Damped Natural Frequency

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Jae-hoon Kang - One of the best experts on this subject based on the ideXlab platform.

  • Closed-form exact solutions for hysteretically Damped longitudinal free and forced vibrations of tapered beams
    Acta Mechanica, 2018
    Co-Authors: Yeong-bin Yang, Jae-hoon Kang
    Abstract:

    Exact solutions for hysteretically Damped free vibrations of tapered longitudinal beams are obtained instead of unDamped free vibrations. Also forced vibrations of tapered longitudinal beams with hysteretical damping are studied by a closed-form exact method. The hysteretically Damped Natural Frequency equations are exactly derived. Accurate longitudinal amplitude versus forcing Frequency curves showing the forced response due to distributed loading are plotted with various hysteretical damping parameters. The present method is capable to be applied to a tapered tall building with hysteretic damping subjected to longitudinal harmonic loads like earthquake loads.

  • Closed-Form Exact Solutions for Viscously Damped Free and Forced Vibrations of Longitudinal and Torsional Bars
    International Journal of Structural Stability and Dynamics, 2017
    Co-Authors: Jae-hoon Kang
    Abstract:

    This paper studies the viscously Damped free and forced vibrations of longitudinal and torsional bars. The method is exact and yields closed form solution for the vibration displacement in contrast with the well-known eigenfunction superposition (ES) method, which requires expression of the distributed forcing functions and displacement response functions as infinite series sums of free vibration eigenfunctions. The viscously Damped Natural Frequency equation and the critical viscous damping equation are exactly derived for the bars. Then the viscously Damped free vibration frequencies and corresponding Damped mode shapes are calculated and plotted, aside from the unDamped free vibration and corresponding mode shapes typically computed and used in vibration problems. The longitudinal or torsional amplitude versus forcing Frequency curves showing the forced response to distributed loadings are plotted for various viscous damping parameters. It is found that the viscous damping affects the Natural frequenci...

  • Viscously Damped free and forced vibrations of circular and annular membranes by a closed form exact method
    Thin-walled Structures, 2017
    Co-Authors: Jae-hoon Kang
    Abstract:

    Abstract In the present paper, viscously Damped free and forced vibrations of circular and annular membranes are investigated using a closed form exact method. Instead of unDamped Natural frequencies which are typically computed and applied in the free and forced vibration analysis, viscously Damped Natural frequencies are done. It is certain that the viscous damping affects the Natural frequencies. The viscously Damped Natural Frequency equation and the critical viscous damping equation are exactly derived. In the viscously Damped free vibration analysis, effects on viscous damping on Natural frequencies are studied. In the viscously Damped forced vibration analysis, vibratory amplitudes are derived in a closed form exact manner. Accurate displacement amplitude vs. forcing Frequency curves showing the forced response due to distributed harmonic loading are displayed.

  • Closed form exact solutions of viscously Damped free and forced vibrations of rectangular membranes
    Journal of Vibration and Control, 2016
    Co-Authors: Jae-hoon Kang
    Abstract:

    In the present study, viscously Damped free and forced vibrations of a rectangular membrane are investigated using a closed form exact method. The method is exact and yields closed form expressions for the vibratory displacements. This is in contrast with the well known eigenfunction superposition method which requires expressing the distributed forcing functions and the displacement response functions as infinite sums of free vibration eigenfunctions. Instead of unDamped Natural frequencies which are typically computed and applied in the free and forced vibrations, Damped Natural frequencies are done. The Damped Natural Frequency equation and the critical viscous damping equation are exactly derived. In the Damped free vibration, effects of viscous damping on Natural frequencies and mode shapes are studied. Some contour plots of Damped mode shapes are given. Accurate displacement amplitude vs. forcing Frequency curves showing the forced response due to distributed loading are displayed.

  • Hysterically Damped free and forced vibrations of axial and torsional bars by a closed form exact method
    Journal of Sound and Vibration, 2016
    Co-Authors: Jae-hoon Kang
    Abstract:

    Abstract Hysterically Damped free and forced vibrations of axial and torsional bars are investigated using a closed form exact method. The method is exact and yields closed form expressions for the vibratory displacements. This is in contrast with the well known eigenfunction superposition method which requires expressing the distributed forcing functions and the displacement response functions as infinite sums of free vibration eigenfunctions. The hysterically Damped free vibration frequencies and corresponding Damped mode shapes are calculated and plotted instead of unDamped free vibration and mode shapes which is typically computed and applied in vibration problems. The hysterically Damped Natural Frequency equations are exactly derived. Accurate axial or torsional amplitude vs. forcing Frequency curves showing the forced response due to distributed loading are displayed with various hysteretic damping parameters.

