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http://hdl.handle.net/10985/8562
Time-domain computation of the response of composite layered anisotropic plates to a localized source
DESCHAMPS, Marc; DUCASSE, Eric
This paper describes how a modal approach in the time-domain can be suitable for calculating the elastodynamic field in a layered plate. This elastodynamic field is generated by impulsive sources located in a small region of a composite plate consisting of anisotropic layers stuck together. The aim is to calculate the transient response of the elastic plate around the location of the sources, generally emitting nn-cycle pulses. First, we apply a 2D Fourier transform to the wave equation with respect to the coordinates in the plate plane, and then, in the 2D spectrum domain, for any given wave-vector in the plate plane, solving a vibration problem with respect to time and position in the direction perpendicular to the plate. The solution is expressed as the sum of mode responses, each mode having a resonance frequency and a shape which depend on the wave-vector in the plate plane. These calculations are different from those obtained by the usual method in the harmonic domain, where the modes are searched for a fixed frequency, such as Lamb waves, i.e. guided waves that propagate along the plate. In our case, the solution is given as a summation of plate resonances, i.e. a decomposition on the real eigenfrequencies, associated to Lamb waves with the same fixed wave-vector. This difference is of importance since only Lamb modes with real frequencies and real-valued wavenumbers in the plate plane are involved here, contrary to the usual harmonic methods, where these modes can be evanescent. This is of great interest as it can simplify the calculation of the generated field near the source. Finally, we obtain a solution in the physical domain by performing an inverse 2D Fourier transform. After a detailed description of the method, results are shown for two typical plates. It is emphasized that the method is accurate for observation points located both above or below the source and reasonably far from it along the plate.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/85622014-01-01T00:00:00ZDESCHAMPS, MarcDUCASSE, EricThis paper describes how a modal approach in the time-domain can be suitable for calculating the elastodynamic field in a layered plate. This elastodynamic field is generated by impulsive sources located in a small region of a composite plate consisting of anisotropic layers stuck together. The aim is to calculate the transient response of the elastic plate around the location of the sources, generally emitting nn-cycle pulses. First, we apply a 2D Fourier transform to the wave equation with respect to the coordinates in the plate plane, and then, in the 2D spectrum domain, for any given wave-vector in the plate plane, solving a vibration problem with respect to time and position in the direction perpendicular to the plate. The solution is expressed as the sum of mode responses, each mode having a resonance frequency and a shape which depend on the wave-vector in the plate plane. These calculations are different from those obtained by the usual method in the harmonic domain, where the modes are searched for a fixed frequency, such as Lamb waves, i.e. guided waves that propagate along the plate. In our case, the solution is given as a summation of plate resonances, i.e. a decomposition on the real eigenfrequencies, associated to Lamb waves with the same fixed wave-vector. This difference is of importance since only Lamb modes with real frequencies and real-valued wavenumbers in the plate plane are involved here, contrary to the usual harmonic methods, where these modes can be evanescent. This is of great interest as it can simplify the calculation of the generated field near the source. Finally, we obtain a solution in the physical domain by performing an inverse 2D Fourier transform. After a detailed description of the method, results are shown for two typical plates. It is emphasized that the method is accurate for observation points located both above or below the source and reasonably far from it along the plate.A nonstandard wave decomposition to ensure the convergence of Debye series for modeling wave propagation in an immersed anisotropic elastic plate
http://hdl.handle.net/10985/7388
A nonstandard wave decomposition to ensure the convergence of Debye series for modeling wave propagation in an immersed anisotropic elastic plate
DESCHAMPS, Marc; DUCASSE, Eric
When ultrasonic guided waves in an immersed plate are expressed as Debye series, they are considered as the result of successive reflections from the plate walls. Against all expectations, the Debye series can diverge for any geometry if inhomogeneous waves are involved in the problem. For an anisotropic elastic plate immersed in a fluid, this is the case if the incidence angle is greater than the first critical angle.Physically, this divergence can be explained by the energy coupling between two inhomogeneous waves of same kind of polarization, which are expressed by conjugate wavenumbers. Each of these latter inhomogeneous waves does not transfer energy but a linear combination of them can do it. Mathematically, this is due to the fact that inhomogeneous waves do not constitute a basis orthogonal in the sense of energy, contrarily to homogeneous