simple beam structures, it is shown that the mode complexity factor can also be calculated by curve-"tting the mode to an ellipse and computing the ratio of its radii.
Mechanics Research Communications, 2010
The spectral element method is used to model a cracked rod, where the crack is modeled as a local... more The spectral element method is used to model a cracked rod, where the crack is modeled as a localized flexibility. The crack flexibility is derived using Castigliano's theorem, and the uncertainties are modeled by the parametric probabilistic approach. The probabilistic model is constructed directly for the variable of interest, i.e., the crack flexibility. Two different probabilistic models, where the probability density functions are constructed using the Maximum Entropy Principle, are used and compared. It is shown that the model with more uncertainty is the one constructed with less information. Monte Carlo simulations are performed in order to estimate the frequency response function envelopes.
Este trabalho consiste no estudo de propagacao de incertezas aleatorias atraves de metodo que per... more Este trabalho consiste no estudo de propagacao de incertezas aleatorias atraves de metodo que permite estimar deflexoes de carregamentos estaticos a partir de dados de avaliacao dinâmica. Com este proposito, um modelo numerico foi desenvolvido para a realizacao de simulacoes decarregamentos estaticos cujas condicoes de contorno empregadas sao similares as usualmente praticadas pela industria automobilistica em avaliacoes de rigidez de carrocerias. As frequencias naturais e os modos de vibrar tambem foram calculados pela resolucao do problema de autovalor e autovetor das matrizes de massa e rigidez do modelo. Estes ultimos dados foram entao utilizados pelo metodo para estimar os mesmos coeficientes de rigidez obtidos da simulacao de carregamento estatico. Em seguida, incertezas aleatorias devidamente modeladas foram incorporadas aos parâmetros modais. Ferramentas de analise de propagacao de incertezas, como Monte Carlo e propagacao linear de covariância, foram aplicadas na verificacao da incerteza da estimacao feita pelo metodo quando seus parâmetros de entrada sao incertos. Por ultimo, ensaios experimentais de carregamento estatico e analise modal experimental foram realizados para validacao do metodo frente as incertezas associadas a estas medicoes. Resultados sao apresentados e comentados Abstract
O objetivo deste trabalho foi estudar a aplicabilidade de uma metodologia de controle de vibracoe... more O objetivo deste trabalho foi estudar a aplicabilidade de uma metodologia de controle de vibracoes em estruturas usando uma abordagem de intensidade estrutural (SI). Tal metodologia (ASIC) foi entao aplicada ao estudo de vigas e placas em flexao. Tecnicas de estimativa da SI em estruturas foram revistas e foram utilizados acelerometros e sensores cerâmicos piezeletricos para as medidas de vibracao. Para fins de controle, as estruturas foram identificadas usando algoritmos Q-Markov Cover e os modelos obtidos foram utilizados em simulacoes numericas. Experimentos tambem foram implementados. Para o caso do controle da SI em vigas, o ASIC foi comparado com outras metodologias quais sejam, o FXLMS, o FXLMS MIMO e o metodo de Gibbs-Fuller. O ASIC se mostrou em media ligeiramente mais efetivo que o Gibbs-Fuller para os casos de excitacao tonal e bastante mais efetivo para os casos de multi-frequencia. Ja para o caso de controle de placas, foi utilizada uma configuracao com um atuador e oit...
Structural intensity is an alternative way of analyzing vibrations where the emphasis is put on t... more Structural intensity is an alternative way of analyzing vibrations where the emphasis is put on the spatial flow distribution of the active part of the vibration energy. The active vibration energy is directly related to the injection and dissipation of energy, which can be used to localize energy sources and sinks. Given that structural damage generally causes local dissipation of energy, structural intensity plots can be used to detect damage. A technique based on the computation of structural intensity using spatially dense vibration data measurements to calculate energy flow maps in plates is presented as a diagnostic tool to locate structural damage. Operational deflection shapes measured over the surface of the plate at particular frequencies are curve-fitted using a two-dimensional discrete Fourier series approximation, which minimizes the effects of spatial leakage. Effects of various modeling assumptions on damage localization are explored using numerical studies.
