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.

Influence of natural frequencies and source correlation fields on random response of panels

"Materials Central, Contract no. AF33(616)-6828, Project no. 7351."

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to dear with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses. (C) 1998 Elsevier Science S.A. All rights reserved.

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

Power Secant Method applied to natural frequency extraction of Timoshenko beam structures

This work deals with an improved plane frame formulation whose exact dynamic stiffness matrix (DSM) presents, uniquely, null determinant for the natural frequencies. In comparison with the classical DSM, the formulation herein presented has some major advantages: local mode shapes are preserved in the formulation so that, for any positive frequency, the DSM will never be ill-conditioned; in the absence of poles, it is possible to employ the secant method in order to have a more computationally efficient eigenvalue extraction procedure. Applying the procedure to the more general case of Timoshenko beams, we introduce a new technique, named ""power deflation"", that makes the secant method suitable for the transcendental nonlinear eigenvalue problems based on the improved DSM. In order to avoid overflow occurrences that can hinder the secant method iterations, limiting frequencies are formulated, with scaling also applied to the eigenvalue problem. Comparisons with results available in the literature demonstrate the strength of the proposed method. Computational efficiency is compared with solutions obtained both by FEM and by the Wittrick-Williams algorithm.

Determination of resonant frequencies of triangular and rectangular microstrip antennas, using artificial neural networks

This paper presents models that can be used in the design of microstrip antennas for mobile communications. The antennas can be triangular or rectangular. The presented models are compared with deterministic and empirical models based on artificial neural networks (ANN) presented in the literature. The models are based on Perceptron Multilayer (PML) and Radial Basis Function (RBF) ANN. RBF based models presented the best results. Also, the models can be embedded in CAD systems, in order to design microstrip antennas for mobile communications.

New contributions to the determination of resonance frequencies of rectangular microstrip antennas by neural networks

This paper uses artificial neural networks (ANN) to compute the resonance frequencies of rectangular microstrip antennas (MSA), used in mobile communications. Perceptron Multi-layers (PML) networks were used, with the Quasi-Newton method proposed by Broyden, Fletcher, Goldfarb and Shanno (BFGS). Due to the nature of the problem, two hundred and fifty networks were trained, and the resonance frequency for each test antenna was calculated by statistical methods. The estimate resonance frequencies for six test antennas were compared with others results obtained by deterministic and ANN based empirical models from the literature, and presented a better agreement with the experimental values.

ANALYSIS OF THE NATURAL VIBRATION FREQUENCY TEST METHOD TO OBTAIN THE MODULUS OF ELASTICITY OF WOOD STRUCTURAL COMPONENTS

There are several techniques to characterize the elastic modulus of wood and those currently using the natural frequencies of vibration stand out as they are non-destructive techniques, producing results that can be repeated and compared over time. This study reports on the effectiveness of the testing methods based on the natural frequencies of vibration versus static bending to obtain the elastic properties of reforested structural wood components usually employed in civil construction. The following components were evaluated: 24 beams of Eucalyptus sp. with nominal dimensions (40 x 60 x 2.000 mm) and 14 beams of Pinus oocarpa with nominal dimensions (45 x 90 x 2.300 mm) both without treatment; 30 boards with nominal dimensions (40 x 240 x 2.010 mm) and 30 boards with nominal dimensions (40 x 240 x 3.050 mm), both of Pinus oocarpa and with chromate copper arsenate (CCA) preservative treatment. The results obtained in thiswork show good correlation when compared to the results obtained by the static bending mechanical method, especially when applying the natural frequency of longitudinal vibration. The use of longitudinal frequency was reliable and practical, therefore recommended for determining the modulus of elasticity of wood structural elements. It was also found that no specific support is needed for the specimens using the longitudinal frequency, as well as no previous calibrations, reducing the execution time and enabling to test many samples.

On the initiation of boudinage and folding instabilities in layered elasto-visco-plastic solids - Insights from natural microstructures and numerical simulations

The present understanding of the initiation of boudinage and folding structures is based on viscosity contrasts and stress exponents, considering an intrinsically unstable state of the layer. The criterion of localization is believed to be prescribed by geometry-material interactions, which are often encountered in natural structures. An alternative localization phenomenon has been established for ductile materials, in which instability emerges for critical material parameters and loading rates from homogeneous conditions. In this thesis, conditions are sought under which this type of instability prevails and whether localization in geological materials necessarily requires a trigger by geometric imperfections. The relevance of critical deformation conditions, material parameters and the spatial configuration of instabilities are discussed in a geological context. In order to analyze boudinage geometries, a numerical eigenmode analysis is introduced. This method allows determining natural frequencies and wavelengths of a structure and inducing perturbations on these frequencies. In the subsequent coupled thermo-mechanical simulations, using a grain size evolution and end-member flow laws, localization emerges when material softening through grain size sensitive viscous creep sets in. Pinch-and-swell structures evolve along slip lines through a positive feedback between the matrix response and material bifurcations inside the layer, independent from the mesh-discretization length scale. Since boudinage and folding are considered to express the same general instability, both structures should arise independently of the sign of the loading conditions and for identical material parameters. To this end, the link between material to energy instabilities is approached by means of bifurcation analyses of the field equations and finite element simulations of the coupled system of equations. Boudinage and folding structures develop at the same critical energy threshold, where dissipative work by temperature-sensitive creep overcomes the diffusive capacity of the layer. This finding provides basis for a unified theory for strain localization in layered ductile materials. The numerical simulations are compared to natural pinch-and-swell microstructures, tracing the adaption of grain sizes, textures and creep mechanisms in calcite veins. The switch from dislocation to diffusion creep relates to strain-rate weakening, which is induced by dissipated heat from grain size reduction, and marks the onset of continuous necking. The time-dependent sequence uncovers multiple steady states at different time intervals. Microstructurally and mechanically stable conditions are finally expressed in the pinch-and-swell end members. The major outcome of this study is that boudinage and folding can be described as the same coupled energy-mechanical bifurcation, or as one critical energy attractor. This finding allows the derivation of critical deformation conditions and fundamental material parameters directly from localized structures in the field.