Joseph Bentsman - One of the best experts on this subject based on the ideXlab platform.

  • Modeling and control of resonance effects in steel casting mold oscillators
    Acta Mechanica, 2019
    Co-Authors: Oyuna O. Angatkina, Vivek Natarajan, Zhelin Chen, M. Ding, Joseph Bentsman
    Abstract:

    A methodology for capturing resonance in a continuous-casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beams is proposed. The mechanism of the mold motion distortion generation in the mold oscillator is clearly delineated. Nontrivial Damped Natural Frequency and resonance Frequency calculations are carried out. Then, for a finite-difference analytical beam model approximation, a discovery of monotonic dependence on spatial approximation accuracy of the beam resonance Frequency under the fixed mass and of the mass under the fixed resonance Frequency is demonstrated numerically. Based on these findings, a novel beam parameters selection procedure for the precise attainment of the desired resonance and Damped Natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the beam model parameters to match the actual resonance frequencies exhibited by thin and thick slab casting mold oscillators at, respectively, the Nucor Decatur and the AK Steel Dearborn steel mills, is demonstrated. The resulting resonance Frequency value for the latter is then used to guide the internal-model-principle-based controller design for resonance suppression in the software testbed for the AK Steel caster mold oscillator.

  • ACC - Capturing and suppressing resonance in steel casting mold oscillation systems using Timoshenko beam model
    2015 American Control Conference (ACC), 2015
    Co-Authors: Oyuna O. Angatkina, Vivek Natarajan, Zhelin Chen, Joseph Bentsman
    Abstract:

    A methodology for development of high fidelity control-oriented continuous casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beam models is proposed. Nontrivial Damped Natural Frequency calculation is carried out. For a finite-difference approximation of analytical model, monotonic dependence on spatial approximation accuracy of the resonance Frequency under the fixed mass and of the mass under the fixed resonance Frequency is discovered. Based on these findings, a novel beam parameter selection procedure for precise attainment of the desired resonance and Damped Natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the model parameters to resonance frequencies exhibited by thin and thick slab casting mold oscillators at the Nucor Decatur and Severstal Dearborn steel mills, respectively, is demonstrated. Assessment of controller efficacy in suppression of the undesirable oscillations in the software testbed fitted to Severstal caster is shown.

Oyuna O. Angatkina - One of the best experts on this subject based on the ideXlab platform.

  • Modeling and control of resonance effects in steel casting mold oscillators
    Acta Mechanica, 2019
    Co-Authors: Oyuna O. Angatkina, Vivek Natarajan, Zhelin Chen, M. Ding, Joseph Bentsman
    Abstract:

    A methodology for capturing resonance in a continuous-casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beams is proposed. The mechanism of the mold motion distortion generation in the mold oscillator is clearly delineated. Nontrivial Damped Natural Frequency and resonance Frequency calculations are carried out. Then, for a finite-difference analytical beam model approximation, a discovery of monotonic dependence on spatial approximation accuracy of the beam resonance Frequency under the fixed mass and of the mass under the fixed resonance Frequency is demonstrated numerically. Based on these findings, a novel beam parameters selection procedure for the precise attainment of the desired resonance and Damped Natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the beam model parameters to match the actual resonance frequencies exhibited by thin and thick slab casting mold oscillators at, respectively, the Nucor Decatur and the AK Steel Dearborn steel mills, is demonstrated. The resulting resonance Frequency value for the latter is then used to guide the internal-model-principle-based controller design for resonance suppression in the software testbed for the AK Steel caster mold oscillator.

  • ACC - Capturing and suppressing resonance in steel casting mold oscillation systems using Timoshenko beam model
    2015 American Control Conference (ACC), 2015
    Co-Authors: Oyuna O. Angatkina, Vivek Natarajan, Zhelin Chen, Joseph Bentsman
    Abstract:

    A methodology for development of high fidelity control-oriented continuous casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beam models is proposed. Nontrivial Damped Natural Frequency calculation is carried out. For a finite-difference approximation of analytical model, monotonic dependence on spatial approximation accuracy of the resonance Frequency under the fixed mass and of the mass under the fixed resonance Frequency is discovered. Based on these findings, a novel beam parameter selection procedure for precise attainment of the desired resonance and Damped Natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the model parameters to resonance frequencies exhibited by thin and thick slab casting mold oscillators at the Nucor Decatur and Severstal Dearborn steel mills, respectively, is demonstrated. Assessment of controller efficacy in suppression of the undesirable oscillations in the software testbed fitted to Severstal caster is shown.