waves. To avoid that difficulty, an orthogonalization of these inhomogeneous waves is required. Doing so, nonstandard upgoing and downgoing waves in the plate are introduced to ensure the convergence of the new Debye series written in the basis formed by these latter waves. The case of an aluminum plate immersed in water illustrates this study by giving numerical results and a detailed description of the latter nonstandard waves. The different reflection and refraction coefficients at each plate interface are analyzed in terms of Debye series convergence and of distribution of energy fluxes between the waves in the plate. From that investigation, an interesting physical phenomenon is described for one specific pair “angle of incidence/frequency”. For this condition, the quasi-energy brought by the incident harmonic plane wave crosses the plate without any conversion to reflected waves either at the first interface or at the second interface. In this zone, there is a perfect impedance matching between the fluid and the plate.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/73882012-01-01T00:00:00ZDESCHAMPS, MarcDUCASSE, EricWhen ultrasonic guided waves in an immersed plate are expressed as Debye series, they are considered as the result of successive reflections from the plate walls. Against all expectations, the Debye series can diverge for any geometry if inhomogeneous waves are involved in the problem. For an anisotropic elastic plate immersed in a fluid, this is the case if the incidence angle is greater than the first critical angle.Physically, this divergence can be explained by the energy coupling between two inhomogeneous waves of same kind of polarization, which are expressed by conjugate wavenumbers. Each of these latter inhomogeneous waves does not transfer energy but a linear combination of them can do it. Mathematically, this is due to the fact that inhomogeneous waves do not constitute a basis orthogonal in the sense of energy, contrarily to homogeneous waves. To avoid that difficulty, an orthogonalization of these inhomogeneous waves is required. Doing so, nonstandard upgoing and downgoing waves in the plate are introduced to ensure the convergence of the new Debye series written in the basis formed by these latter waves. The case of an aluminum plate immersed in water illustrates this study by giving numerical results and a detailed description of the latter nonstandard waves. The different reflection and refraction coefficients at each plate interface are analyzed in terms of Debye series convergence and of distribution of energy fluxes between the waves in the plate. From that investigation, an interesting physical phenomenon is described for one specific pair “angle of incidence/frequency”. For this condition, the quasi-energy brought by the incident harmonic plane wave crosses the plate without any conversion to reflected waves either at the first interface or at the second interface. In this zone, there is a perfect impedance matching between the fluid and the plate.Transient 3D elastodynamic field in an embedded multilayered anisotropic plate
http://hdl.handle.net/10985/10734
Transient 3D elastodynamic field in an embedded multilayered anisotropic plate
MORA, Pierric; DUCASSE, Eric; DESCHAMPS, Marc
The aim of this paper is to study the ultrasonic response to a transient source that radiates ultrasonic waves in a 3D embedded multilayered anisotropic and dissipative plate. The source can be inside the plate or outside, in a fluid loading the plate for example. In the context of Non-Destructive Testing applied to composite materials, our goal is to create a robust algorithm to calculate ultrasonic field, irrespective of the source and receiver positions. The principle of the method described in this paper is well-established. This method is based on time analysis using the Laplace transform. In the present work, it has been customized for computing ultrasonic source interactions with multilayered dissipative anisotropic plates. The fields are transformed in the 2D Fourier wave-vector domain for the space variables related to the plate surface, and they are expressed in the partial-wave basis. Surprisingly, this method has been very little used in the ultrasonic community, while it is a useful tool which complements the much used technique based on generalized Lamb wave decomposition. By avoiding mode analysis -- which can be problematic in some cases -- exact numerical calculations (i.e., approximations by truncating infinite series that may be poorly convergent are not needed) can be made in a relatively short time for immersed plates and viscoelastic layers. Even for 3D cases, numerical costs are relatively low. Special attention is given to separate up- and down-going waves, which is a simple matter when using the Laplace transform. Numerical results show the effectiveness of this method. Three examples are presented here to investigate the quality of the model and the robustness of the algorithm: first, a comparison of experiment and simulation for a monolayer carbon-epoxy plate, where the diffracted field is due to a source located on the first free surface of the sample, for both dissipative and non-dissipative cases; second, the basic configuration of an aluminum plate immersed in water has been chosen to study wave propagation in ZGV (Zero Group Velocity) conditions; finally, a 2D plate consisting of 8 stacked carbon-epoxy layers immersed in water is treated, with a source located inside the plate, distributed in depth and extending over four layers.