Mode Localization in a Nearly Cyclic Symmetric System

Thesis (Ph.D.)--University of Washington, 2016-06

Mechanical vibration characteristics of bell-type pump maintings

This thesis describes an analytical and experimental study to determine the mechanical characteristics of the pump mounting, bell housing type. For numerical purposes, the mount was modelled as a thin circular cylindrical shell with cutouts, stiffened with rings and stringers; the boundary conditions were considered to be either clamped-free or clamped-supporting rigid heavy mass. The theoretical study was concerned with both the static response and the free vibration characteristics of the mount. The approach was based on the Rayleigh-Ritz approximation technique using beam characteristic (axial) and trigonometric (Circumferential) functions in the displacement series, in association with the Love - Timoshenko thin shell theory. Studies were carried out to determine the effect of the supported heavy mass on the static response, frequencies and mode shapes; in addition, the effects of stringers, rings and cutouts on vibration characteristics were investigated. The static and dynamic formulations were both implemented on the Hewlett Packard 9845 computer. The experimental study was conducted to evaluate the results of the natural frequencies and mode shapes, predicted numerically. In the experimental part, a digital computer was used as an experiment controller, which allowed accurate and quick results. The following observations were made: 1. Good agreements were obtained with the results of other investigators. 2. Satisfactory agreement was achieved between the theoretical and experimental results. 3. Rings coupled the axial modal functions of the plain cylinder and tended to increase frequencies, except for the torsion modes where frequencies were reduced. Stringers coupled the circumferential modal functions and tended to decrease frequencies. The effect of rings was stronger than that of stringers. 4. Cutouts tended to reduce frequencies; in general, but this depends on the location of the cutouts; if they are near the free edge then an increase in frequencies is obtained. Cutouts coupled both axial and circumferential modal functions. 5. The supported heavy mass had similar effects to those of the rings, but in an exaggerated manner, particularly in the reduction of torsion frequencies. 6. The method of analysis was found to be a convenient analytical tool for estimating the overall behaviour of the shell with cutouts.

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.

EVALUATING VIBRATIONS ON A SMALL-SCALE MODEL OF A TIMBER FOOTBRIDGE

In Brazil, the study of pedestrian-induced vibration on footbridges has been undertaken since the early 1990s, for concrete and steel footbridges. However, there are no recorded studies of this kind for timber footbridges. Brazilian code ABNT NBR 7190 (1997) gives design requirements only for static loads in the case of timber footbridges, without considering the serviceability limit state from pedestrian-induced vibrations. The aim of this work is to perform a theoretical dynamic, numerical and experimental analysis on simply-supported timber footbridges, by using a small-scale model developed from a 24 m span and 2 m width timber footbridge, with two main timber beams. Span and width were scaled down (1:4) to 6 m e 0.5 in, respectively. Among the conclusions reached herein, it is emphasized that the Euler-Bernoulli beam theory is suitable for calculating the vertical and lateral first natural frequencies in simply-supported timber footbridges; however, special attention should be given to the evaluation of lateral bending stiffness, as it leads to conservative values.

State protection under collective damping and diffusion

In this paper we provide a recipe for state protection in a network of oscillators under collective damping and diffusion. Our strategy is to manipulate the network topology, i.e., the way the oscillators are coupled together, the strength of their couplings, and their natural frequencies, in order to create a relaxation-diffusion-free channel. This protected channel defines a decoherence-free subspace (DFS) for nonzero-temperature reservoirs. Our development also furnishes an alternative approach to build up DFSs that offers two advantages over the conventional method: it enables the derivation of all the network-protected states at once, and also reveals, through the network normal modes, the mechanism behind the emergence of these protected domains.

Dynamic behavior analysis of drill-threading process when machining AISI Al-Si-Cu(4) alloy

Conventional threading operations involve two distinct machining processes: drilling and threading. Therefore, it is time consuming for the tools must be changed and the workpiece has to be moved to another machine. This paper presents an analysis of the combined process (drilling followed by threading) using a single tool for both operations: the tap-milling tool. Before presenting the methodology used to evaluate this hybrid tool, the ODS (operating deflection shapes) basics is shortly described. ODS and finite element modeling (FEM) were used during this research to optimize the process aiming to achieve higher stable machining conditions and increasing the tool life. Both methods allowed the determination of the natural frequencies and displacements of the machining center and optimize the workpiece fixture system. The results showed that there is an excellent correlation between the dynamic stability of the machining center-tool holder and the tool life, avoiding a tool premature catastrophic failure. Nevertheless, evidence showed that the tool is very sensitive to work conditions. Undoubtedly, the use of ODS and FEM eliminate empiric decisions concerning the optimization of machining conditions and increase drastically the tool life. After the ODS and FEM studies, it was possible to optimize the process and work material fixture system and machine more than 30,000 threaded holes without reaching the tool life limit and catastrophic fail.