Author
Shaopu Yang
Bio: Shaopu Yang is an academic researcher from Shijiazhuang Railway Institute. The author has contributed to research in topics: Vibration & Duffing equation. The author has an hindex of 13, co-authored 45 publications receiving 677 citations.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the incremental harmonic balance method (IHBM) is extended to analyze the nonlinear dynamics of a spur gear pair and some new results are obtained, where the backlash, time-varying stiffness and static transmission error are represented by the multi-order harmonic series through Fourier expansion.
151 citations
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TL;DR: In this article, the primary resonance of a Duffing oscillator with fractional-order derivative is investigated by the averaging method, and the effect of the fractional order derivative on the system dynamics is analyzed.
115 citations
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TL;DR: In this article, the primary resonance of a 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.
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. p1∈[0 1] and p2∈[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.
82 citations
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TL;DR: In this paper, the primary resonance of van der Pol (VDP) oscillator with fractional-order derivative is studied analytically and numerically, and the results certify the correctness and satisfactory precision of the approximately analytical solution.
Abstract: 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.
59 citations
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TL;DR: In this article, the approximately analytical solution of van der Pol (VDP) oscillator with two kinds of fractional-order derivatives is obtained based on averaging method, which could characterize the effects of the fractional parameters on the limit cycle in fractional order VDP oscillator.
Abstract: In this paper the approximately analytical solution of van der Pol (VDP) oscillator with two kinds of fractional-order derivatives is obtained based on averaging method. Two equivalent system parameters, i.e. equivalent damping coefficient and equivalent stiffness coefficient, are defined, which could characterize the effects of the fractional parameters on the limit cycle in fractional-order VDP oscillator. The same points and differences between the traditional integer-order and fractional-order VDP oscillator are analyzed and summarized in detail. The differences are focused on the convergence speed and frequency characteristic of the limit cycle in VDP oscillator. The comparison between the analytical and numerical solution verifies the correctness and satisfactory precision of the approximately analytical solution. At last, the effects of the fractional parameters on the convergence speed and frequency characteristic of the limit cycle in fractional-order VDP oscillator are illustrated based on some typical system parameters.
48 citations
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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …
33,785 citations
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TL;DR: In this article, the authors investigated the dynamics of a two-stage gear system involving backlash and time-dependent mesh stiffness, and the results obtained appeared to be the phenomenon of loss of teeth contact because of the discontinuity of the kinematic movement between the motives and receiving components of the system.
163 citations
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TL;DR: Some representative results on fuzzy fractional differential equations, controllability, approximate controllable, optimal control, and optimal feedback control for several different kinds of fractional evolution equations are surveyed.
142 citations
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TL;DR: A review of proper orthogonal decomposition (POD) methods for order reduction in a variety of research areas is presented in this paper, where the historical development and basic mathematical formulation of the POD method are introduced.
129 citations
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TL;DR: Zhang et al. as discussed by the authors used vector autoregressive model to analyze the influence of the changes in carbon dioxide emissions in the steel industry and found that energy efficiency plays a dominant role in reducing carbon dioxide emission.
116 citations