Esta dissertacao tem como objetivo geral levar `a realidade industrial subsidios para a modelagem... more Esta dissertacao tem como objetivo geral levar `a realidade industrial subsidios para a modelagem e analise de sistemas mecânicos lineares com variabilidade, assim como metodologias computacionais para quantificacao de incertezas, para fins de aplicacao em projeto. Neste sentido, foram realizados estudos sobre tecnicas de modelagem e analise estocastica de sistemas mecânicos lineares aplicadas, inicialmente, a algumas estruturas simples, de baixo custo computacional, por meio de simulacoes em MatLabR. Propoe-se uma abordagem probabilistica para a modelagem de incertezas baseada no Principio da Maxima Entropia para a flexibilidade relativa a uma trinca aberta e nao propagante em uma barra modelada atraves do Metodo do Elemento Espectral (SEM). Tambem e apresentada uma abordagem para o tratamento de problemas de campo aleatorio utilizando o SEM, onde sao utilizadas solucoes analiticas da decomposicao de Karhunen-Lo`eve. Uma formulacao para elementos de viga do tipo Euler-Bernoulli e a...
In this work, the harmonic forced response of coupled mechanical systems composed of one-dimensio... more In this work, the harmonic forced response of coupled mechanical systems composed of one-dimensional periodic structures and elastic junctions are computed by means of the wave finite element (WFE) method. In the present study, the receptance matrices of the periodic structures are formulated on the basis of numerical wave modes. Also, the Craig-Bampton (CB) method, enhanced with a wave-based selection procedure of the fixed-interface modes, is used to derive the receptance matrices of the junctions. The assembly between the periodic structures and the junctions follows from a classic domain decomposition technique. The proposed WFE-based approach is validated through the analysis of a 3D aircraft fuselage involving stiffened cylindrical shells. The relevance of the WFE-based approach, in terms of accuracy and CPU time saving, is highlighted in comparison with the conventional FE and CB method.
Thermoacoustic core (TAC) is the element of a thermoacoustic system in which the temperature fiel... more Thermoacoustic core (TAC) is the element of a thermoacoustic system in which the temperature field is heterogeneous. It typically consists of a waveguide section enclosing an open porous material, a thermal buffer tube, and heat exchangers to establish the thermal gradient. The knowledge of its acoustic transfer matrix (T-matrix) allows predicting the performance of thermoacoustic engines. If the porous material inside the TAC is of simple geometry, one can obtain the T-matrix both theoretically and experimentally. On the other hand, in the case of complex geometry, the theoretical approach is restricted to the availability of geometrical parameters of equivalent simple materials. A reliable experimental approach is therefore of major interest in this case. Three experimental methods for the T-matrix evaluation are analyzed on their results for different porous materials inside the TAC, either of simple or complex geometry. Two of them are configurations of the classical two-load me...
Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and w... more Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and with the financial and infrastructural support from the Brazilian funding agency CAPES, from LAUM, and from UNICAMP, to which I am deeply grateful. I would like to thank M. Yves Aurégan, Research Director CNRS, and M. Joël Gilbert, Director of LAUM, for being welcome during the two years period that I lived in Le Mans as a Ph.D. Student. Writing this "Acknowledgments"essay is not a simple task. To accomplish this doctorate I depended on so many people, in so particularly different ways, that I can be sure that I will be unfair in my following words. But what I am indeed sure of is that I will do my best. What those forgotten or insufficiently acknowledged people can be sure of is that, even though not fairly mentioned here, they are imprinted in my heart.
The dynamic behavior of structural waveguides has attracted attention of many researchers that se... more The dynamic behavior of structural waveguides has attracted attention of many researchers that seek to develop new efficient methods taking advantage of the periodic characteristic of such struc-tures. This paper shows that it is possible to build the spectral dynamic matrix for a whole structure using the wavenumbers and the displacement and force wave vectors obtained by solving the eigen-value problem for the transfer matrix of a section of the waveguide. For this purpose, firstly, the procedure is demonstrated using a 1-D model. The analytical and numerical results are compared and are shown to agree well for a structural frame, which combines longitudinal, bending and shear effects. Then, the same methodology is applied to an elastic solid model. In this case, good results are obtained even including higher-order wave modes. This highlights the potential of this method as an efficient and easy way to compute the forced response of waveguides with arbitrary cross-sections. It al...
