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Gallezot Matthieu - One of the best experts on this subject based on the ideXlab platform.
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Forward models based on a modal approach for fast topological imaging of open elastic waveguides
HAL CCSD, 2020Co-Authors: Gallezot MatthieuAbstract:National audienceThis talk presents numerical models of the propagation and the diffraction of waves in open waveguides, i.e. with an unbounded cross-section. These structures are widely encountered in civil engineering (embedded rock bolts, buried pipes...). The models are based on modal decompositions of the source or at the boundaries of a finite element box enclosing a diffracting object. I first recall that guided modes are solutions of an eigenvalue problem written on the waveguide's cross-section truncated with a perfectly matched layer (PML). To guarantee the uniqueness of the modal expansions, an Orthogonality Relationship is derived. I then detail the complicated nature of the modal basis in open waveguides, and how it is modified when a perfectly matched layer (PML) is introduced in the transverse direction. Through several numerical test cases, I discuss whether and how the modal expansions can be truncated to reduce the computational cost. Finally, these models are combined to efficiently simulate topological imaging of open waveguides. The imaging function is the topological energy computed from the forward and adjoint fields, which are solutions of the forced response problem (same solver with two different sources). The synthetic diffracted field is obtained using both the forced response and the diffraction model
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Numerical modelling of non-destructive testing of buried waveguides
2018Co-Authors: Gallezot MatthieuAbstract:De nombreux éléments de structures de génie civil sont élancés et partiellement enfouis dans un milieu solide. Les ondes guidées sont souvent utilisées pour le contrôle non destructif (CND) de ces éléments. Ces derniers sont alors considérés comme des guides d’ondes ouverts, dans lesquels la plupart des ondes sont atténuées par des fuites dans le milieu environnant. D’autre part le problème est non borné, ce qui le rend difficile à appréhender sur le plan numérique. La combinaison d’une approche par éléments finis semi-analytique (SAFE) et de la méthode des couches parfaitement adaptées (PML) a été utilisée dans une thèse antérieure pour calculer numériquement trois types de modes (modes piégés, modes à fuite et modes de PML). Seuls les modes piégés et à fuite sont utilisés pour la représentation des courbes de dispersion. Les modes de PML sont non intrinsèques à la physique. L’objectif premier de cette thèse est d’obtenir, par superposition modale sur les modes calculés, les champs émis et diffracté dans les guides d’ondes ouverts. Nous montrons dans un premier temps que les trois types de modes appartiennent à la base modale. Une relation d’orthogonalité est obtenue dans la section du guide(incluant la PML) pour garantir l’unicité des solutions. La réponse forcée du guide peut alors être calculée rapidement par une somme sur les modes en tout point du guide. Des superpositions modales sont également utilisées pour construire des frontières transparentes au bord d’un petit domaine élément fini incluant un défaut, permettant ainsi de calculer le champ diffracté. Au cours de ces travaux, nous étudions les conditions d’approximation des solutions par des superpositions modales, limitées seulement aux modes à fuite, ce qui permet de réduire le coût des calculs. De plus, la généralité des méthodes proposées est démontrée par des calculs hautes fréquences (intéressantes pour le CND) et sur des guides tridimensionnels. Le deuxième objectif de cette thèse est de proposer une méthode d’imagerie pour la localisation de défauts. La méthode de l’imagerie topologique est appliquée aux guides d’ondes. Le cadre théorique général, de type optimisation sous contrainte, est rappelé. Le formalisme modal permet un calcul rapide de l’image. Nous l’appliquons pour simuler un guide d’onde endommagé, et nous montrons l’influence du type de champ émis (monomodal, dispersif,multimodal) ainsi que des configurations de mesure sur la qualité de l’image obtenue.Various elements of civil engineering structures are elongated and partially embedded in a solid medium. Guided waves can be used for the nondestructive evaluation (NDE) of such elements. The latteris therefore considered as an open waveguide, in which most of waves are attenuated by leakage losses into the surrounding medium. Furthermore, the problem is difficult to solve numerically because of its unboundedness. In aprevious thesis, it has been shown that the semi-analytical finite-element method (SAFE) and perfectly matched layers(PML) can be coupled for the numerical computation of modes. It yields three types of modes: trapped modes,leaky modes and PML modes. Only trapped and leaky modes are useful for the post-processing of dispersion curves. PML modes are non-intrinsic to the physics. The major aim of this thesis is to obtain the propagated and diffracted fields, based on modal superpositions on the numerical modes. First, we show that the three types of modes belong to the modal basis. To guarantee the uniqueness of the solutions an Orthogonality Relationship is derived on the section including the PML. The forced response can then be obtained very efficiently with a modal expansion at any point of the waveguide. Modal expansions are also used to build transparent boundaries at the cross-sections of a small finite-element domain enclosing a defect, thereby yielding the diffracted field. Throughout this work, we study whether solutions can be obtained with modal expansions on leaky modes only, which enables to reduce the computational cost. Besides, solutions are obtained at high frequencies (which are of interest for NDE) and in tridimensional waveguides, which demonstrates the generality of the methods. The second objective of this thesis is to propose an imaging method to locate defects. The topological imaging method is applied to a waveguide configuration. The general theoretical framework is recalled, based on constrained optimization theory. The image can be quickly computed thanks to the modal formalism. The case of a damaged waveguide is then simulated to assess the influence on image quality of the emitted field characteristics (monomodal, dispersive or multimodal)and of the measurement configuration
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Simulation numérique du contrôle non-destructif des guides d’ondes enfouis
HAL CCSD, 2018Co-Authors: Gallezot MatthieuAbstract:Various elements of civil engineering structures are elongated and partially embedded in a solid medium. Guided waves can be used for the nondestructive evaluation (NDE) of such elements. The latteris therefore considered as an open waveguide, in which most of waves are attenuated by leakage losses into the surrounding medium. Furthermore, the problem is difficult to solve numerically because of its unboundedness. In aprevious thesis, it has been shown that the semi-analytical finite-element method (SAFE) and perfectly matched layers(PML) can be coupled for the numerical computation of modes. It yields three types of modes: trapped modes,leaky modes and PML modes. Only trapped and leaky modes are useful for the post-processing of dispersion curves. PML modes are non-intrinsic to the physics. The major aim of this thesis is to obtain the propagated and diffracted fields, based on modal superpositions on the numerical modes. First, we show that the three types of modes belong to the modal basis. To guarantee the uniqueness of the solutions an Orthogonality Relationship is derived on the section including the PML. The forced response can then be obtained very efficiently with a modal expansion at any point of the waveguide. Modal expansions are also used to build transparent boundaries at the cross-sections of a small finite-element domain enclosing a defect, thereby yielding the diffracted field. Throughout this work, we study whether solutions can be obtained with modal expansions on leaky modes only, which enables to reduce the computational cost. Besides, solutions are obtained at high frequencies (which are of interest for NDE) and in tridimensional waveguides, which demonstrates the generality of the methods. The second objective of this thesis is to propose an imaging method to locate defects. The topological imaging method is applied to a waveguide configuration. The general theoretical framework is recalled, based on constrained optimization theory. The image can be quickly computed thanks to the modal formalism. The case of a damaged waveguide is then simulated to assess the influence on image quality of the emitted field characteristics (monomodal, dispersive or multimodal)and of the measurement configuration.De nombreux éléments de structures de génie civil sont élancés et partiellement enfouis dans un milieu solide. Les ondes guidées sont souvent utilisées pour le contrôle non destructif (CND) de ces éléments. Ces derniers sont alors considérés comme des guides d’ondes ouverts, dans lesquels la plupart des ondes sont atténuées par des fuites dans le milieu environnant. D’autre part le problème est non borné, ce qui le rend difficile à appréhender sur le plan numérique. La combinaison d’une approche par éléments finis semi-analytique (SAFE) et de la méthode des couches parfaitement adaptées (PML) a été utilisée dans une thèse antérieure pour