The Experts below are selected from a list of 69342 Experts worldwide ranked by ideXlab platform
Shaopu Yang - One of the best experts on this subject based on the ideXlab platform.
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Primary Resonance of Computer Numerical Control Worktable With Clearance and Friction
Journal of Computational and Nonlinear Dynamics, 2020Co-Authors: Jiangchuan Niu, Zhishuang Zhao, Yongjun Shen, Shaopu YangAbstract:Abstract Computer numerical control (CNC) worktable is the most important part of CNC machines. The CNC worktable exhibits complex nonlinear dynamic behaviors in the milling process. The physical model and mathematical model of CNC worktable are presented, where the nonlinear factors such as clearance and friction are considered. The Primary Resonance of computer numerical control worktable with clearance and friction under harmonic excitation is investigated. The approximate analytical solution of Primary Resonance is obtained by using the averaging method. The stability condition of the steady-state solution is also exhibited. It is found that the clearance affects the dynamic characteristics of the system in the form of equivalent nonlinear stiffness, and the friction coefficient acts in the form of equivalent nonlinear damping. The correctness of the approximate analytical solutions is verified by comparing the numerical results with the approximate analytical solutions. The approximate analytical solution is in good agreement with its corresponding numerical solution. The effects of clearance and friction on the dynamic characteristics of the system are analyzed in detail. The stick-slip vibration induced by friction is also analyzed by phase portrait at low feed velocity of machine tool. The results can provide a reference for the dynamic analysis of CNC worktable.
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Primary Resonance of Dry-Friction Oscillator With Fractional-Order Proportional-Integral-Derivative Controller of Velocity Feedback
Journal of Computational and Nonlinear Dynamics, 2016Co-Authors: Yongjun Shen, Jiangchuan Niu, Shaopu YangAbstract:The classical mass-on-moving-belt model describing friction-induced vibration is studied. The Primary Resonance of dry-friction oscillator with fractional-order PID (FOPID) controller of velocity feedback is investigated by Krylov–Bogoliubov–Mitropolsky (KBM) asymptotic method, and the approximately analytical solution is obtained. The effects of the parameters in FOPID controller on dynamical properties are characterized by five equivalent parameters. Those equivalent parameters could distinctly illustrate the effects of the parameters in FOPID controller on the dynamical response. The effects of dry friction on the dynamical properties are characterized in the form of the equivalent linear damping and nonlinear damping. The amplitude-frequency equation for steady-state solution associated with the stability condition is also studied. A comparison of the analytical solution with the numerical results is fulfilled, and their satisfactory agreement verifies the correctness of the approximately analytical results. Finally, the effects of the coefficients and orders in FOPID controller on the amplitude-frequency curves are analyzed, and the control performances of FOPID and traditional integer-order proportional-integral-derivative (PID) controllers are compared. The comparison results show that FOPID controller is better than traditional integer-order PID controller for controlling the Primary Resonance of dry-friction oscillator, when the coefficients of the two controllers are the same. This presents theoretical basis for scholars and engineers to design similar fractional-order controlled system.
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Primary Resonance of fractional-order van der Pol oscillator
Nonlinear Dynamics, 2014Co-Authors: Yongjun Shen, Peng Wei, Shaopu YangAbstract:In this paper the Primary Resonance of van der Pol (VDP) oscillator with fractional-order derivative is studied analytically and numerically. At first the approximately analytical solution is obtained by the averaging method, and it is found that the fractional-order derivative could affect the dynamical properties of VDP oscillator, which is characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. Moreover, the amplitude–frequency equation for steady-state solution is established, and the corresponding stability condition is also presented based on Lyapunov theory. Then, the comparisons of several different amplitude–frequency curves by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. At last, the effects of the two fractional parameters, i.e., the fractional coefficient and the fractional order, on the amplitude–frequency curves are investigated for some typical excitation amplitudes, which are different from the traditional integer-order VDP oscillator.
