The Experts below are selected from a list of 29226 Experts worldwide ranked by ideXlab platform

Talaganis Spyridon - One of the best experts on this subject based on the ideXlab platform.

  • The Distributional Stress-Energy Quadrupole
    2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on the quadrupole which has up to two partial or derivatives of the delta function. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example modelling a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves a second derivative and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way.Comment: 38 pages, 2 figure

  • The distributional stress-energy quadrupole
    'IOP Publishing', 2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example motivated from a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves second derivatives and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way

  • The Distributional Stress-Energy Quadrupole
    'IOP Publishing', 2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example motivated from a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves second derivatives and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way.Comment: 42 pages, 2 figures. Accepted by Classical and Quantum Gravity. url=http://iopscience.iop.org/article/10.1088/1361-6382/abccd

  • The Distributional Stress-Energy Quadrupole
    2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on the quadrupole which has up to two partial or derivatives of the delta function. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example modelling a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves a second derivative and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way

Touzé Cyril - One of the best experts on this subject based on the ideXlab platform.

  • Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
    'Elsevier BV', 2021
    Co-Authors: Vizzaccaro Alessandra, Shen Yichang, Salles Loïc, Blahoš Jiří, Touzé Cyril
    Abstract:

    International audienceThe direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate reduced-order models (ROM) relying on invariant manifold theory. The proposed reduction strategy is direct and simulation free, in the sense that it allows to pass from physical Coordinates (FE nodes) to normal Coordinates, describing the dynamics in an invariant-based span of the phase space. The number of master modes for the ROM is not a priori limited since a complete Change of Coordinate is proposed. The underlying theory ensures the quality of the predictions thanks to the invariance property of the reduced subspace, together with their curvatures in phase space that accounts for the nonresonant nonlinear couplings. The method is applied to a beam discretised with 3D elements and shows its ability in recovering internal resonance at high energy. Then a fan blade model is investigated and the correct prediction given by the ROMs are assessed and discussed. A method is proposed to approximate an aggregate value for the damping, that takes into account the damping coefficients of all the slave modes, and also using the Rayleigh damping model as input. Frequency-response curves for the beam and the blades are then exhibited, showing the accuracy of the proposed method

  • Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
    2020
    Co-Authors: Vizzaccaro Alessandra, Shen Yichang, Salles Loïc, Blahoš Jiří, Touzé Cyril
    Abstract:

    The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate reduced-order models (ROM) relying on invariant manifold theory. The proposed reduction strategy is direct and simulation free, in the sense that it allows to pass from physical Coordinates (FE nodes) to normal Coordinates, describing the dynamics in an invariant-based span of the phase space. The number of master modes for the ROM is not a priori limited since a complete Change of Coordinate is proposed. The underlying theory ensures the quality of the predictions thanks to the invariance property of the reduced subspace, together with their curvatures in phase space that accounts for the nonresonant nonlinear couplings. The method is applied to a beam discretised with 3D elements and shows its ability in recovering internal resonance at high energy. Then a fan blade model is investigated and the correct prediction given by the ROMs are assessed and discussed. A method is proposed to approximate an aggregate value for the damping, that takes into account the damping coefficients of all the slave modes, and also using the Rayleigh damping model as input. Frequency-response curves for the beam and the blades are then exhibited, showing the accuracy of the proposed method.Comment: 34 pages, 10 figures, 2 tables, submitted to CMAM

Gratus Jonathan - One of the best experts on this subject based on the ideXlab platform.