calculer numériquement trois types de modes (modes piégés, modes à fuite et modes de PML). Seuls les modes piégés et à fuite sont utilisés pour la représentation des courbes de dispersion. Les modes de PML sont non intrinsèques à la physique. L’objectif premier de cette thèse est d’obtenir, par superposition modale sur les modes calculés, les champs émis et diffracté dans les guides d’ondes ouverts. Nous montrons dans un premier temps que les trois types de modes appartiennent à la base modale. Une relation d’orthogonalité est obtenue dans la section du guide(incluant la PML) pour garantir l’unicité des solutions. La réponse forcée du guide peut alors être calculée rapidement par une somme sur les modes en tout point du guide. Des superpositions modales sont également utilisées pour construire des frontières transparentes au bord d’un petit domaine élément fini incluant un défaut, permettant ainsi de calculer le champ diffracté. Au cours de ces travaux, nous étudions les conditions d’approximation des solutions par des superpositions modales, limitées seulement aux modes à fuite, ce qui permet de réduire le coût des calculs. De plus, la généralité des méthodes proposées est démontrée par des calculs hautes fréquences (intéressantes pour le CND) et sur des guides tridimensionnels. Le deuxième objectif de cette thèse est de proposer une méthode d’imagerie pour la localisation de défauts. La méthode de l’imagerie topologique est appliquée aux guides d’ondes. Le cadre théorique général, de type optimisation sous contrainte, est rappelé. Le formalisme modal permet un calcul rapide de l’image. Nous l’appliquons pour simuler un guide d’onde endommagé, et nous montrons l’influence du type de champ émis (monomodal, dispersif,multimodal) ainsi que des configurations de mesure sur la qualité de l’image obtenue
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Simulation numérique du contrôle non-destructif des guides d'ondes enfouis
HAL CCSD, 2018Co-Authors: Gallezot MatthieuAbstract:Various elements of civil engineering structures are elongated and partially embedded in a solid medium. Guided waves can be used for the non- destructive evaluation (NDE) of such elements. The latter is therefore considered as an open waveguide, in which most of waves are attenuated by leakage losses into the surrounding medium. Furthermore, the problem is difficult to solve numerically because of its unboundedness. In a previous thesis, it has been shown that the semi-analytical finite-element method (SAFE) and perfectly matched layers (PML) can be coupled for the numerical computation of modes. It yields three types of modes: trapped modes, leaky modes and PML modes. Only trapped and leaky modes are useful for the post-processing of dispersion curves. PML modes are non-intrinsic to the physics. The major aim of this thesis is to obtain the propagated and diffracted fields, based on modal superpositions on the numerical modes. First, we show that the three types of modes belong to the modal basis. To guarantee the uniqueness of the solutions an Orthogonality Relationship is derived on the section including the PML. The forced response can then be obtained very efficiently with a modal expansion at any point of the waveguide. Modal expansions are also used to build transparent boundaries at the cross-sections of a small finite-element domain enclosing a defect, thereby yielding the diffracted field. Throughout this work, we study whether solutions can be obtained with modal expansions on leaky modes only, which enables to reduce the computational cost. Besides, solutions are obtained at high frequencies (which are of interest for NDE) and in tridimensional waveguides, which demonstrates the generality of the methods. The second objective of this thesis is to propose an imaging method to locate defects. The topological imaging method is applied to a waveguide configuration. The general theoretical framework is recalled, based on constrained optimization theory. The image can be quickly computed thanks to the modal formalism. The case of a damaged waveguide is then simulated to assess the influence on image quality of the emitted field characteristics (monomodal, dispersive or multimodal) and of the measurement configuration.De nombreux éléments de structures de génie civil sont élancés et partiellement enfouis dans un milieu solide. Les ondes guidées sont souvent utilisées pour le contrôle non destructif (CND) de ces éléments. Ces derniers sont alors considérés comme des guides d'ondes ouverts, dans lesquels la plupart des ondes sont atténuées par des fuites dans le milieu environnant. D'autre part le problème est non borné, ce qui le rend difficile à appréhender sur le plan numérique. La combinaison d'une approche par éléments finis semi-analytique (SAFE) et de la méthode des