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/107342016-01-01T00:00:00ZMORA, PierricDUCASSE, EricDESCHAMPS, MarcThe aim of this paper is to study the ultrasonic response to a transient source that radiates ultrasonic waves in a 3D embedded multilayered anisotropic and dissipative plate. The source can be inside the plate or outside, in a fluid loading the plate for example. In the context of Non-Destructive Testing applied to composite materials, our goal is to create a robust algorithm to calculate ultrasonic field, irrespective of the source and receiver positions. The principle of the method described in this paper is well-established. This method is based on time analysis using the Laplace transform. In the present work, it has been customized for computing ultrasonic source interactions with multilayered dissipative anisotropic plates. The fields are transformed in the 2D Fourier wave-vector domain for the space variables related to the plate surface, and they are expressed in the partial-wave basis. Surprisingly, this method has been very little used in the ultrasonic community, while it is a useful tool which complements the much used technique based on generalized Lamb wave decomposition. By avoiding mode analysis -- which can be problematic in some cases -- exact numerical calculations (i.e., approximations by truncating infinite series that may be poorly convergent are not needed) can be made in a relatively short time for immersed plates and viscoelastic layers. Even for 3D cases, numerical costs are relatively low. Special attention is given to separate up- and down-going waves, which is a simple matter when using the Laplace transform. Numerical results show the effectiveness of this method. Three examples are presented here to investigate the quality of the model and the robustness of the algorithm: first, a comparison of experiment and simulation for a monolayer carbon-epoxy plate, where the diffracted field is due to a source located on the first free surface of the sample, for both dissipative and non-dissipative cases; second, the basic configuration of an aluminum plate immersed in water has been chosen to study wave propagation in ZGV (Zero Group Velocity) conditions; finally, a 2D plate consisting of 8 stacked carbon-epoxy layers immersed in water is treated, with a source located inside the plate, distributed in depth and extending over four layers.Mode computation of immersed multilayer plates by solving an eigenvalue problem
http://hdl.handle.net/10985/22400
Mode computation of immersed multilayer plates by solving an eigenvalue problem
DESCHAMPS, Marc; DUCASSE, Eric
The aim of this paper is to compute modes of immersed multilayer plates by writing and solving an eigenvalue problem. The method can be applied to any kind of material with layers, i.e., fluid, anisotropic and viscoelastic. The two external interfaces of the plate can be described as either vacuum/vacuum, fluid/vacuum, or fluid/fluid with a single fluid or fluid/fluid with two different fluids. The method is based on the discretization of the plate by using a finite differences scheme in its vertical direction. One global state vector is associated with inner discretized positions of each layer, and two local state vectors characterize the physical state at its bounds. Interfacial state vectors are introduced in certain situations at external and internal plate interfaces. With these state vectors and after pertinent algebraic manipulations, an eigenvalue system is built. Its solutions are searched by fixing the slowness, wavevector or frequency of guided waves.
These three parameterizations correspond to three different physical models. For each case, discussions of dispersion curves and attenuation curves are given for guided modes in a plate loaded by fluids at one or two sides. This numerical tool is shown to provide convenience and accuracy.
Fri, 27 May 2022 00:00:00 GMThttp://hdl.handle.net/10985/224002022-05-27T00:00:00ZDESCHAMPS, MarcDUCASSE, EricThe aim of this paper is to compute modes of immersed multilayer plates by writing and solving an eigenvalue problem. The method can be applied to any kind of material with layers, i.e., fluid, anisotropic and viscoelastic. The two external interfaces of the plate can be described as either vacuum/vacuum, fluid/vacuum, or fluid/fluid with a single fluid or fluid/fluid with two different fluids. The method is based on the discretization of the plate by using a finite differences scheme in its vertical direction. One global state vector is associated with inner discretized positions of each layer, and two local state vectors characterize the physical state at its bounds. Interfacial state vectors are introduced in certain situations at external and internal plate interfaces. With these state vectors and after pertinent algebraic manipulations, an eigenvalue system is built. Its solutions are searched by fixing the slowness, wavevector or frequency of guided waves.
These three parameterizations correspond to three different physical models. For each case, discussions of dispersion curves and attenuation curves are given for guided modes in a plate loaded by fluids at one or two sides. This numerical tool is shown to provide convenience and accuracy.