Transient bending of a piezoelectric circular plate

Thin, piezoelectric circular plates are frequently used as active components in transducer and smart materials applications. This paper reports on the exact, explicit solution for the transient motion of a piezoelectric circular plate, built-in or simply supported on the edge and electrically grounded over the entire surface. Expressed by elementary Bessel functions and obtained via exact inverse Laplace transforms, the solution enables the efficient calculation of accurate system parameters. (C) 2004 Elsevier Ltd. All rights reserved.

A semi- analytic finite element approach to the stress analysis of circular plate

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Post-failure behaviour of impulsively loaded circular plates

The dynamic plastic response of a simply supported circular plate is analysed. Emphasis is given to the plate behaviour after it has broken free from the supports due to a local material failure. The theoretical rigid plastic analysis predicts various features of the response such as the time to failure, residual kinetic energy and the critical velocity at failure. The residual kinetic energy of the plate could be significant enough to cause secondary impact damage. It is shown that the shape of the plate changes after breaking free from the supports, which is important for forensic investigations. The solution for various cases were proven to be exact in the context of the upper and lower bounds theorems of the theory of plasticity. (C) 2009 Elsevier Ltd. All rights reserved.

Influence of a liquid on the natural frequencies of almost circular plates

In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.

Induced Damping on Vibrating Circular Plates Submerged in still Fluid

When a structure vibrates immersed in a fluid it is known that the dynamic properties of the system are modified. The surrounding fluid will, in general, contribute to the inertia, the rigidity and the damping coefficient of the coupled fluid-structure system. For light structures, like spacecraft antennas, even when the fluid is air the contribution to the dynamic properties can be important. For not so light structures the ratio of the equivalent fluid/structure mass and rigidity can be very small and the fluid contribution could be neglected. For the ratio of equivalent fluid/structure damping both terms are of the same order and therefore the fluid contribution must be studied. The working life of the spacecraft structure would be on space and so without any surrounding fluid. The response of a spacecraft structure on its operational life would be attenuated by the structural damping alone but when the structure is dynamically tested on the earth the dynamic modal test is performed with the fluid surrounding it. The results thus are contaminated by the effects of the fluid. If the damping added by the fluid is of the same order as the structural damping the response of the structure in space can be quite different to the response predicted on earth. It is therefore desirable to have a method able to determine the amount of damping induced by the fluid and that should be subtracted of the total damping measured on the modal vibration test. In this work, a method for the determination of the effect of the surrounding fluid on the dynamic characteristics of a circular plate has been developed. The plate is assumed to vibrate harmonically with the vacuum modes and the generalized forces matrix due to the fluid is thus computed. For a compressible fluid this matrix is formed by complex numbers including terms of inertia, rigidity and damping. The matrix due to the fluid loading is determined by a boundary element method (BEM). The BEM used is of circular rings on the plate surface so the number of elements to obtain an accurate result is very low. The natural frequencies of the system are computed by an iteration procedure one by one and also the damping fluid contribution. Comparisons of the present method with various experimental data and other theories show the efficiency and accuracy of the method for any support condition of the plate.

Piezoaeroelastic Modeling and Analysis of a Generator Wing with Continuous and Segmented Electrodes

Unmanned air vehicles (UAVs) and micro air vehicles (MAVs) constitute unique application platforms for vibration-based energy harvesting. Generating usable electrical energy during their mission has the important practical value of providing an additional energy source to run small electronic components. Electrical energy can be harvested from aeroelastic vibrations of lifting surfaces of UAVs and MAVs as they tend to have relatively flexible wings compared to their larger counterparts. In this work, an electromechanically coupled finite element model is combined with an unsteady aerodynamic model to develop a piezoaeroelastic model for airflow excitation of cantilevered plates representing wing-like structures. The electrical power output and the displacement of the wing tip are investigated for several airflow speeds and two different electrode configurations (continuous and segmented). Cancelation of electrical output occurs for typical coupled bending-torsion aeroelastic modes of a cantilevered generator wing when continuous electrodes are used. Torsional motions of the coupled modes become relatively significant when segmented electrodes are used, improving the broadband performance and altering the flutter speed. Although the focus is placed on the electrical power that can be harvested for a given airflow speed, shunt damping effect of piezoelectric power generation is also investigated for both electrode configurations.