Special attention has been dedicated to the development of efficient numerical methods for comput... more Special attention has been dedicated to the development of efficient numerical methods for computation of the dynamic behavior of long structures. In this case, analyses via conventional finite element method (FEM) require high computational time as frequency rises. This happens because interpolation functions for finite elements yield parametric models in the time domain and harmonic analyses are performed in the frequency domain. The Spectral Element Model (SEM), as formalized by Doyle [1], is an alternative to FE analysis for these structures. It avoids the need of mesh refinement. Nevertheless, the method requires derivation of the equations of motion, which becomes cumbersome if higher-order effects should be taken into account. This work proposes a hybrid method which brings together the advantages of SEM and FEM in modeling complex, long structures, named here ”wave spectral finite element method” (WSFEM). Assuming the waveguide is periodic along one dimension, a thin slice o...
In this work, the harmonic forced response of coupled mechanical systems composed of one-dimensio... more In this work, the harmonic forced response of coupled mechanical systems composed of one-dimensional periodic structures and elastic junctions are computed by means of the wave finite element (WFE) method. In the present study, the receptance matrices of the periodic structures are formulated on the basis of numerical wave modes. Also, the Craig-Bampton (CB) method, enhanced with a wave-based selection procedure of the fixed-interface modes, is used to derive the receptance matrices of the junctions. The assembly between the periodic structures and the junctions follows from a classic domain decomposition technique. The proposed WFE-based approach is validated through the analysis of a 3D aircraft fuselage involving stiffened cylindrical shells. The relevance of the WFE-based approach, in terms of accuracy and CPU time saving, is highlighted in comparison with the conventional FE and CB method.
The design of periodic layered structures with desired wave dispersion characteristics is a subje... more The design of periodic layered structures with desired wave dispersion characteristics is a subject of great potential use in vibration isolation. In this work, the modelling of a one-dimensional periodic layered structure is performed using the wave spectral finite element method (WSFEM). Wave spectral finite elements are developed based on post processing a short segment of the waveguide modelled with conventional structural finite elements. The dynamic stiffness spectral element matrices are developed for the different layered materials and applied to model the forced response of a finite periodic layered rod. The periodic rod is assumed to consist of a sequence of unit cells, each cell consisting of two layers of different materials with contrasting properties. The frequency spectrum of the periodic rod is deter-mined by the layered structure layout, so that the periodic rod structure can be designed to have the desired band gap by adjusting the thickness of each layer and total...
Journal of Sound and Vibration, 2007
Finite element models have been used by many authors to provide accurate estimations of coupling ... more Finite element models have been used by many authors to provide accurate estimations of coupling loss factors. Although much progress has been achieved in this area, little attention has been paid to the influence of uncertain parameters in the finite element model used to estimate these factors. It is well known that, in the mid-frequency range, uncertainty is a major issue. In this context, a spectral element method combined with a special implementation of a fuzzyset-based method, which is called the transformation method, is proposed as an alternative to compute coupling loss factors. The proposed technique is applied to a frame-type junction, which can consist of two beams connected at an arbitrary angle. In this context, two problems are investigated. In the first one, the influence of the confidence intervals of the coupling loss factors on the estimated energy envelopes assuming a unit power input is considered. In the other problem the influence of the envelope of the input power obtained considering the confidence intervals of the coupling loss factors is also taken into account. The estimates of the intervals are obtained by using the spectral element method combined with a fuzzy-set-based method. Results using a Monte Carlo analysis for the estimation of the coupling loss factors under the influence of uncertain parameters are shown for comparison and verification of the fuzzy method.
