Analysis of functionally graded sandwich plate structures with piezoelectric skins, using B-spline finite strip method

Functionally graded materials are composite materials wherein the composition of the constituent phases can vary in a smooth continuous way with a gradation which is function of its spatial coordinates. This characteristic proves to be an important issue as it can minimize abrupt variations of the material properties which are usually responsible for localized high values of stresses, and simultaneously providing an effective thermal barrier in specific applications. In the present work, it is studied the static and free vibration behaviour of functionally graded sandwich plate type structures, using B-spline finite strip element models based on different shear deformation theories. The effective properties of functionally graded materials are estimated according to Mori-Tanaka homogenization scheme. These sandwich structures can also consider the existence of outer skins of piezoelectric materials, thus achieving them adaptive characteristics. The performance of the models, are illustrated through a set of test cases. (C) 2012 Elsevier Ltd. All rights reserved.

Low-cost vibration sensors: tendencies and applications in condition monitoring of machines and structures

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

Benchmark exact solutions for the static analysis of multi-layered piezoelectric composite using PVDF

The three-dimensional (3D) exact solutions developed in the early 1970s by Pagano for simply supported multilayered orthotropic composite plates and later in the 1990s extended to piezoelectric plates by Heyliger have been extremely useful in the assessment and development of advanced laminated plate theories and related finite element models. In fact, the well-known test cases provided by Pagano and by Heyliger in those earlier works are still used today as benchmark solutions. However, the limited number of test cases whose 3D exact solutions have been published has somewhat restricted the assessment of recent advanced models to the same few test cases. This work aims to provide additional test cases to serve as benchmark exact solutions for the static analysis of multilayered piezoelectric composite plates. The method introduced by Heyliger to derive the 3D exact solutions has been successfully implemented using symbolic computing and a number of new test cases are here presented thoroughly. Specifically, two multilayered plates using PVDF piezoelectric material are selected as test cases under two different loading conditions and considering three plate aspect ratios for thick, moderately thick and thin plate, in a total of 12 distinct test cases. (C) 2013 Elsevier Ltd. All rights reserved.

Layerwise mixed models for analysis of multilayered piezoelectric composite plates using least-squares formulation

This work provides an assessment of layerwise mixed models using least-squares formulation for the coupled electromechanical static analysis of multilayered plates. In agreement with three-dimensional (3D) exact solutions, due to compatibility and equilibrium conditions at the layers interfaces, certain mechanical and electrical variables must fulfill interlaminar C-0 continuity, namely: displacements, in-plane strains, transverse stresses, electric potential, in-plane electric field components and transverse electric displacement (if no potential is imposed between layers). Hence, two layerwise mixed least-squares models are here investigated, with two different sets of chosen independent variables: Model A, developed earlier, fulfills a priori the interiaminar C-0 continuity of all those aforementioned variables, taken as independent variables; Model B, here newly developed, rather reduces the number of independent variables, but also fulfills a priori the interlaminar C-0 continuity of displacements, transverse stresses, electric potential and transverse electric displacement, taken as independent variables. The predictive capabilities of both models are assessed by comparison with 3D exact solutions, considering multilayered piezoelectric composite plates of different aspect ratios, under an applied transverse load or surface potential. It is shown that both models are able to predict an accurate quasi-3D description of the static electromechanical analysis of multilayered plates for all aspect ratios.

Modification of MOR by desilication treatments: Structural, textural and acidic characterization

The effect of several desilication experimental parameters (base concentration, temperature and time) on the characteristics of MOR zeolite was studied. The samples were characterized by X-ray diffraction, Al-27 and Si-29 MAS-NMR, chemical analysis, and FTIR (framework vibration region). The textural characterization was made by N-2 adsorption and the acidity was evaluated by pyridine adsorption followed by FTIR and by the catalytic model reaction of n-heptane cracking. The alkaline treatments promoted the Si extraction from the zeolite framework, without considerable loss of crystallinity and, as it was envisaged, an important increase of the mesoporous structure was attained. A linear correlation between the number of framework Si per unit cell. N-Si and the asymmetric stretching wavenumber, nu(i), was observed. The acidity characterization shows that the desilicated samples exhibit practically the same acid properties than the parent HMOR zeolite. The optimum desilication conditions were those used to obtain sample M/0.2/85/2, i.e., sample treated with 0.2 M NaOH solution at 85 degrees C for 2 h.