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Primary Resonance of duffing oscillator with two kinds of fractional order derivatives
International Journal of Non-linear Mechanics, 2012Co-Authors: Yongjun Shen, Shaopu Yang, Haijun XingAbstract:Abstract In this paper, the Primary Resonance of Duffing oscillator with two kinds of fractional-order derivatives is investigated analytically. Based on the averaging method, the approximately analytical solution and the amplitude–frequency equation are obtained. The effects of the two kinds of fractional-order derivatives on the system dynamics are analyzed, and it is found that these two kinds of fractional-order derivatives could affect not only the linear viscous damping, but also the linear stiffness, which could be characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. The different effects are analyzed based on these two deduced equivalent parameters, when the two fractional orders are limited in the typical intervals, i.e. p 1 ∈[0 1] and p 2 ∈[1 2]. Moreover, the comparisons of the amplitude–frequency curves obtained by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. Especially, the effects of the parameters in the second kind of fractional-order derivative are studied when the coefficient of the first kind of fractional-order derivative is zero or not. At last, two special cases for the coefficient of the second kind of fractional-order derivative are analyzed, which could make engineers obtain satisfactory vibration control performance and keep the frequency characteristic almost unchanged. These results are very useful in vibration control engineering.
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Primary Resonance of Duffing oscillator with fractional-order derivative
Communications in Nonlinear Science and Numerical Simulation, 2012Co-Authors: Yongjun Shen, Shaopu Yang, Xing Haijun, Guo-sheng GaoAbstract:Abstract In this paper the Primary Resonance of Duffing oscillator with fractional-order derivative is researched by the averaging method. At first the approximately analytical solution and the amplitude–frequency equation are obtained. Additionally, the effect of the fractional-order derivative on the system dynamics is analyzed, and it is found that the fractional-order derivative could affect not only the viscous damping, but also the linear stiffness, which is characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. This conclusion is remarkably different from the existing research results about nonlinear system with fractional-order derivative. Moreover, the comparisons of the amplitude–frequency curves by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. At last, the effects of the two parameters of the fractional-order derivative, i.e. the fractional coefficient and the fractional order, on the amplitude–frequency curves are investigated, which are different from the traditional integer-order Duffing oscillator.
A. Maccari - One of the best experts on this subject based on the ideXlab platform.
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Vibration Control for the Primary Resonance of a Cantilever Beam by a Time Delay State Feedback
Journal of Sound and Vibration, 2003Co-Authors: A. MaccariAbstract:Abstract The Primary Resonance of a cantilever beam under state feedback control with a time delay is investigated. By means of the asymptotic perturbation method, two slow-flow equations on the amplitude and phase of the oscillator are obtained and external excitation–response and frequency–response curves are shown. Vibration control and high-amplitude response suppression can be performed with appropriate time delay and feedback gains. Moreover, energy considerations are used in order to investigate existence and characteristics of quasiperiodic modulated motion for the cantilever beam. It can be demonstrated that appropriate choices for the feedback gains and the time delay can exclude the possibility of modulated motion and reduce the amplitude peak of the Primary Resonance. Analytical results are verified with numerical simulations.
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Vibration control for the Primary Resonance of the van der Pol oscillator by a time delay state feedback
International Journal of Non-Linear Mechanics, 2003Co-Authors: A. MaccariAbstract:Abstract We investigate the Primary Resonance of an externally excited van der Pol oscillator under state feedback control with a time delay. By means of the asymptotic perturbation method, two slow-flow equations on the amplitude and phase of the oscillator are obtained and external excitation–response and frequency–response curves are shown. We discuss how vibration control and high amplitude response suppression can be performed with appropriate time delay and feedback gains. Moreover, energy considerations are used in order to investigate existence and characteristics of limit cycles of the slow-flow equations. A limit cycle corresponds to a two-period modulated motion for the van der Pol oscillator. We demonstrate that appropriate choices for the feedback gains and the time delay can exclude the possibility of modulated motion and reduce the amplitude peak of the Primary Resonance. Analytical results are verified with numerical simulations.