couches parfaitement adaptées (PML) a été utilisée dans une thèse antérieure pour calculer numériquement trois types de modes (modes piégés, modes à fuite et modes de PML). Seuls les modes piégés et à fuite sont utilisés pour la représentation des courbes de dispersion. Les modes de PML sont non intrinsèques à la physique. L'objectif premier de cette thèse est d'obtenir, par superposition modale sur les modes calculés, les champs émis et diffracté dans les guides d'ondes ouverts. Nous montrons dans un premier temps que les trois types de modes appartiennent à la base modale. Une relation d'orthogonalité est obtenue dans la section du guide (incluant la PML) pour garantir l'unicité des solutions. La réponse forcée du guide peut alors être calculée rapidement par une somme sur les modes en tout point du guide. Des superpositions modales sont également utilisées pour construire des frontières transparentes au bord d'un petit domaine élément fini incluant un défaut, permettant ainsi de calculer le champ diffracté. Au cours de ces travaux, nous étudions les conditions d'approximation des solutions par des superpositions modales, limitées seulement aux modes à fuite, ce qui permet de réduire le coût des calculs. De plus, la généralité des méthodes proposées est démontrée par des calculs hautes fréquences (intéressantes pour le CND) et sur des guides tridimensionnels. Le deuxième objectif de cette thèse est de proposer une méthode d'imagerie pour la localisation de défauts. La méthode de l'imagerie topologique est appliquée aux guides d'ondes. Le cadre théorique général, de type optimisation sous contrainte, est rappelé. Le formalisme modal permet un calcul rapide de l'image. Nous l'appliquons pour simuler un guide d'onde endommagé, et nous montrons l'influence du type de champ émis (monomodal, dispersif, multimodal) ainsi que des configurations de mesure sur la qualité de l'image obtenue
Sondipon Adhikari - One of the best experts on this subject based on the ideXlab platform.
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Calculation of Eigensolution Derivatives for Nonviscously Damped Systems Using Nelson’s Method
2016Co-Authors: Sondipon Adhikari, Michael I. FriswellAbstract:A method to calculate the derivatives of the eigenvalues and eigenvectors of multiple-degree-of-freedom damped linear dynamic systems with respect to arbitrary design parameters is presented. In contrast to the traditional viscous damping model, a more general nonviscous damping model is considered. The nonviscous damping model is such that the damping forces depend on the past history of velocities via convolution integrals over given kernel functions. Because of the general nature of the damping, eigensolutions are generally complex valued, and eigenvectors do not satisfy the classical Orthogonality Relationship. The proposed method to calculate the eigenvector derivative depends only on the eigenvector concerned. Numerical examples are provided to illustrate the derived results. Nomenclature c j = constant associated with the derivative of u j D(s) = dynamic stiffness matrix d j = constant associated with the derivative of v j G(s) = Laplace transform of G(t) G(t) = nonviscous damping matrix K = stiffness matrix L [ ] = Laplace transform of [] M = mass matrix m = total number of eigenvectors N = number of degrees of freedom of the system n = number of relaxation parameters p = design parameter rank ( ) = rank of a matrix s = Laplace domain parameter u j = j th eigenvector (t) = displacement vector v j = j th adjoint (left) eigenvector x j = vector associated with the derivative of u j yj = vector associated with the derivative of v j θ j = normalization constant for the j th eigenvector λ j = j th eigenvalue μk = relaxation parameters Subscripts ()T = matrix transpose () ′ = derivative with respect to s I
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derivative of eigensolutions of nonviscously damped linear systems
AIAA Journal, 2002Co-Authors: Sondipon AdhikariAbstract:Derivatives of eigenvalues and eigenvectors of multiple-degree-of-freedom damped linear dynamic systems with respect to arbitrary design parameters are presented. In contrast to the traditional viscous damping model, a more general nonviscous damping model is considered. The nonviscous damping model is such that the damping forces depend on the past history of velocities via convolution integrals over some kernel functions. Because of the general nature of the damping, eigensolutions are generally complex valued, and eigenvectors do not satisfy any Orthogonality Relationship. It is shown that under such general conditions the derivative of eigensolutions can be expressed in a way similar to that of undamped or viscously damped systems. Numerical examples are provided to illustrate the derived results.