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

  • Modeling and control of resonance effects in steel casting mold oscillators
    Acta Mechanica, 2019
    Co-Authors: Oyuna O. Angatkina, Vivek Natarajan, Zhelin Chen, M. Ding, Joseph Bentsman
    Abstract:

    A methodology for capturing resonance in a continuous-casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beams is proposed. The mechanism of the mold motion distortion generation in the mold oscillator is clearly delineated. Nontrivial Damped Natural Frequency and resonance Frequency calculations are carried out. Then, for a finite-difference analytical beam model approximation, a discovery of monotonic dependence on spatial approximation accuracy of the beam resonance Frequency under the fixed mass and of the mass under the fixed resonance Frequency is demonstrated numerically. Based on these findings, a novel beam parameters selection procedure for the precise attainment of the desired resonance and Damped Natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the beam model parameters to match the actual resonance frequencies exhibited by thin and thick slab casting mold oscillators at, respectively, the Nucor Decatur and the AK Steel Dearborn steel mills, is demonstrated. The resulting resonance Frequency value for the latter is then used to guide the internal-model-principle-based controller design for resonance suppression in the software testbed for the AK Steel caster mold oscillator.

  • ACC - Capturing and suppressing resonance in steel casting mold oscillation systems using Timoshenko beam model
    2015 American Control Conference (ACC), 2015
    Co-Authors: Oyuna O. Angatkina, Vivek Natarajan, Zhelin Chen, Joseph Bentsman
    Abstract:

    A methodology for development of high fidelity control-oriented continuous casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beam models is proposed. Nontrivial Damped Natural Frequency calculation is carried out. For a finite-difference approximation of analytical model, monotonic dependence on spatial approximation accuracy of the resonance Frequency under the fixed mass and of the mass under the fixed resonance Frequency is discovered. Based on these findings, a novel beam parameter selection procedure for precise attainment of the desired resonance and Damped Natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the model parameters to resonance frequencies exhibited by thin and thick slab casting mold oscillators at the Nucor Decatur and Severstal Dearborn steel mills, respectively, is demonstrated. Assessment of controller efficacy in suppression of the undesirable oscillations in the software testbed fitted to Severstal caster is shown.

Vivek Natarajan - One of the best experts on this subject based on the ideXlab platform.

  • Modeling and control of resonance effects in steel casting mold oscillators
    Acta Mechanica, 2019
    Co-Authors: Oyuna O. Angatkina, Vivek Natarajan, Zhelin Chen, M. Ding, Joseph Bentsman
    Abstract:

    A methodology for capturing resonance in a continuous-casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beams is proposed. The mechanism of the mold motion distortion generation in the mold oscillator is clearly delineated. Nontrivial Damped Natural Frequency and resonance Frequency calculations are carried out. Then, for a finite-difference analytical beam model approximation, a discovery of monotonic dependence on spatial approximation accuracy of the beam resonance Frequency under the fixed mass and of the mass under the fixed resonance Frequency is demonstrated numerically. Based on these findings, a novel beam parameters selection procedure for the precise attainment of the desired resonance and Damped Natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the beam model parameters to match the actual resonance frequencies exhibited by thin and thick slab casting mold oscillators at, respectively, the Nucor Decatur and the AK Steel Dearborn steel mills, is demonstrated. The resulting resonance Frequency value for the latter is then used to guide the internal-model-principle-based controller design for resonance suppression in the software testbed for the AK Steel caster mold oscillator.

  • ACC - Capturing and suppressing resonance in steel casting mold oscillation systems using Timoshenko beam model
    2015 American Control Conference (ACC), 2015
    Co-Authors: Oyuna O. Angatkina, Vivek Natarajan, Zhelin Chen, Joseph Bentsman
    Abstract:

    A methodology for development of high fidelity control-oriented continuous casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beam models is proposed. Nontrivial Damped Natural Frequency calculation is carried out. For a finite-difference approximation of analytical model, monotonic dependence on spatial approximation accuracy of the resonance Frequency under the fixed mass and of the mass under the fixed resonance Frequency is discovered. Based on these findings, a novel beam parameter selection procedure for precise attainment of the desired resonance and Damped Natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the model parameters to resonance frequencies exhibited by thin and thick slab casting mold oscillators at the Nucor Decatur and Severstal Dearborn steel mills, respectively, is demonstrated. Assessment of controller efficacy in suppression of the undesirable oscillations in the software testbed fitted to Severstal caster is shown.