A numerical solution of the dispersion equation of the guided wave propagation in N-layered media

The theory of guided wave propagation in N-layered media is presented. The derivation of the dispersion equation is obtained from the application of appropriate boundary and continuity conditions to the solution of the general wave propagation. The resulting dispersion equation is given in the form of a determinant of a 4Nx4N coefficient matrix. A numerical procedure is proposed to represent and solve the implicit equation resulting. The validity and efficiency of the proposed numerical model is discussed. Dispersion curves characterizing the N-layered material are obtained and compared to published results. In order to illustrate the use of the model to different practical applications, such as coating problems of plasma spray on a turbine blade, aircraft multiple layers, ice detection, etc. a sensitivity analysis of the dispersion curves respect to depth imperfections is given

Modelo numérico basado en el método de los elementos finitos para el estudio de la hidrodinámica de bahías y estuarios

Se ha desarrollado un modelo implícito no lineal 2-D en EF para la resolución de las ecuaciones de aguas poco profundas. La discretización espacial se ha realizado por medio de elementos lagrangianos isoparamétricos. Se ha aplicado la integración numérica de Simpson para obtener las matrices elementales, y para la integración temporal se han utilizado diferentes esquemas en diferencias finitas, comprobándose el modelo con diferentes ejemplos

Numerical model for the study of hydrodynamics on bays and estuaries

A nonlinear implicit finite element model for the solution of two-dimensional (2-D) shallow water equations, based on a Galerkin formulation of the 2-D estuaries hydrodynamic equations, has been developed. Spatial discretization has been achieved by the use of isoparametric, Lagrangian elements. To obtain the different element matrices, Simpson numerical integration has been applied. For time integration of the model, several schemes in finite differences have been used: the Cranck-Nicholson iterative method supplies a superior accuracy and allows us to work with the greatest time step Δt; however, central differences time integration produces a greater velocity of calculation. The model has been tested with different examples to check its accuracy and advantages in relation to computation and handling of matrices. Finally, an application to the Bay of Santander is also presented

Finite element simulation of dispersion in the Bay of Santander

Two mathematical models are used to simulate pollution in the Bay of Santander. The first is the hydrodynamic model that provides the velocity field and height of the water. The second gives the pollutant concentration field as a resultant. Both models are formulated in two-dimensional equations. Linear triangular finite elements are used in the Galerkin procedure for spatial discretization. A finite difference scheme is used for the time integration. At each time step the calculated results of the first model are input to the second model as field data. The efficiency and accuracy of the models are tested by their application to a simple illustrative example. Finally a case study in simulation of pollution evolution in the Bay of Santander is presente

Structural damage identification using dynamic numerical models

In this paper a review of two main groups of structural damage identification methods by dynamic tests is presented. The first group is concerned with metallic thin structures damages or imperfections and the second one with reinforced concrete beam structures damages. 1. The first group is addressed to the detection of potential imperfections, fissures and cracks appearing in industrial machines, aeronautical structures and motor engines. They are typically metallic structures and the tests are carried under controlled environment conditions, such as in a laboratory. The application of body waves, and more often, guided waves, as Rayleigh and Lamb waves, as dynamic excitation in order to detect the damage, is described. The studied imperfections have been divided into three classes. • Cracks, related to the structural safety. They are penetrating a significant part of the plate thickness. • The second class of imperfections are small cracks or fissures, and they can be called partially penetrating ones because they are extended only to a small part of the plate thickness. Imperfections of this class are difficult to detect, because sometimes they can not be observed on the plate surfaces. • Finally, the third class of imperfections are the superficial cracks and they are more related to the durability of the structure than to its safety. These imperfections are more connected to structural protection to the environment, i.e. to protective painting and coating. Dynamic models used to detect the first class of imperfections have been Kirchhoff or Reissner bending thin plate. The crack detection can be achieved quite accurately by comparison between the first spatial derivatives of the mode shapes of the uncracked and cracked plates. Partially penetrating and superficial cracks have been identified by application as dynamic input of Lamb and Rayleigh waves respectively. The use of these guide waves seems to be a very promising technique for imperfection detection. However, computational problems appear. They are related to the small time step and the large number of the finite elements needed in order to reach a suitable accuracy level. 2. The second part of the paper treats a different group of dynamic identification and location of damage in civil and building structures. In particular the damage in reinforced concrete beams,typically used in bridge and building structures is studied. Detection procedures in this part differ of the first ones, because the existing structure is tested in the field and reinforced concrete is rather heterogenous material in comparison to metallic material. Normally, potential cracks are detected, during the free vibrations of the structure, by estimation of the changes either of its natural frequencies, or in its mode shapes or in the measure of its dynamic flexibility. However,in general, the differences of these values between uncracked and cracked beams are small and in some cases they can not be distinguished from the inherent measurement errors occurring during the tests. After reviewing several different models applied to crack detection, one based on the linear elasticity has been developed. In this model the cracks are assumed to remain open and the rest of the structure to behave elastically, Using this model a sensitivity analysis of the presence of cracks,depth and location, respect to the variation of the structure natural frequencies and modes shapes can be carried out. Using this approach a crack identification methodology is proposed. Finally,some possible modifications of the proposed methodology aimed to improve the accuracy and reliability of the obtained results are discussed

The information content of financial report announcements of Saudi Arabian listed firms

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