Yongjun Shen - One of the best experts on this subject based on the ideXlab platform.
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Primary Resonance of Computer Numerical Control Worktable With Clearance and Friction
Journal of Computational and Nonlinear Dynamics, 2020Co-Authors: Jiangchuan Niu, Zhishuang Zhao, Yongjun Shen, Shaopu YangAbstract:Abstract Computer numerical control (CNC) worktable is the most important part of CNC machines. The CNC worktable exhibits complex nonlinear dynamic behaviors in the milling process. The physical model and mathematical model of CNC worktable are presented, where the nonlinear factors such as clearance and friction are considered. The Primary Resonance of computer numerical control worktable with clearance and friction under harmonic excitation is investigated. The approximate analytical solution of Primary Resonance is obtained by using the averaging method. The stability condition of the steady-state solution is also exhibited. It is found that the clearance affects the dynamic characteristics of the system in the form of equivalent nonlinear stiffness, and the friction coefficient acts in the form of equivalent nonlinear damping. The correctness of the approximate analytical solutions is verified by comparing the numerical results with the approximate analytical solutions. The approximate analytical solution is in good agreement with its corresponding numerical solution. The effects of clearance and friction on the dynamic characteristics of the system are analyzed in detail. The stick-slip vibration induced by friction is also analyzed by phase portrait at low feed velocity of machine tool. The results can provide a reference for the dynamic analysis of CNC worktable.
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Primary Resonance of Dry-Friction Oscillator With Fractional-Order Proportional-Integral-Derivative Controller of Velocity Feedback
Journal of Computational and Nonlinear Dynamics, 2016Co-Authors: Yongjun Shen, Jiangchuan Niu, Shaopu YangAbstract:The classical mass-on-moving-belt model describing friction-induced vibration is studied. The Primary Resonance of dry-friction oscillator with fractional-order PID (FOPID) controller of velocity feedback is investigated by Krylov–Bogoliubov–Mitropolsky (KBM) asymptotic method, and the approximately analytical solution is obtained. The effects of the parameters in FOPID controller on dynamical properties are characterized by five equivalent parameters. Those equivalent parameters could distinctly illustrate the effects of the parameters in FOPID controller on the dynamical response. The effects of dry friction on the dynamical properties are characterized in the form of the equivalent linear damping and nonlinear damping. The amplitude-frequency equation for steady-state solution associated with the stability condition is also studied. A comparison of the analytical solution with the numerical results is fulfilled, and their satisfactory agreement verifies the correctness of the approximately analytical results. Finally, the effects of the coefficients and orders in FOPID controller on the amplitude-frequency curves are analyzed, and the control performances of FOPID and traditional integer-order proportional-integral-derivative (PID) controllers are compared. The comparison results show that FOPID controller is better than traditional integer-order PID controller for controlling the Primary Resonance of dry-friction oscillator, when the coefficients of the two controllers are the same. This presents theoretical basis for scholars and engineers to design similar fractional-order controlled system.
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Primary Resonance of fractional-order van der Pol oscillator
Nonlinear Dynamics, 2014Co-Authors: Yongjun Shen, Peng Wei, Shaopu YangAbstract:In this paper the Primary Resonance of van der Pol (VDP) oscillator with fractional-order derivative is studied analytically and numerically. At first the approximately analytical solution is obtained by the averaging method, and it is found that the fractional-order derivative could affect the dynamical properties of VDP oscillator, which is characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. Moreover, the amplitude–frequency equation for steady-state solution is established, and the corresponding stability condition is also presented based on Lyapunov theory. Then, the comparisons of several different amplitude–frequency curves by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. At last, the effects of the two fractional parameters, i.e., the fractional coefficient and the fractional order, on the amplitude–frequency curves are investigated for some typical excitation amplitudes, which are different from the traditional integer-order VDP oscillator.
