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1. Numerical and experimental study on the lateral contact model of a circular rod moving in a circular channel | |||
Wu Feng,Zhao Ke,Wu Xuanlong,Zhao Liliang,Zhao Yuelin | |||
Mechanics 27 February 2023 | |||
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Abstract:When a rod moves in a circular channel, high-frequency collisions occur between the rod and the channel wall. Contact models are crucial for predicting the motion of the rod. This paper conducts experimental studies on the movement of a rod in a circular channel and compares four different contact models based on experimental data. To improve the computational efficiency of simulating high-frequency collisions between the rod and the pipe wall, a time-averaging method is used to establish a time-averaged collision equation. This equation uses time-averaged displacement as the basic variable and handles contact problems through time-averaged gap functions and time-averaged contact forces. Two time-averaged contact models are proposed through polishing methods and machine learning, and comparison with experimental data shows that these models can ensure the accuracy of rod motion analysis while improving computational efficiency. | |||
TO cite this article:Wu Feng,Zhao Ke,Wu Xuanlong, et al. Numerical and experimental study on the lateral contact model of a circular rod moving in a circular channel[OL].[27 February 2023] http://en.paper.edu.cn/en_releasepaper/content/4759296 |
2. Frequency and damping trimming of a microresonator via delayed feedback signals | |||
HAN Jianxin,ZHANG Qichang,WANG Wei | |||
Mechanics 28 October 2015 | |||
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Abstract:A study on an electrically actuated microresonator is carried out to investigate its dynamic characteristic with delayed displacement and velocity feedback signals. The amplitude of AC voltage is relatively smaller than that of DC voltage in real cases, which yields a small amplitude vibration around its equilibrium position. For delayed stability purpose, delay-independent region based on the linearized equation is analytically derived and then numerically verified. Then, the method of multiple scales is used to determine the frequency response equation under primary resonance of the system. Explicit expressions of the effective natural angular frequency and damping ratio are deduced, respectively. Results show that these two types of delayed feedback signals can induce frequency and damping trimming of the system. An ideal situation, when one type of signal can only tune one vibration property, is discussed in detail. Four cases of delay conditions are defined to decouple the two trimming phenomena. Finally, both the perturbation solution and numerical results are used to verify the correctness of our analysis. | |||
TO cite this article:HAN Jianxin,ZHANG Qichang,WANG Wei. Frequency and damping trimming of a microresonator via delayed feedback signals[OL].[28 October 2015] http://en.paper.edu.cn/en_releasepaper/content/4659192 |
3. Fuzzy fractional-order fast terminal sliding mode control for some chaotic micro-components | |||
HAN Jianxin,ZHANG Qichang,WANG Wei,WANG Jing | |||
Mechanics 27 October 2015 | |||
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Abstract:In this paper, a novel fractional-order fast terminal sliding mode control method, based on an integer-order scheme, is proposed to stabilize the chaotic motion of two typical micro-components. Fractional Lyapunov stability theorem is applied to analytically guarantee the asymptotic stability of the system with uncertainties and external disturbances. To reduce chattering, a fuzzy logic algorithm is designed to replace the traditional signum function in switching law. Finally, numerical simulations with both the fractional-order and integer-order control laws are carried out, respectively. Results show that the proposed control law is effective in the suppression of chaos. | |||
TO cite this article:HAN Jianxin,ZHANG Qichang,WANG Wei, et al. Fuzzy fractional-order fast terminal sliding mode control for some chaotic micro-components[OL].[27 October 2015] http://en.paper.edu.cn/en_releasepaper/content/4659189 |
4. Stable configurations of the noncircular cross section elastic rod model with singularity theory | |||
WANG Wei,LIN Zhi | |||
Mechanics 08 January 2014 | |||
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Abstract:The stable configuration of elastic rod model under perturbation is researched by using the singularity theory. We consider the reduced Kirchhoff equations of the noncircular cross section elastic rod characterized by the inequality of the bending rigidities. For the possible buckling configurations belong to the minima along the elastic energy curve, it is analogue to the research of static bifurcation of the equilibrium and described as a 2-codimension unfolding. From that we realize the emergency of buckling configuration under perturbation is strongly connected with the correlations between different governing parameters. These correlations can be analytically detected with the variation in the transition set and bifurcation diagrams from the singularity theory. We also find the criterion of the localized buckling process. The process, following the buckling configuration, connects with the homoclinicity in the physical parameter regions and has been verified with numerical simulation in this article. | |||
TO cite this article:WANG Wei,LIN Zhi. Stable configurations of the noncircular cross section elastic rod model with singularity theory[OL].[ 8 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4580025 |
5. The analytical analysis of the asymmetric elastic rod | |||
WANG Wei,CHEN Tao | |||
Mechanics 04 January 2014 | |||
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Abstract:The analytical equation of the asymmetric elastic rod governed by the ordinary differential equation is obtained. We reconstruct the Kirchhoff equations with the complex coordinates and introduce a novel transformation parameter. They change the initial non-circular character of the cross section into a nearly cross section case, and approximately result the Duffing type ordinary differential equations. Perturbation methods basing on these equations permit our expectation to explore the intrinsic properties of DNA double helix within the framework of analytical research not merely the numerical simulations, such as structural inhomogeneity and periodically varying of bending rigidities. | |||