s.n., Feb 24, 2014
O projeto de um motor termoacustico (TA) se torna viabilizado a medida da confiabilidade de sua p... more O projeto de um motor termoacustico (TA) se torna viabilizado a medida da confiabilidade de sua previsao de desempenho. Uma tentativa para o exito nessa previsao vem do conhecimento da matriz de transferencia do nucleo termoacustico (NTA), que pode ser explorada em modelos analiticos para o motor considerado. A matriz de transferencia por si so pode ser obtida ou por modelagem analitica ou medicoes acusticas. As ultimas, no entanto, consistem em uma opcao interessante para se evitar consideracoes termo-fisicas ou geometricas de estruturas complexas, uma vez que o NTA e tratado como uma caixa preta. No entanto, antes de se prosseguir com a abordagem experimental, uma solucao analitica e apresentada, apenas para fins de comparacao, mas que contempla somente os casos de materiais de geometria simples, tal como um catalisador de cerâmica, por exemplo. Em relacao a abordagem experimental, tres diferentes metodos sao apresentados. Um metodo classico de duas cargas e aplicado em duas configuracoes distintas e, alem disso, um metodo alternativo com base em medicoes de impedância e aqui desenvolvido e aplicado. Uma comparacao entre estas tres abordagens e realizada por meio de uma avaliacao de performance experimental e tambem por uma analise de sensibilidade, de modo a se conhecer as perspectivas de viabilidade de cada metodo. Quatro diferentes materiais sao testados, cada um sendo usado como o elemento poroso colocado no interior do NTA, que e por sua vez submetido a diferentes regimes de gradiente de temperatura. Estes materiais sao escolhidos de tal maneira a cobrir uma vasta gama de porosidades compreendidas entre esperados stack puro e regenerador puro. O metodo alternativo foi bem sucedido no seu objectivo para todos os materiais, ao contrario do metodo classico de duas cargas. Desta forma, as matrizes de transferencia medidas sao aplicadas em uma modelagem dedicada a prever tanto a frequencia operacional como o ganho de amplificacao TA intrinseca. Tais parâmetros sao otimizados em simulacoes para dois modelos de motores TA basicos, um de onda estacionaria e outro progressiva, variando-se parâmetros geometricos dos componentes anexos ao NTA. Uma analise comparativa mostra em que condicoes o limiar TA e esperado ou nao para cada material, e tambem revela as limitacoes do aparato experimental no que se refere as dimensoes adequadas para melhor se ajustarem as investigacoes de desempenho. Abstract
Engineering Vibroacoustic Analysis, 2016
ABSTRACT Thermoacoustic refrigeration has been developed since the early eighties, mostly in the ... more ABSTRACT Thermoacoustic refrigeration has been developed since the early eighties, mostly in the United States, Europe and Japan. However, in the last decade, a few research groups have started preliminary investigations in Brazil. At Unicamp specifically, a demonstrative apparatus was built in order to reproduce the thermoacoustic effect, aiming at refrigeration or heat pumping applications. The construction elements involved were very simple, consisting basically of an acrylic tube, an automotive catalyser (stack) and a moveable piston directly connected to a small shaker. The purpose of the shaker is to provide mechanical power, acoustically, inside the tube filled with atmospheric air. As a consequence of this input power, acoustic waves cross the stack on its axial direction through its longitudinal holes. When this happens at a resonance frequency of the air inside the tube and a standing wave is formed, a gas parcel has its expansion and contraction at fixed spots, establishing therefore only one way of thermal interaction with the stack internal walls, so that a net heat is transferred from one end to another of the stack. The lenght of the tube must be chosen as a function of the first mode wavelength of the standing wave, which is a function of the stack hole dimensions, and the stack must be positioned in a suitable way with respect to the wave pattern. Measurements showed a consistent temperature difference of 2.2ºC between the stack ends, which demonstrated the presence of the thermoacoustic effect in this apparatus. Ongoing investigations aim at improving the insulation conditions, incrementing the gas pressure and specific power input, and also the installation of heat exchangers, according to proper analytical considerations. In this paper, the operative principle of a standing wave thermoacoustic refrigerator is reviwed and the preliminary results obtained with the demonstration apparatus are presented and discussed.
Shock and Vibration, 2013
Structural spectral elements are formulated using the analytical solution of the applicable elast... more Structural spectral elements are formulated using the analytical solution of the applicable elastodynamic equations and, therefore, mesh refinement is not needed to analyze high frequency behavior provided the elastodynamic equations used remain valid. However, for modeling complex structures, standard spectral elements require long and cumbersome analytical formulation. In this work, a method to build spectral finite elements from a finite element model of a slice of a structural waveguide (a structure with one dimension much larger than the other two) is proposed. First, the transfer matrix of the structural waveguide is obtained from the finite element model of a thin slice. Then, the wavenumbers and wave propagation modes are obtained from the transfer matrix and used to build the spectral element matrix. These spectral elements can be used to model homogeneous waveguides with constant cross section over long spans without the need of refining the finite element mesh along the w...