Michael I. Friswell - One of the best experts on this subject based on the ideXlab platform.
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Calculation of Eigensolution Derivatives for Nonviscously Damped Systems Using Nelson’s Method
2016Co-Authors: Sondipon Adhikari, Michael I. FriswellAbstract:A method to calculate the derivatives of the eigenvalues and eigenvectors of multiple-degree-of-freedom damped linear dynamic systems with respect to arbitrary design parameters is presented. In contrast to the traditional viscous damping model, a more general nonviscous damping model is considered. The nonviscous damping model is such that the damping forces depend on the past history of velocities via convolution integrals over given kernel functions. Because of the general nature of the damping, eigensolutions are generally complex valued, and eigenvectors do not satisfy the classical Orthogonality Relationship. The proposed method to calculate the eigenvector derivative depends only on the eigenvector concerned. Numerical examples are provided to illustrate the derived results. Nomenclature c j = constant associated with the derivative of u j D(s) = dynamic stiffness matrix d j = constant associated with the derivative of v j G(s) = Laplace transform of G(t) G(t) = nonviscous damping matrix K = stiffness matrix L [ ] = Laplace transform of [] M = mass matrix m = total number of eigenvectors N = number of degrees of freedom of the system n = number of relaxation parameters p = design parameter rank ( ) = rank of a matrix s = Laplace domain parameter u j = j th eigenvector (t) = displacement vector v j = j th adjoint (left) eigenvector x j = vector associated with the derivative of u j yj = vector associated with the derivative of v j θ j = normalization constant for the j th eigenvector λ j = j th eigenvalue μk = relaxation parameters Subscripts ()T = matrix transpose () ′ = derivative with respect to s I
Luo Jian-hui - One of the best experts on this subject based on the ideXlab platform.
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HAMILTONIAN SOLUTION SYSTEM FOR THICK PLATES AND ITS VARIATIONAL PRINCIPLE AND Orthogonality Relationship
Engineering mechanics, 2004Co-Authors: Luo Jian-huiAbstract:The Hamiltonian solution system is generalized to the Reissner-Mindlin thick plate problems. The Hamiltonian dual differential equations for thick plates are derived and the functional expressions of Hamiltonian variational principle are obtained using the variable substitution and multiplier method. Two Orthogonality Relationships of the thick plate theory are proposed and demonstrated. The Hamiltonian solution system for thick plates provides a new effective tool for the development of analytical solutions and finite element solutions of thick plates.
K.b. Ghazaryan - One of the best experts on this subject based on the ideXlab platform.
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Orthogonality Relationship FOR SHEAR WAVE MODES IN PIEZOELECTRIC WAVEGUIDE
Mechanics - Proceedings of National Academy of Sciences of Armenia, 2013Co-Authors: K.b. GhazaryanAbstract:In the framework of the full set of Maxwell equations and dynamic equations of the elasticity theory an Orthogonality Relationship is derived for interconnected electro-magneto-elastic shear wave modes in piezoelectric waveguide.