Influencia de un fluido en las características dinámicas de placas circulares y casicirculares

La influencia de un fluido en las características dinámicas de estructuras se ha estudiado desde hace tiempo. Sin embargo muchos estudios se refieren a aplicaciones bajo el agua, como es el caso del sonar de un submarino por lo que el fluido circundante se considera líquido (sin efectos de compresibilidad). Más recientemente en aplicaciones acústicas y espaciales tales como antenas o paneles muy ligeros, ha sido estudiada la influencia en las características dinámicas de una estructura rodeada por un fluido de baja densidad. Por ejemplo se ha mostrado que el efecto del aire en el transmisor-reflector del Intelsat VI C-B con un diámetro de 3,2 metros y con un peso de sólo 34,7 kg disminuye la primera frecuencia en torno a un 20% con respecto a su valor en vacío. Por tanto es importante en el desarrollo de estas grandes y ligeras estructuras disponer de un método con el que estimar el efecto del fluido circundante sobre las frecuencias naturales de éstas. De esta manera se puede evitar el ensayo de la estructura en una cámara de vacío que para el caso de una gran antena o panel puede ser difícil y costoso. Se ha desarrollado un método de elementos de contorno (BEM) para la determinación del efecto del fluido en las características dinámicas de una placa circular. Una vez calculados analíticamente los modos de vibración de la placa en vacío, la matriz de masa añadida debido a la carga del fluido se determina por el método de elementos de contorno. Este método utiliza anillos circulares de manera que el número de elementos para obtener unos resultados precisos es muy bajo. Se utiliza un procedimiento de iteración para el cálculo de las frecuencias naturales del acoplamiento fluido-estructura para el caso de fluido compresible. Los resultados del método se comparan con datos experimentales y otros modelos teóricos mostrando la precisión y exactitud para distintas condiciones de contorno de la placa. Por otro lado, a veces la geometría de la placa no es circular sino casi-circular y se ha desarrollado un método de perturbaciones para determinar la influencia de un fluido incompresible en las características dinámicas de placas casi-circulares. El método se aplica a placas con forma elíptica y pequeña excentricidad. Por una parte se obtienen las frecuencias naturales y los modos de deformación de la placa vibrando en vacío. A continuación, se calculan los coeficientes adimensionales de masa virtual añadida (factores NAVMI). Se presentan los resultados de estos factores y el efecto del fluido en las frecuencias naturales. ABSTRACT The influence of the surrounding fluid on the dynamic characteristics of structures has been well known for many years. However most of these works were more concerned with underwater applications, such as the sonar of a submarine and therefore the surrounding fluid was considered a liquid (negligible compressibility effects). Recently for acoustical and spatial applications such as antennas or very light panels the influence on the dynamic characteristics of a structure surrounded by a fluid of low density has been studied. Thus it has been shown that the air effect for the Intelsat VI C-B transmit reflector with a diameter of 3,2 meters and weighting only 34,7 kg decreases the first modal frequency by 20% with respect to the value in vacuum. It is important then, in the development of these light and large structures to have a method that estimates the effect that the surrounding fluid will have on the natural frequencies of the structure. In this way it can be avoided to test the structure in a vacuum chamber which for a large antenna or panel can be difficult and expensive A BEM method for the determination of the effect of the surrounding fluid on the dynamic characteristics of a circular plate has been developed. After the modes of the plate in vacuum are calculated in an analytical form, the added mass matrix due to the fluid loading is determined by a boundary element method. This method uses circular rings so the number of elements to obtain an accurate result is very low. An iteration procedure for the computation of the natural frequencies of the couple fluid-structure system is presented for the case of the compressibility effect of air. Comparisons of the present method with various experimental data and other theories show the efficiency and accuracy of the method for any support condition of the plate. On the other hand, sometimes the geometry of the plate is not circular but almost-circular, so a perturbation method is developed to determine the influence of an incompressible fluid on the dynamic characteristics of almost-circular plates. The method is applied to plates of elliptical shape with low eccentricity. First, the natural frequencies and the mode shapes of the plate vibrating in vacuum are obtained. Next, the nondimensional added virtual mass coefficients (NAVMI factors) are calculated. Results of this factors and the effect of the fluid on the natural frequencies are presented.

