Acoustic-Emission Wave Response to a Dislocation Source in Layered Media

2014 ◽  
Vol 598 ◽  
pp. 135-140
Author(s):  
Rui Chong Zhang
Keyword(s):  
Acoustic Emission ◽  
Wave Propagation ◽  
Free Surface ◽  
Integral Transformation ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Arbitrary Orientation ◽  
Dislocation Source ◽  
Time Space

This paper presents synthesis of acoustic-emission (AE) wave propagation in multi-layer materials and simulation of AE wave responses at free surface. In particular, the AE source is modelled as an arbitrary-orientation dislocation over an inclined-to-surface fault within one layer or at the layer-to-layer interface, while the materials are assumed as multi-layer media, each of which is homogeneous, isotropic and linearly elastic. With the use of the integral transformation approach, the three-dimensional wave propagation in the materials is solved in transformed or frequency-wavenumber domain. Subsequently, a closed-form solution for wave responses at free surface is found, which can then be converted in time-space domain. Numerical examples are finally provided for illustration.

Synthesis of Acoustic-Emission Wave Propagation in Multi-Layer Media

2013 ◽  
Vol 321-324 ◽  
pp. 1321-1330
Author(s):  
Rui Chong Zhang ◽  
Alhamid Alamin
Keyword(s):  
Acoustic Emission ◽  
Wave Propagation ◽  
Free Surface ◽  
Integral Transformation ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Arbitrary Orientation ◽  
Numerical Examples ◽  
Time Space

This paper presents synthesis of acoustic-emission (AE) wave propagation in multi-layer materials and simulation of AE wave responses at free surface. In particular, the AE source is modelled as an arbitrary-orientation dislocation over an inclined-to-surface fault within one layer or at the layer-to-layer interface, while the materials are assumed as multi-layer media, each of which is homogeneous, isotropic and linearly elastic. With the use of the integral transformation approach, the three-dimensional wave propagation in the materials is solved in transformed or frequency-wavenumber domain. Subsequently, a closed-form solution for wave responses at free surface is found, which can then be converted in time-space domain. Numerical examples are finally provided for illustration.

MODELLING OF ACOUSTIC EMISSION SOURCE AND WAVE RESPONSE IN LAYERED MATERIALS

2014 ◽  
Vol 44 (1) ◽  
pp. 21-44 ◽  
Author(s):  
A. Alamin ◽  
R. Zhang
Keyword(s):  
Acoustic Emission ◽  
Wave Propagation ◽  
Integral Transformation ◽  
Layered Media ◽  
Transformation Method ◽  
Wave Number ◽  
Dislocation Source ◽  
Frequency Wave ◽  
Wave Response ◽  
Time Space

Abstract This study proposes a model of wave propagation in layered media for the use in acoustic emission (AE) studies. This model aims to find an AE response at a free surface to the propagating waves originating at a dislocation source either in one layer medium or a layer-to-layer interface. Each of the layered media is assumed to be homogenous, linear elastic and isotropic. An integral transformation method has been applied to determine the wave response in frequency-wave number domain, which is then converted to time-space domain. In the numerical examples, we first select truncated values with the finite integral transformation, so that no wave interference happens in the responses from wave reflection at truncated boundaries. Next, we simulate wave propagation in an elastic half space, and compare results obtained with that from other kind bottom boundary. Next, we introduce a dis- location source in interface and compare a simulated AE wave response obtained with that computed in the layered medium to demonstrate the performance of the model. In each simulation, the results show good agreement with the reference solutions.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Isaiah Ramos ◽  
Young Ho Park ◽  
Jordan Ulibarri-Sanchez
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Structural Damage ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Analytical Results ◽  
Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

scholarly journals SOLUTION OF THE MULTIDIMENSIONAL DIFFUSION EQUATION USING LIE SYMMETRIES: SIMULATION OF POLLUTANT DISPERSION IN THE ATMOSPHERE

2005 ◽  
Vol 4 (2) ◽  
Author(s):  
J. R. Zabadal ◽  
C. A. Poffal
Keyword(s):  
Differential Operators ◽  
Hybrid Methods ◽  
Formal Solution ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Pollutant Dispersion ◽  
Form Solution ◽  
Lie Symmetries ◽  
Advection Equation ◽  
Mean Values

Several analytical, numerical and hybrid methods are being used to solve diffusion and diffusion advection problems. In this work, a closed form solution of the three-dimensional diffusion advection equation in a Cartesian coordinate system is obtained by applying rules, based on the Lie symmetries, to manipulate the exponential of the differential operators that appear in its formal solution. There are many advantages of applying these rules: the increase in processing velocity so that the solution may be obtained in real time, the reduction in the amount of memory required to perform the necessary tasks in order to obtain the solution, since the analytical expressions can be easily manipulated in post-processing and also the discretization of the domain may not be necessary in some cases, avoiding the use of mean values for some parameters involved. These rules yield good results when applied to obtain solutions for problems in fluid mechanics and in quantum mechanics. In order to show the performance of the method, a one-dimensional scenario of the pollutant dispersion in a stable boundary layer is simulated, considering that the horizontal component of the velocity field is dominant and constant, disregarding the other components. The results are compared with data available in the literature.

Induction Proof for a General Exponential Integral Formula

1995 ◽  
Vol 80 (2) ◽  
pp. 424-426
Author(s):  
Frank O'Brien ◽  
Sherry E. Hammel ◽  
Chung T. Nguyen
Keyword(s):  
Closed Form ◽  
Integral Formula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Probability Method ◽  
Exponential Integral ◽  
Need To Evaluate ◽  
Three Dimensional Space

The authors' Poisson probability method for detecting stochastic randomness in three-dimensional space involved the need to evaluate an integral for which no appropriate closed-form solution could be located in standard handbooks. This resulted in a formula specifically calculated to solve this integral in closed form. In this paper the calculation is verified by the method of mathematical induction.

scholarly journals SOLUTION OF THE MULTIDIMENSIONAL DIFFUSION EQUATION USING LIE SYMMETRIES: SIMULATION OF POLLUTANT DISPERSION IN THE ATMOSPHERE

2005 ◽  
Vol 4 (2) ◽  
pp. 197
Author(s):  
J. R. Zabadal ◽  
C. A. Poffal
Keyword(s):  
Differential Operators ◽  
Hybrid Methods ◽  
Formal Solution ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Pollutant Dispersion ◽  
Form Solution ◽  
Lie Symmetries ◽  
Advection Equation ◽  
Mean Values

Several analytical, numerical and hybrid methods are being used to solve diffusion and diffusion advection problems. In this work, a closed form solution of the three-dimensional diffusion advection equation in a Cartesian coordinate system is obtained by applying rules, based on the Lie symmetries, to manipulate the exponential of the differential operators that appear in its formal solution. There are many advantages of applying these rules: the increase in processing velocity so that the solution may be obtained in real time, the reduction in the amount of memory required to perform the necessary tasks in order to obtain the solution, since the analytical expressions can be easily manipulated in post-processing and also the discretization of the domain may not be necessary in some cases, avoiding the use of mean values for some parameters involved. These rules yield good results when applied to obtain solutions for problems in fluid mechanics and in quantum mechanics. In order to show the performance of the method, a one-dimensional scenario of the pollutant dispersion in a stable boundary layer is simulated, considering that the horizontal component of the velocity field is dominant and constant, disregarding the other components. The results are compared with data available in the literature.

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

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