Damping Matrix

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Christian Soize - One of the best experts on this subject based on the ideXlab platform.

  • Uncertainty quantification in computational linear structural dynamics for viscoelastic composite structures
    Computer Methods in Applied Mechanics and Engineering, 2017
    Co-Authors: Rémi Capillon, Christophe Desceliers, Christian Soize
    Abstract:

    This paper deals with the analysis of a stochastic reduced-order computational model in computational linear dynamics for linear viscoelastic composite structures in the presence of uncertainties. The computational framework proposed is based on a recent theoretical work that allows for constructing the stochastic reduced-order model using the nonparametric probabilistic approach. In the frequency domain, the generalized Damping Matrix and the generalized stiffness Matrix of the stochastic computational reduced-order model are random matrices. Due to the causality of the dynamical system, these two frequency-dependent random matrices are statistically dependent and are linked by a compatibility equation induced by the causality of the system, involving a Hilbert transform. The computational aspects related to the nonparametric stochastic modeling of the reduced stiffness Matrix and the reduced Damping Matrix that are frequency-dependent random matrices are presented. A dedicated numerical approach is developed for obtaining an efficient computation of the Cauchy principal value integrals involved in those equations for which an integration over a broad frequency domain is required. A computational analysis of the propagation of uncertainties is conducted for a composite viscoelastic structure in the frequency range. It is shown that the uncertainties on the Damping Matrix have a strong influence on the observed statistical dispersion of the stiffness Matrix.

  • Vibration Damping in low-frequency range due to structural complexity. A Model based on the theory of fuzzy structures and model parameters estimation.
    Computers and Structures, 1996
    Co-Authors: Christian Soize
    Abstract:

    We present a modeling of the structural dissipation due to internal structural complexity, adapted to the low-frequency range for which the frequency response function of the master structure can be constructed by the modal synthesis. This vibration Damping model is deduced from the theory of fuzzy structures which was previously developed by the author. Presently, this model uses only the mean part of the probabilistic fuzzy law of the fuzzy substructure. We give an explicit model of the generalized Damping Matrix induced by the internal structural complexity. This generalized Damping Matrix depends on parameters related to the fuzzy substructure. Finally, model updating considerations are studied and an example is presented.

Paul Fromme - One of the best experts on this subject based on the ideXlab platform.

  • Modelling wind turbine tower-rotor interaction through an aerodynamic Damping Matrix
    Journal of Sound and Vibration, 2020
    Co-Authors: Chao Chen, Philippe Duffour, Paul Fromme
    Abstract:

    Abstract Current wind turbine modelling packages mainly adopt a complex methodology in which aerodynamic forces are coupled with the motion of the wind turbine components at every time step. This can result in long simulation run times, detrimental for the large number of simulations required for fatigue or reliability analyses. This contribution presents an efficient wind turbine modelling methodology based on blade element momentum theory and a linearization of the aerodynamic forces. This allows the wind-rotor interaction to be reduced to static forces applied at the tower top, with additional terms proportional to the tower velocities expressed as an aerodynamic Damping Matrix. This aerodynamic model was implemented as part of a finite element model of the tower and was successfully verified against the fully-coupled modelling package FAST. The Damping Matrix components explain key features of the coupling between fore-aft and side-side vibrations of the wind turbine. This coupling causes energy transfers between the two directions, complicating aerodynamic Damping identification. The aerodynamic Damping Matrix offers novel insights and an efficient method to describe the aerodynamic Damping of wind turbines.

  • Identification of aerodynamic Damping Matrix for operating wind turbines
    Mechanical Systems and Signal Processing, 1
    Co-Authors: Chao Chen, Philippe Duffour, Kaoshan Dai, Ying Wang, Paul Fromme
    Abstract:

    Abstract Accurate knowledge of wind turbine tower vibration Damping is essential for the estimation of fatigue life. However, the responses in the fore-aft and side-side directions are coupled through the wind-rotor interaction under operational conditions. This causes energy transfers and complicates aerodynamic Damping identification using conventional Damping ratios. Employing a reduced two-degree of freedom wind turbine model developed in this paper, this coupling can be accurately expressed by an unconventional aerodynamic Damping Matrix. Simulated time series obtained from this model were successfully verified against the outputs from the wind turbine simulation tool FAST. Based on the reduced system obtained, a Matrix-based identification method is proposed to identify the aerodynamic Damping for numerically simulated wind turbine tower responses. Applying harmonic excitations to the tower allowed the frequency response functions of the wind turbine system to be obtained and the aerodynamic Damping Matrix to be extracted. Results from this identification were compared to traditional operational modal analysis methods including standard and modified stochastic subspace identification. The Damping in the fore-aft direction was successfully identified by all methods, but results showed that the identified Damping Matrix performs better in capturing the aerodynamic Damping and coupling for the side-side responses.

S.v. Modak - One of the best experts on this subject based on the ideXlab platform.

  • Damping Matrix Identification by Finite Element Model Updating Using Frequency Response Data
    International Journal of Structural Stability and Dynamics, 2017
    Co-Authors: S. Pradhan, S.v. Modak
    Abstract:

    Accurate modeling of Damping is essential for prediction of vibration response of a structure. This paper presents a study of Damping Matrix identification method using experimental data. The identification is done by performing finite element (FE) model updating using normal frequency response functions (FRFs). The paper addresses some key issues like data incompleteness and computation of the normal FRFs for carrying out the model updating using experimental data. The effect of various levels of Damping in structures on the performance of the identification techniques is also investigated. Experimental studies on three beam structures made up of mild steel, cast iron and acrylic are presented to demonstrate the effectiveness of the identification techniques for different levels of Damping.

  • A Review of Damping Matrix Identification Methods in Structural Dynamics
    Volume 12: Vibration Acoustics and Wave Propagation, 2012
    Co-Authors: Sharad K. Pradhan, S.v. Modak
    Abstract:

    Damping Matrix modeling and identification has important applications in many engineering fields such as vibration analysis and control, modal analysis, condition monitoring and structural dynamic modifications. A Damping model should represent both the mechanism and spatial distribution of the energy loss in the system. In contrast to the mass and stiffness matrices, formulation of the Damping Matrix still stands as a big challenge in modeling a linear dynamic system. Several methods have been proposed in the literature to identify the Damping and the parameters of a Damping Matrix from measurements on a vibrating system. It is felt that a review of the various approaches developed would help to compare their main features and their relative advantages or limitations to allow for choosing the most suitable method for a particular application. In view of this, this paper presents a review of the methods of Damping identification in general, but with more emphasis on the methods developed in the framework of finite element model updating.Copyright © 2012 by ASME

  • A method for Damping Matrix identification using frequency response data
    Mechanical Systems and Signal Processing, 2012
    Co-Authors: Sharad K. Pradhan, S.v. Modak
    Abstract:

    Abstract Accurate modeling of Damping in structures is of great importance for vibration response analysis and control. This paper addresses the issue of identification of Damping Matrix of a structure by posing it as a finite element Damping Matrix updating problem. Many of the current updating approaches, dealing with updating of Damping Matrix, perform simultaneous updating of mass, stiffness and Damping matrices. However, such a strategy is faced with numerical problems in practical implementation, since the magnitude of stiffness and mass Matrix elements is generally much more than that of the Damping Matrix elements causing difficulties in accurate identification of the Damping Matrix. Some other approaches divide the process of updating of the mass and stiffness Matrix and the Damping Matrix into two stages, but their application is restricted to structures with low levels of Damping. This paper addresses these issues by developing an updating formulation that seeks to separate updating of the Damping Matrix from that of updating of the stiffness and the mass Matrix. The proposed Damping Matrix updating method utilizes the concept of normal frequency response functions (FRFs) available in the literature. The method is formulated so as to reduce the difference between the complex FRFs, which can be measured in practice, and the normal FRFs, whose estimates can be obtained from the measured complex FRFs. The effectiveness of the proposed method is demonstrated through a numerical study on a simple but representative beam structure. The issue of coordinate incompleteness and robustness of the method under presence of noise is investigated. It is found that the proposed method is effective in the accurate identification of the Damping Matrix in cases of complete, incomplete and noisy data and is not limited by the level of Damping in the structure.