Journal of Sound and Vibration, 2012
A large number of inverse problems in acoustics consist of a reverse propagation of the acoustic ... more A large number of inverse problems in acoustics consist of a reverse propagation of the acoustic pressure measured with an array of microphones. The goal is usually to identify the acoustic source location and strength or the surface velocity of a vibrating structure. The quality of the results obtained depends on the propagation model, on the accuracy of the pressure measurements and, finally, on the inverse problem conditioning. How to quantify this quality is the issue addressed in this paper. For this purpose, a geometrical interpretation of the inverse acoustic problem is proposed. The main application will, eventually, be nearfield acoustic holography (NAH), but it is expected that the proposed approach will also apply to other types of inverse acoustic problems. First, the geometrical representation of the inverse problem is proposed. The inverse problem is stated from a direct linear problem in the frequency domain. For each frequency, an overdetermined system of linear complex algebraic equations must be inverted. The concept of quality is discussed and a quality index is proposed based upon the residue of the inverse problem, solved in a mean square sense. Then, a simple one-dimensional (plane wave) acoustic example consisting of a source and two pressure measurements is used to illustrate the proposed geometrical representation of the inverse problem and the quality criterion inspired by it. In the simple example, the propagation model can be improved by searching for a reflection coefficient at the origin of the simulated hologram. This reflection coefficient is used to simulate the presence of a hidden source placed behind the source. An artificial attenuation is introduced to simulate the effect of geometrical attenuation present in real NAH problems. Again, using the geometrical representation, it is shown how, from an improved propagation model together with a given measurement noise level in the hologram, one can guarantee a certain quality level of the inverse procedure. Finally, numerical results show, in a preliminary way, how the identified source strength converges towards the exact velocity when the estimated propagation model tends to the exact propagation model.
Journal of Sound and Vibration, 2002
This paper discusses the well-known, but often misunderstood, concept of complex modes of dynamic... more This paper discusses the well-known, but often misunderstood, concept of complex modes of dynamic structures. It shows how complex modes can be interpreted in terms of wave propagation phenomena caused by either localized damping or propagation to the surrounding media. Numerical simulation results are presented for di!erent kinds of structures exhibiting modal and wave propagation characteristics: straight beams, an L-shaped beam, and a three-dimensional frame structure. The input/output transfer relations of these structures are obtained using a spectral formulation known as the spectral element method (SEM). With this method, it is straightforward to use in"nite elements, usually known as throw-o! elements, to represent the propagation to in"nity, which is a possible cause of modal complexity. With the SEM model, the exact dynamic behavior of structures can be investigated. The mode complexity of these structures is investigated. It is shown that mode complexity characterizes a behavior that is halfway between purely modal and purely propagative. A coe$cient for quantifying mode complexity is introduced. The mode complexity coe$cient consists of the correlation coe$cient between the real and imaginary parts of the eigenvector, or of the operational de#ection shape (ODS). It is shown that, far from discontinuities, this coe$cient is zero in the case of pure wave propagation in which case the plot of the ODS in the complex plane is a perfect circle. In the other extreme situation, a "nite structure without damping (or with proportional damping), where the mode shape (or the ODS) is a straight line on the complex plane, has a unitary complexity coe$cient. For simple beam structures, it is shown that the mode complexity factor can also be calculated by curve-"tting the mode to an ellipse and computing the ratio of its radii.
Mechanics Research Communications, 2010
The spectral element method is used to model a cracked rod, where the crack is modeled as a local... more The spectral element method is used to model a cracked rod, where the crack is modeled as a localized flexibility. The crack flexibility is derived using Castigliano's theorem, and the uncertainties are modeled by the parametric probabilistic approach. The probabilistic model is constructed directly for the variable of interest, i.e., the crack flexibility. Two different probabilistic models, where the probability density functions are constructed using the Maximum Entropy Principle, are used and compared. It is shown that the model with more uncertainty is the one constructed with less information. Monte Carlo simulations are performed in order to estimate the frequency response function envelopes.