  • The Distributional Stress-Energy Quadrupole
    2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on the quadrupole which has up to two partial or derivatives of the delta function. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example modelling a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves a second derivative and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way.Comment: 38 pages, 2 figure

  • The distributional stress-energy quadrupole
    'IOP Publishing', 2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example motivated from a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves second derivatives and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way

  • The Distributional Stress-Energy Quadrupole
    'IOP Publishing', 2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example motivated from a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves second derivatives and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way.Comment: 42 pages, 2 figures. Accepted by Classical and Quantum Gravity. url=http://iopscience.iop.org/article/10.1088/1361-6382/abccd

  • The Distributional Stress-Energy Quadrupole
    2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on the quadrupole which has up to two partial or derivatives of the delta function. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example modelling a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves a second derivative and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way

Vizzaccaro Alessandra - One of the best experts on this subject based on the ideXlab platform.

  • Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
    'Elsevier BV', 2021
    Co-Authors: Vizzaccaro Alessandra, Shen Yichang, Salles Loïc, Blahoš Jiří, Touzé Cyril
    Abstract:

    International audienceThe direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate reduced-order models (ROM) relying on invariant manifold theory. The proposed reduction strategy is direct and simulation free, in the sense that it allows to pass from physical Coordinates (FE nodes) to normal Coordinates, describing the dynamics in an invariant-based span of the phase space. The number of master modes for the ROM is not a priori limited since a complete Change of Coordinate is proposed. The underlying theory ensures the quality of the predictions thanks to the invariance property of the reduced subspace, together with their curvatures in phase space that accounts for the nonresonant nonlinear couplings. The method is applied to a beam discretised with 3D elements and shows its ability in recovering internal resonance at high energy. Then a fan blade model is investigated and the correct prediction given by the ROMs are assessed and discussed. A method is proposed to approximate an aggregate value for the damping, that takes into account the damping coefficients of all the slave modes, and also using the Rayleigh damping model as input. Frequency-response curves for the beam and the blades are then exhibited, showing the accuracy of the proposed method

  • Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
    2020
    Co-Authors: Vizzaccaro Alessandra, Shen Yichang, Salles Loïc, Blahoš Jiří, Touzé Cyril
    Abstract:

    The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate reduced-order models (ROM) relying on invariant manifold theory. The proposed reduction strategy is direct and simulation free, in the sense that it allows to pass from physical Coordinates (FE nodes) to normal Coordinates, describing the dynamics in an invariant-based span of the phase space. The number of master modes for the ROM is not a priori limited since a complete Change of Coordinate is proposed. The underlying theory ensures the quality of the predictions thanks to the invariance property of the reduced subspace, together with their curvatures in phase space that accounts for the nonresonant nonlinear couplings. The method is applied to a beam discretised with 3D elements and shows its ability in recovering internal resonance at high energy. Then a fan blade model is investigated and the correct prediction given by the ROMs are assessed and discussed. A method is proposed to approximate an aggregate value for the damping, that takes into account the damping coefficients of all the slave modes, and also using the Rayleigh damping model as input. Frequency-response curves for the beam and the blades are then exhibited, showing the accuracy of the proposed method.Comment: 34 pages, 10 figures, 2 tables, submitted to CMAM

Pinto Paolo - One of the best experts on this subject based on the ideXlab platform.

  • The Distributional Stress-Energy Quadrupole
    2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on the quadrupole which has up to two partial or derivatives of the delta function. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example modelling a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves a second derivative and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way.Comment: 38 pages, 2 figure

  • The distributional stress-energy quadrupole
    'IOP Publishing', 2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example motivated from a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves second derivatives and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way

  • The Distributional Stress-Energy Quadrupole
    'IOP Publishing', 2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example motivated from a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves second derivatives and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way.Comment: 42 pages, 2 figures. Accepted by Classical and Quantum Gravity. url=http://iopscience.iop.org/article/10.1088/1361-6382/abccd

  • The Distributional Stress-Energy Quadrupole
    2020
    Co-Authors: Gratus Jonathan, Pinto Paolo, Talaganis Spyridon
    Abstract:

    We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on the quadrupole which has up to two partial or derivatives of the delta function. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example modelling a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the Change of Coordinate formula which involves a second derivative and two integrals. We also show how to define the quadrupole without reference to a Coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a Coordinate free way