Análise de microestrutura e de características geotécnicas de misturas de resíduo de polimento de porcelanato e solo

Brazil is a country in development, rich in natural resources. In order to grow sustainably, it is necessary to Brazil to preserve its environment, which is an expressive challenge, especially to industries, such as those producing ceramic materials. This study was developed using Porcelain Tile Polishing Residue (RPP) in blends with soil to build compacted fills. This residue is a slurry generated during the polishing process of porcelain tiles and contains powdery material from the polished tile, the abrasives used during the process and cooling water. The RPP was collected from a private company located in Conde/PB and it was mixed with a sandy-clayey soil, to build the fills. Laboratorial tests were conducted with pure soil, pure RPP and blends in proportions of 5%, 10%, 15% and 20% of RPP in addition to the dry mass of pure soil. The Chemical and Physical Characterization tests performed were: specific solid weight, grain size distribution, laser analysis of grain size distribution, Atterberg limits, X ray fluorescence, X ray diffraction, scanning electron microscopy and soil compaction,. The materials and blends were also compacted and direct shear tests and plate load tests were performed. Plate load tests were conducted using a circular plate with 30 cm diameter, on specimens of pure soil and 5% blend, compacted in a metallic box inside the Soil Mechanics Laboratory of the Federal University of Rio Grande do Norte, Brazil. Both mechanical tests performed were conducted under inundated conditions, willing to reduce the influence of soil suction. An evaluation of the results of the tests performed shows that RPP is a fine material, with grain size distribution smaller than 0,015mm, composed mainly of silica and alumina, and particles in angular shape. The soil was characterized as a clayey sand, geologically known as a lateritic soil, with high percentages of alumina and iron oxide, and particles with rounded shape. Both the Soil and the blends presented low plasticity, while the residue showed a medium plasticity. Direct shear tests showed that the addition of RPP did not cause major changes into blends’ friction angle data, however, it was possible to note that, for the proportions studied, that is a tendency of obtain lower shear stresses for higher percentages of RPP in the blends. Both pure soil and 5% mixture showed a punching disruption for the Plate load test. For this same test, the allowable stress for 5% mixture was 44% higher than the pure soil, and smaller vertical settlement results for all stresses.

Análise de microestrutura e de características geotécnicas de misturas de resíduo de polimento de porcelanato e solo

Brazil is a country in development, rich in natural resources. In order to grow sustainably, it is necessary to Brazil to preserve its environment, which is an expressive challenge, especially to industries, such as those producing ceramic materials. This study was developed using Porcelain Tile Polishing Residue (RPP) in blends with soil to build compacted fills. This residue is a slurry generated during the polishing process of porcelain tiles and contains powdery material from the polished tile, the abrasives used during the process and cooling water. The RPP was collected from a private company located in Conde/PB and it was mixed with a sandy-clayey soil, to build the fills. Laboratorial tests were conducted with pure soil, pure RPP and blends in proportions of 5%, 10%, 15% and 20% of RPP in addition to the dry mass of pure soil. The Chemical and Physical Characterization tests performed were: specific solid weight, grain size distribution, laser analysis of grain size distribution, Atterberg limits, X ray fluorescence, X ray diffraction, scanning electron microscopy and soil compaction,. The materials and blends were also compacted and direct shear tests and plate load tests were performed. Plate load tests were conducted using a circular plate with 30 cm diameter, on specimens of pure soil and 5% blend, compacted in a metallic box inside the Soil Mechanics Laboratory of the Federal University of Rio Grande do Norte, Brazil. Both mechanical tests performed were conducted under inundated conditions, willing to reduce the influence of soil suction. An evaluation of the results of the tests performed shows that RPP is a fine material, with grain size distribution smaller than 0,015mm, composed mainly of silica and alumina, and particles in angular shape. The soil was characterized as a clayey sand, geologically known as a lateritic soil, with high percentages of alumina and iron oxide, and particles with rounded shape. Both the Soil and the blends presented low plasticity, while the residue showed a medium plasticity. Direct shear tests showed that the addition of RPP did not cause major changes into blends’ friction angle data, however, it was possible to note that, for the proportions studied, that is a tendency of obtain lower shear stresses for higher percentages of RPP in the blends. Both pure soil and 5% mixture showed a punching disruption for the Plate load test. For this same test, the allowable stress for 5% mixture was 44% higher than the pure soil, and smaller vertical settlement results for all stresses.

Optimized square Fresnel zone plates for microoptics applications

Polygonal Fresnel zone plates with a low number of sides have deserved attention in micro and nanoptics, because they can be straightforwardly integrated in photonic devices, and, at the same time, they represent a balance between the high-focusing performance of a circular zone plate and the easiness of fabrication at micro and nano-scales of polygons. Among them, the most representative family are Square Fresnel Zone Plates (SFZP). In this work, we propose two different customized designs of SFZP for optical wavelengths. Both designs are based on the optimization of a SFZP to perform as close as possible as a usual Fresnel Zone Plate. In the first case, the criterion followed to compute it is the minimization of the difference between the area covered by the angular sector of the zone of the corresponding circular plate and the one covered by the polygon traced on the former. Such a requirement leads to a customized polygon-like Fresnel zone. The simplest one is a square zone with a pattern of phases repeating each five zones. On the other hand, an alternative SFZP can be designed guided by the same criterion but with a new restriction. In this case, the distance between the borders of different zones remains unaltered. A comparison between the two lenses is carried out. The irradiance at focus is computed for both and suitable merit figures are defined to account for the difference between them.