Este trabalho consiste no estudo de propagacao de incertezas aleatorias atraves de metodo que per... more Este trabalho consiste no estudo de propagacao de incertezas aleatorias atraves de metodo que permite estimar deflexoes de carregamentos estaticos a partir de dados de avaliacao dinâmica. Com este proposito, um modelo numerico foi desenvolvido para a realizacao de simulacoes decarregamentos estaticos cujas condicoes de contorno empregadas sao similares as usualmente praticadas pela industria automobilistica em avaliacoes de rigidez de carrocerias. As frequencias naturais e os modos de vibrar tambem foram calculados pela resolucao do problema de autovalor e autovetor das matrizes de massa e rigidez do modelo. Estes ultimos dados foram entao utilizados pelo metodo para estimar os mesmos coeficientes de rigidez obtidos da simulacao de carregamento estatico. Em seguida, incertezas aleatorias devidamente modeladas foram incorporadas aos parâmetros modais. Ferramentas de analise de propagacao de incertezas, como Monte Carlo e propagacao linear de covariância, foram aplicadas na verificacao da incerteza da estimacao feita pelo metodo quando seus parâmetros de entrada sao incertos. Por ultimo, ensaios experimentais de carregamento estatico e analise modal experimental foram realizados para validacao do metodo frente as incertezas associadas a estas medicoes. Resultados sao apresentados e comentados Abstract
O objetivo deste trabalho foi estudar a aplicabilidade de uma metodologia de controle de vibracoe... more O objetivo deste trabalho foi estudar a aplicabilidade de uma metodologia de controle de vibracoes em estruturas usando uma abordagem de intensidade estrutural (SI). Tal metodologia (ASIC) foi entao aplicada ao estudo de vigas e placas em flexao. Tecnicas de estimativa da SI em estruturas foram revistas e foram utilizados acelerometros e sensores cerâmicos piezeletricos para as medidas de vibracao. Para fins de controle, as estruturas foram identificadas usando algoritmos Q-Markov Cover e os modelos obtidos foram utilizados em simulacoes numericas. Experimentos tambem foram implementados. Para o caso do controle da SI em vigas, o ASIC foi comparado com outras metodologias quais sejam, o FXLMS, o FXLMS MIMO e o metodo de Gibbs-Fuller. O ASIC se mostrou em media ligeiramente mais efetivo que o Gibbs-Fuller para os casos de excitacao tonal e bastante mais efetivo para os casos de multi-frequencia. Ja para o caso de controle de placas, foi utilizada uma configuracao com um atuador e oit...
Structural intensity is an alternative way of analyzing vibrations where the emphasis is put on t... more Structural intensity is an alternative way of analyzing vibrations where the emphasis is put on the spatial flow distribution of the active part of the vibration energy. The active vibration energy is directly related to the injection and dissipation of energy, which can be used to localize energy sources and sinks. Given that structural damage generally causes local dissipation of energy, structural intensity plots can be used to detect damage. A technique based on the computation of structural intensity using spatially dense vibration data measurements to calculate energy flow maps in plates is presented as a diagnostic tool to locate structural damage. Operational deflection shapes measured over the surface of the plate at particular frequencies are curve-fitted using a two-dimensional discrete Fourier series approximation, which minimizes the effects of spatial leakage. Effects of various modeling assumptions on damage localization are explored using numerical studies.
Esta dissertacao tem como objetivo geral levar `a realidade industrial subsidios para a modelagem... more Esta dissertacao tem como objetivo geral levar `a realidade industrial subsidios para a modelagem e analise de sistemas mecânicos lineares com variabilidade, assim como metodologias computacionais para quantificacao de incertezas, para fins de aplicacao em projeto. Neste sentido, foram realizados estudos sobre tecnicas de modelagem e analise estocastica de sistemas mecânicos lineares aplicadas, inicialmente, a algumas estruturas simples, de baixo custo computacional, por meio de simulacoes em MatLabR. Propoe-se uma abordagem probabilistica para a modelagem de incertezas baseada no Principio da Maxima Entropia para a flexibilidade relativa a uma trinca aberta e nao propagante em uma barra modelada atraves do Metodo do Elemento Espectral (SEM). Tambem e apresentada uma abordagem para o tratamento de problemas de campo aleatorio utilizando o SEM, onde sao utilizadas solucoes analiticas da decomposicao de Karhunen-Lo`eve. Uma formulacao para elementos de viga do tipo Euler-Bernoulli e a...