Analisador de vibrações de dois canais baseado em computador

O presente trabalho teve como principal objectivo o desenvolvimento de um analisador de vibrações de dois canais baseado em computador, para a realização de diagnóstico no âmbito do controlo de condição de máquinas. Foi desenvolvida uma aplicação num computador comum, no software LabVIEW, que através de transdutores de aceleração do tipo MEMS conectados via USB, faz a recolha de dados de vibração e procede ao seu processamento e apresentação ao utilizador. As ferramentas utilizadas para o processamento de dados são ferramentas comuns encontradas em vários analisadores de vibrações disponíveis no mercado. Estas podem ser: gráficos de espectro de frequência, sinal no tempo, cascata ou valores de nível global de vibração, entre outras. Apesar do analisador desenvolvido não apresentar inovação nas ferramentas de análise adoptadas, este pretende ser distinguido pelo baixo custo, simplicidade e carácter didáctico. Este trabalho vem evidenciar as vantagens, desvantagens e potencialidades de um analisador desta natureza. São tiradas algumas conclusões quanto à sua capacidade de diagnóstico de avarias, capacidades como ferramenta didáctica, sensores utilizados e linguagem de programação escolhida. Como conclusões principais, o trabalho revela que os sensores escolhidos não são os indicados para efectuar o diagnóstico de avarias em ambiente industrial, contudo são ideais para tornar este analisador numa boa ferramenta didáctica e de treino.

Análise de conforto de ciclistas por simulação multicorpo

Este trabalho apresenta um estudo sobre o comportamento dinâmico das bicicletas com o principal objectivo de quantificar o conforto de um ciclista. Neste trabalho serão estudados dois tipos de bicicletas: uma apenas com suspensão dianteira e outra com suspensão dianteira e traseira (ou suspensão total), e três classes de pavimento: um mais sinuoso, um mais suave e um intermédio. Para cada uma destas situações o que se pretende é analisar a quantidade de vibração que é transmitida para o corpo do ciclista através dos três pontos de contacto existentes entre ambos: Assento, guiador e pedais. Os valores obtidos são comparados entre os vários casos e também com valores referência, fornecidos por normas, afim de analisar a situação de conforto do ciclista. Após a realização dos estudos o que se verificou é que o ciclista está numa situação mais desconfortável em pisos mais sinuosos, e que nesta situação se utilizar uma bicicleta de suspensão total está sujeito a vibrações inferiores. No entanto, o mais importante a concluir é que em qualquer uma das situações estudadas o ciclista encontra-se sempre dentro de uma zona conforto segundo as normas utilizadas.

Dimensionamento de um passadiço pedonal em estrutura metálica, com fundações em betão armado

A elaboração deste projecto, integrado no âmbito do Trabalho Final de Mestrado, para a obtenção do grau de Mestre em Engenharia Civil, tem como objectivo o dimensionamento de um passadiço pedonal em estrutura metálica, com fundações em betão armado. Este documento inclui quase todos os elementos necessários ao projecto de execução da referida estrutura. Para o dimensionamento do passadiço pedonal procedeu-se à quantificação das acções e posteriormente à verificação da segurança de todos os elementos estruturais tendo por base os critérios e especificações técnicas preconizados nas Normas Europeias relativas ao projecto estrutural (Eurocódigos estruturais). Tratando-se de um passadiço destinado à circulação de peões e cuja estrutura metálica apresenta um certo grau de flexibilidade devido à esbelteza dos elementos estruturais, esta poderá estar sujeita a acções dinâmicas periódicas provocadas pelas pessoas quando percorrem o passadiço, podendo ocasionar certos níveis de vibração que sob o ponto de vista de segurança estrutural serão pouco relevantes, sendo no entanto excessivos do ponto de vista do conforto humano. Foi por isso efectuado um estudo dinâmico, com o objectivo de caracterizar a resposta dinâmica da estrutura quando solicitada a carregamentos de natureza periódica como é o caso da acção do peão, de modo a garantir que a utilização desta estrutura esteja dentro dos parâmetros de conforto aceitáveis. A modelação da estrutura e consequente discretização geral desta, foi feita recorrendo a programa de elementos finitos, SAP2000, versão 14.0.0. O dimensionamento das ligações constitui outros dos aspectos fundamentais no projecto desta estrutura metálica.

Damage detection and quantification using transmissibility

Structures experience various types of loads along their lifetime, which can be either static or dynamic and may be associated to phenomena of corrosion and chemical attack, among others. As a consequence, different types of structural damage can be produced; the deteriorated structure may have its capacity affected, leading to excessive vibration problems or even possible failure. It is very important to develop methods that are able to simultaneously detect the existence of damage and to quantify its extent. In this paper the authors propose a method to detect and quantify structural damage, using response transmissibilities measured along the structure. Some numerical simulations are presented and a comparison is made with results using frequency response functions. Experimental tests are also undertaken to validate the proposed technique. (C) 2011 Elsevier Ltd. All rights reserved.

Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh's quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained through impact tests. The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes, considering the shape functions defined in branches. Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

Estudo e desenvolvimento de um sensor de chuva piezoelétrico para automóveis

A presença de sistemas eletrónicos nos veículos automóveis tem vindo a aumentar de forma considerável nos últimos 30 anos, tornando possível o aumento dos padrões de eficiência, segurança e conforto dos mesmos. Os sistemas de acionamento automático dos limpa-para-brisas, baseados em sensores de chuva óticos, têm registado um crescimento quase exponencial nos últimos 10 a 15 anos; no ano 2000, apenas 5 % dos veículos novos produzidos na Europa estavam equipados com este sistema, hoje é um equipamento amplamente difundido na oferta automóvel existente. O presente trabalho consistiu no estudo de uma solução para deteção de chuva em veículos automóveis com a aplicação de um sensor piezoelétrico, tendo em vista a obtenção de uma solução mais versátil e aplicável em vários pontos do veículo. As reduzidas dimensões, a elevada sensibilidade do sensor e a facilidade de aplicação nas superfícies de ensaio foram fatores que motivaram a escolha deste tipo de equipamento como elemento sensorial. As hipóteses definidas para o procedimento laboratorial basearam-se nas conclusões obtidas em estudos anteriormente desenvolvidos no campo dos sensores de chuva para automóveis e nas capacidades dos materiais piezoelétricos para medição de pluviosidade. Os sensores foram instalados sob as superfícies do veículo que apresentavam, simultaneamente, uma maior exposição à pluviosidade, quando este está em movimento, e um menor risco de sofrer danos. Os resultados obtidos permitiram concluir que a utilização deste tipo de sensores permite detetar elevados níveis de pluviosidade e em superfícies com considerável capacidade de deformação elástica. A sua implementação futura em veículos automóveis exige mais algum trabalho de melhoria dos processos de fixação dos sensores e do condicionamento de sinal utilizados.

A model updating technique based on FRFs for damped structures

Model updating methods often neglect that in fact all physical structures are damped. Such simplification relies on the structural modelling approach, although it compromises the accuracy of the predictions of the structural dynamic behaviour. In the present work, the authors address the problem of finite element (FE) model updating based on measured frequency response functions (FRFs), considering damping. The proposed procedure is based upon the complex experimental data, which contains information related to the damped FE model parameters and presents the advantage of requiring no prior knowledge about the damping matrix structure or its content, only demanding the definition of the damping type. Numerical simulations are performed in order to establish the applicability of the proposed damped FE model updating technique and its results are discussed in terms of the correlation between the simulated experimental complex FRFs and the ones obtained from the updated FE model.

Dimensionless analysis of constrained damping treatments

One of the most effective ways of controlling vibrations in plate or beam structures is by means of constrained viscoelastic damping treatments. Contrary to the unconstrained configuration, the design of constrained and integrated layer damping treatments is multifaceted because the thickness of the viscoelastic layer acts distinctly on the two main counterparts of the strain energy the volume of viscoelastic material and the shear strain field. In this work, a parametric study is performed exploring the effect that the design parameters, namely the thickness/length ratio, constraining layer thickness, material modulus, natural mode and boundary conditions have on these two counterparts and subsequently, on the treatment efficiency. This paper presents five parametric studies, namely, the thickness/length ratio, the constraining layer thickness, material properties, natural mode and boundary conditions. The results obtained evidence an interesting effect when dealing with very thin viscoelastic layers that contradicts the standard treatment efficiency vs. layer thickness relation; hence, the potential optimisation of constrained and integrated viscoelastic treatments through the use of properly designed thin multilayer configurations is justified. This work presents a dimensionless analysis and provides useful general guidelines for the efficient design of constrained and integrated damping treatments based on single or multi-layer configurations. (C) 2012 Elsevier Ltd. All rights reserved.

Modelling a Rotating Shaft as an Elastically Restrained Bernoulli-Euler Beam

Industrial rotating machines may be exposed to severe dynamic excitations due to resonant working regimes. Dealing with the bending vibration, problem of a machine rotor, the shaft - and attached discs - can be simply modelled using the Bernoulli-Euler beam theory, as a continuous beam subjected to a specific set of boundary conditions. In this study, the authors recall Rayleigh's method to propose an iterative strategy, which allows for the determination of natural frequencies and mode shapes of continuous beams taking into account the effect of attached concentrated masses and rotational inertias, including different stiffness coefficients at the right and the left end sides. The algorithm starts with the exact solutions from Bernoulli-Euler's beam theory, which are then updated through Rayleigh's quotient parameters. Several loading cases are examined in comparison with the experimental data and examples are presented to illustrate the validity of the model and the accuracy of the obtained values.