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Primary Resonance of duffing oscillator with two kinds of fractional order derivatives
International Journal of Non-linear Mechanics, 2012Co-Authors: Yongjun Shen, Shaopu Yang, Haijun XingAbstract:Abstract In this paper, the Primary Resonance of Duffing oscillator with two kinds of fractional-order derivatives is investigated analytically. Based on the averaging method, the approximately analytical solution and the amplitude–frequency equation are obtained. The effects of the two kinds of fractional-order derivatives on the system dynamics are analyzed, and it is found that these two kinds of fractional-order derivatives could affect not only the linear viscous damping, but also the linear stiffness, which could be characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. The different effects are analyzed based on these two deduced equivalent parameters, when the two fractional orders are limited in the typical intervals, i.e. p 1 ∈[0 1] and p 2 ∈[1 2]. Moreover, the comparisons of the amplitude–frequency curves obtained by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. Especially, the effects of the parameters in the second kind of fractional-order derivative are studied when the coefficient of the first kind of fractional-order derivative is zero or not. At last, two special cases for the coefficient of the second kind of fractional-order derivative are analyzed, which could make engineers obtain satisfactory vibration control performance and keep the frequency characteristic almost unchanged. These results are very useful in vibration control engineering.
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Primary Resonance of Duffing oscillator with fractional-order derivative
Communications in Nonlinear Science and Numerical Simulation, 2012Co-Authors: Yongjun Shen, Shaopu Yang, Xing Haijun, Guo-sheng GaoAbstract:Abstract In this paper the Primary Resonance of Duffing oscillator with fractional-order derivative is researched by the averaging method. At first the approximately analytical solution and the amplitude–frequency equation are obtained. Additionally, the effect of the fractional-order derivative on the system dynamics is analyzed, and it is found that the fractional-order derivative could affect not only the viscous damping, but also the linear stiffness, which is characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. This conclusion is remarkably different from the existing research results about nonlinear system with fractional-order derivative. Moreover, the comparisons of the amplitude–frequency curves by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution. At last, the effects of the two parameters of the fractional-order derivative, i.e. the fractional coefficient and the fractional order, on the amplitude–frequency curves are investigated, which are different from the traditional integer-order Duffing oscillator.
Hu Ding - One of the best experts on this subject based on the ideXlab platform.
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Erratum to: Primary Resonance of traveling viscoelastic beam under internal Resonance
Applied Mathematics and Mechanics, 2018Co-Authors: Hu Ding, Linglu Huang, Xiao-ye Mao, Li-qun ChenAbstract:The article “Primary Resonance of traveling viscoelastic beam under internal Resonance”, written by Hu DING, Linglu HUANG, Xiaoye MAO, and Liqun CHEN, was originally published Online First without open access. After publication in Volume 38, Issue 1, Page 1–14, the authors decided to opt for Open Choice and to make the article an open access publication. Therefore, the copyright of the article has been changed to © The Author(s) 2018 and the article is forthwith distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The original article has been corrected.
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Primary Resonance of traveling viscoelastic beam under internal Resonance
Applied Mathematics and Mechanics-english Edition, 2017Co-Authors: Hu Ding, Linglu Huang, Xiao-ye Mao, Li-qun ChenAbstract:Under the 3:1 internal Resonance condition, the steady-state periodic response of the forced vibration of a traveling viscoelastic beam is studied. The viscoelastic behaviors of the traveling beam are described by the standard linear solid model, and the material time derivative is adopted in the viscoelastic constitutive relation. The direct multi-scale method is used to derive the relationships between the excitation frequency and the response amplitudes. For the first time, the real modal functions are employed to analytically investigate the periodic response of the axially traveling beam. The undetermined coefficient method is used to approximately establish the real modal functions. The approximate analytical results are confirmed by the Galerkin truncation. Numerical examples are presented to highlight the effects of the viscoelastic behaviors on the steady-state periodic responses. To illustrate the effect of the internal Resonance, the energy transfer between the internal Resonance modes and the saturation-like phenomena in the steady-state responses is presented.