Vortex evolution in the wake of accelerating low-aspect-ratio plates and three-dimensional bodies of revolution

To find examples of effecient locomotion and manoeuvrability, one need only turn to the elegant solutions natural flyers and swimmers have converged upon. This dissertation is specifically motivated by processes of evolutionary convergence, which have led to the propulsors and body shapes in nature that exhibit strong geometric collapse over diverse scales. These body features are abstracted in the studies presented herein using low-aspect-ratio at plates and a three-dimensional body of revolution (a sphere). The highly-separated vortical wakes that develop during accelerations are systematically characterized as a function of planform shape, aspect ratio, Reynolds number, and initial boundary conditions. To this end, force measurements and time-resolved (planar) particle image velocimetry have been used throughout to quantify the instantaneous forces and vortex evolution in the wake of the bluff bodies. During rectilinear motions, the wake development for the flat plates is primarily dependent on plate aspect ratio, with edge discontinuities and curvature playing only a secondary role. Furthermore, the axisymmetric case, i.e. the circular plate, shows strong sensitivity to Reynolds number, while this sensitivity quickly diminishes with increasing aspect ratio. For rotational motions, global insensitivity to plate aspect ratio has been observed. For the sphere, it has been shown that accelerations play an important role in the mitigation of flow separation. These results - expounded upon in this dissertation - have begun to shed light on the specific vortex dynamics that may be coopted by flying and swimming species of all shapes and sizes towards efficient locomotion.

Analysis of a circular patch antenna radiating in a parallel-plate radial guide

A field matching method is described to analyze a recessed circular cavity radiating into a radial waveguide. Using the wall impedance approach, the analysis is divided into two separate problems of the cavity and its external environment. Based on this analysis, a computer algorithm is developed for determining wall admittances as seen at the edge of the patch in the cavity, the radial admittance matrix for the two-probe feed arrangement, and the input impedance as observed from the coaxial line feeding the cavity. This algorithm is tested against the general-purpose Hewlett-Packard finite-element High Frequency Structure Simulator as well as against measured results. Good agreement in all considered cases is noted.

Pressure drop coefficients for elliptic and circular sections in one, two and three-row arrangements of plate fin and tube heat exchangers

The objective of the present work is the experimental determination of pressure drop coefficients (loss coefficients) for elliptic and circular sections in one, two and three-row arrangements of plate fin and tube heat exchangers. The experiments permitted to correlate the dimensionless loss coefficient with the flow Reynolds number in the rectangular channel formed by the plate fins. The experimental technique consisted of the measurement of the longitudinal pressure distribution along the flow channel, for several values of air mass flow rate. The total number of data runs, each one characterized by the flow Reynolds number, was 216. The present geometry is used in compact heat exchangers for air conditioning systems, heaters, radiators, and others. Also, it is verified the influence of the utilization of elliptic tubes, instead of circular ones, in the pressure drop. The measurements were performed for Reynolds numbers ranging from 200 to 1900.

Experiments on circular arc and flat plate hydrofoils in noncavitating and full cavity flows.

"Department of the Navy. Bureau of Ships. Contract Nonr-220 (12)."

Estudo da influência de chapas de ligação com cavilha na resistência à encurvadura de colunas de aço de secção tubular circular

Neste trabalho estuda-se a resistência à encurvadura (compressão uniforme) de tubos de aço de secção circular, com extremidades rotuladas por meio de cavilhas, tendo em conta a influência da chapa de ligação (gusset plate na designação em língua inglesa). Para o efeito, estuda-se uma ligação-tipo comum com chapa soldada e efetuam-se estudos paramétricos, recorrendo a modelos de elementos finitos de casca, para determinar a influência da chapa na (i) carga crítica e na (ii) carga de colapso do elemento. Os resultados mostram que a influência da chapa não pode ser desprezada para valores reduzidos da esbelteza do elemento. Propõe-se um método expedito e preciso para determinar a carga crítica tendo em conta a influência da chapa.