Chao Chen - One of the best experts on this subject based on the ideXlab platform.

  • Modelling wind turbine tower-rotor interaction through an aerodynamic Damping Matrix
    Journal of Sound and Vibration, 2020
    Co-Authors: Chao Chen, Philippe Duffour, Paul Fromme
    Abstract:

    Abstract Current wind turbine modelling packages mainly adopt a complex methodology in which aerodynamic forces are coupled with the motion of the wind turbine components at every time step. This can result in long simulation run times, detrimental for the large number of simulations required for fatigue or reliability analyses. This contribution presents an efficient wind turbine modelling methodology based on blade element momentum theory and a linearization of the aerodynamic forces. This allows the wind-rotor interaction to be reduced to static forces applied at the tower top, with additional terms proportional to the tower velocities expressed as an aerodynamic Damping Matrix. This aerodynamic model was implemented as part of a finite element model of the tower and was successfully verified against the fully-coupled modelling package FAST. The Damping Matrix components explain key features of the coupling between fore-aft and side-side vibrations of the wind turbine. This coupling causes energy transfers between the two directions, complicating aerodynamic Damping identification. The aerodynamic Damping Matrix offers novel insights and an efficient method to describe the aerodynamic Damping of wind turbines.

  • Identification of aerodynamic Damping Matrix for operating wind turbines
    Mechanical Systems and Signal Processing, 1
    Co-Authors: Chao Chen, Philippe Duffour, Kaoshan Dai, Ying Wang, Paul Fromme
    Abstract:

    Abstract Accurate knowledge of wind turbine tower vibration Damping is essential for the estimation of fatigue life. However, the responses in the fore-aft and side-side directions are coupled through the wind-rotor interaction under operational conditions. This causes energy transfers and complicates aerodynamic Damping identification using conventional Damping ratios. Employing a reduced two-degree of freedom wind turbine model developed in this paper, this coupling can be accurately expressed by an unconventional aerodynamic Damping Matrix. Simulated time series obtained from this model were successfully verified against the outputs from the wind turbine simulation tool FAST. Based on the reduced system obtained, a Matrix-based identification method is proposed to identify the aerodynamic Damping for numerically simulated wind turbine tower responses. Applying harmonic excitations to the tower allowed the frequency response functions of the wind turbine system to be obtained and the aerodynamic Damping Matrix to be extracted. Results from this identification were compared to traditional operational modal analysis methods including standard and modified stochastic subspace identification. The Damping in the fore-aft direction was successfully identified by all methods, but results showed that the identified Damping Matrix performs better in capturing the aerodynamic Damping and coupling for the side-side responses.

Rémi Capillon - One of the best experts on this subject based on the ideXlab platform.

  • Uncertainty quantification in computational linear structural dynamics for viscoelastic composite structures
    Computer Methods in Applied Mechanics and Engineering, 2017
    Co-Authors: Rémi Capillon, Christophe Desceliers, Christian Soize
    Abstract:

    This paper deals with the analysis of a stochastic reduced-order computational model in computational linear dynamics for linear viscoelastic composite structures in the presence of uncertainties. The computational framework proposed is based on a recent theoretical work that allows for constructing the stochastic reduced-order model using the nonparametric probabilistic approach. In the frequency domain, the generalized Damping Matrix and the generalized stiffness Matrix of the stochastic computational reduced-order model are random matrices. Due to the causality of the dynamical system, these two frequency-dependent random matrices are statistically dependent and are linked by a compatibility equation induced by the causality of the system, involving a Hilbert transform. The computational aspects related to the nonparametric stochastic modeling of the reduced stiffness Matrix and the reduced Damping Matrix that are frequency-dependent random matrices are presented. A dedicated numerical approach is developed for obtaining an efficient computation of the Cauchy principal value integrals involved in those equations for which an integration over a broad frequency domain is required. A computational analysis of the propagation of uncertainties is conducted for a composite viscoelastic structure in the frequency range. It is shown that the uncertainties on the Damping Matrix have a strong influence on the observed statistical dispersion of the stiffness Matrix.