TO cite this article:WANG Wei,CHEN Tao. The analytical analysis of the asymmetric elastic rod[OL].[ 4 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4580022 |
6. Stability analysis of double-walled carbon nanotubes with initial stress | |||
YAN Yan,WANG Wenquan | |||
Mechanics 28 March 2013 | |||
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Abstract:In the paper, the stability of the double-walled carbon nanotubes (DWCNTs) under the initial axial stress are studied. Galerkin and harmonic balance method are used to analyze the relation between the amplitudes and the frequencies of the tubes. The results show that the critical initial stress plays a significant control role in the amplitude-frequency curves. When the initial axial stress is less than the critical initial stress, DWCNTs have twice dynamical mode transitions corresponding to twice noncoaxial vibrations, however, when the initial axial stress is larger than the critical initial stress, the topological forms of the amplitude-frequency curve are changeable, which are corresponding to coaxial vibration or three possible noncoaxial vibration type. Since noncoaxial vibration will distort otherwise concentric geometry of multiwall carbon nanotubes, it could crucially affect their physical (such as electronicl) properties. | |||
TO cite this article:YAN Yan,WANG Wenquan. Stability analysis of double-walled carbon nanotubes with initial stress[OL].[28 March 2013] http://en.paper.edu.cn/en_releasepaper/content/4534203 |
7. Stochastic P-bifurcations In Tri-stable van der Pol- Duffing Oscillator | |||
Hao Ying,Wu zhiqiang | |||
Mechanics 20 December 2012 | |||
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Abstract:This paper aims to investigate the stochastic P-bifurcations in the tri-stable van der Pol-Duffing oscillator with Gauss white noise. By using the stochastic averaging method, the stationary probability density function of amplitude is obtained. Then based on the singularity theory of the deterministic system, the explicit parameter conditions for P-bifurcation are deduced, eleven types of qualitatively different probability density curves are founded. Finally the effects of three coefficients, one for linear damping and two for random excitation strength, are discussed. The results are verified by Monte-Carlo numerical simulations. The method used here is also suitable for other systems' P-bifurcation analysis. | |||
TO cite this article:Hao Ying,Wu zhiqiang. Stochastic P-bifurcations In Tri-stable van der Pol- Duffing Oscillator[OL].[20 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4503911 |
8. Relationship between the homotopy analysis method and harmonic balance method | |||
Y.M. Chen,J.K. Liu | |||
Mechanics 09 February 2009 | |||
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Abstract:The relationship between the homotopy analysis method (HAM) and harmonic balance (HB) method is studied. The HAM is employed to obtain the periodic solutions of conservative and self-excited systems, respectively. Different from the usual procedures in the existing literature, the HAM is modified by retaining only several lower harmonics. It is proved that as long as the solution obtained by the modified approach is convergent, it must converge to one HB solution. The Duffing equation, the van der Pol equation and the flutter equation of a two-dimensional airfoil are taken as three illustrative examples to validate the proposed theory. | |||
TO cite this article:Y.M. Chen,J.K. Liu. Relationship between the homotopy analysis method and harmonic balance method[OL].[ 9 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28594 |
9. Uniformly valid frequency solution of the limit cycle of the Duffing-van der Pol equation | |||
Y.M. Chen,J.K. Liu | |||
Mechanics 05 January 2009 | |||
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Abstract:The limit cycle of the Duffing-van der Pol equation is studied. First, an equivalent equation is obtained by considering the product of the frequency of the limit cycle and the coefficient as an independent parameter . Then, the frequency is obtained as a function of and by solving the equivalent equation via the homotopy analysis method. This function provides us with an algebraic equation in . Solving this algebraic equation, an analytical approximation for the frequency is obtained. Numerical examples show that the attained approximation is very accurate and more importantly uniformly valid for all positive values of . | |||
TO cite this article:Y.M. Chen,J.K. Liu. Uniformly valid frequency solution of the limit cycle of the Duffing-van der Pol equation[OL].[ 5 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27342 |
10. A modified variational iteration method for nonlinear oscillators | |||
Chen Yanmao,Liu Jike | |||
Mechanics 05 January 2009 | |||
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Abstract:A modified variational iteration method (VIM) is proposed for nonlinear oscillators. Different from the existing VIM, the algebraic equation deduced at each iteration stage is always linear when the proposed procedure is applied to conservative oscillators. Taking the Duffing and the van der Pol equations as illustrative examples, very excellent approximations can be easily. In addition, it is proved the modified VIM is equivalent to a modified Mickens iteration. Furthermore, the modified VIM is extended by introducing an auxiliary parameter exemplified by two special examples. This parameter provides us with a convenient way to control the convergence of approximation series and adjust convergence rate when necessary. Consequently, the extended method is valid for both weakly and strongly nonlinear oscillators with either small or large amplitude. | |||
TO cite this article:Chen Yanmao,Liu Jike. A modified variational iteration method for nonlinear oscillators[OL].[ 5 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27331 |
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