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Primary Resonance of coupled cantilevers subjected to magnetic interaction
Meccanica, 2016Co-Authors: Guo-ce Zhang, Li-qun Chen, Hu DingAbstract:Based on a distributed-parameter model, the forced vibration of a cantilever pair excited by a sinusoidal base movement is analyzed. Two cantilevers are coupled at their free ends by a linear spring. A nonlinear concentrated magnetic force acts on the tip of one cantilever, serving at the nonlinear boundary condition of the continuous model. The magnetic force is modeled as a fractional function, strongly dependent on the distance between two magnets. Via the method of multiple scales, the Primary Resonance is analyzed for all modes. A second-order approximate solution and its stability condition are analytically captured. It is revealed that the frequency–response curves are sensitive to the distance between the two magnets. The curve may exhibit the hardening-type, softening-type or linear behavior due to the existence of the quadratic nonlinearity. The outcomes are supported by the numerical simulations very well.
Li-qun Chen - One of the best experts on this subject based on the ideXlab platform.
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Erratum to: Primary Resonance of traveling viscoelastic beam under internal Resonance
Applied Mathematics and Mechanics, 2018Co-Authors: Hu Ding, Linglu Huang, Xiao-ye Mao, Li-qun ChenAbstract:The article “Primary Resonance of traveling viscoelastic beam under internal Resonance”, written by Hu DING, Linglu HUANG, Xiaoye MAO, and Liqun CHEN, was originally published Online First without open access. After publication in Volume 38, Issue 1, Page 1–14, the authors decided to opt for Open Choice and to make the article an open access publication. Therefore, the copyright of the article has been changed to © The Author(s) 2018 and the article is forthwith distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The original article has been corrected.
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Primary Resonance of traveling viscoelastic beam under internal Resonance
Applied Mathematics and Mechanics-english Edition, 2017Co-Authors: Hu Ding, Linglu Huang, Xiao-ye Mao, Li-qun ChenAbstract:Under the 3:1 internal Resonance condition, the steady-state periodic response of the forced vibration of a traveling viscoelastic beam is studied. The viscoelastic behaviors of the traveling beam are described by the standard linear solid model, and the material time derivative is adopted in the viscoelastic constitutive relation. The direct multi-scale method is used to derive the relationships between the excitation frequency and the response amplitudes. For the first time, the real modal functions are employed to analytically investigate the periodic response of the axially traveling beam. The undetermined coefficient method is used to approximately establish the real modal functions. The approximate analytical results are confirmed by the Galerkin truncation. Numerical examples are presented to highlight the effects of the viscoelastic behaviors on the steady-state periodic responses. To illustrate the effect of the internal Resonance, the energy transfer between the internal Resonance modes and the saturation-like phenomena in the steady-state responses is presented.
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Primary Resonance of coupled cantilevers subjected to magnetic interaction
Meccanica, 2016Co-Authors: Guo-ce Zhang, Li-qun Chen, Hu DingAbstract:Based on a distributed-parameter model, the forced vibration of a cantilever pair excited by a sinusoidal base movement is analyzed. Two cantilevers are coupled at their free ends by a linear spring. A nonlinear concentrated magnetic force acts on the tip of one cantilever, serving at the nonlinear boundary condition of the continuous model. The magnetic force is modeled as a fractional function, strongly dependent on the distance between two magnets. Via the method of multiple scales, the Primary Resonance is analyzed for all modes. A second-order approximate solution and its stability condition are analytically captured. It is revealed that the frequency–response curves are sensitive to the distance between the two magnets. The curve may exhibit the hardening-type, softening-type or linear behavior due to the existence of the quadratic nonlinearity. The outcomes are supported by the numerical simulations very well.