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APPROXIMATE ANALYTICAL SOLUTION OF THE SELF-EXCITED VIBRATION OF PIECEWISE-SMOOTH SYSTEMS INDUCED BY DRY FRICTION——The Vibration Mechanism of the Chinese Cultural Relic Dragon Washbasin 被引量:5
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作者 刘习军 王大钧 陈予恕 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1998年第1期78-84,共7页
Based on our previous work, a mathematical model of piecewise-smooth systems is established by means of phase-plane orbit analysis, and it is then used to study the intersting phenomena of Chinese cultural relic Drago... Based on our previous work, a mathematical model of piecewise-smooth systems is established by means of phase-plane orbit analysis, and it is then used to study the intersting phenomena of Chinese cultural relic Dragon Washbasin. The mechanism of nonlinear damping is analyzed; the approximate analytical solution of self-excited vibration of piecewise-smooth nonlinear systems induced by dry friction is derived by means of KB Method, the results of which agree well with that of the numerical solution. Therefore, the method presented in this paper is proved to be very efficient in analyzing the self-excited vibration of piecewise-smooth systems induced by dry friction. 展开更多
关键词 self-excited vibration piecewise-smooth systems dry friction
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Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation
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作者 Qian YANG Mingkang NI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2023年第1期81-98,共18页
A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary equation of reaction-diffusion-advection type is studied.A new class of problems in the case when the discontinuous curve which... A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary equation of reaction-diffusion-advection type is studied.A new class of problems in the case when the discontinuous curve which separates the domain is monotone with respect to the time variable is considered.The existence of a smooth solution with an internal layer appearing in the neighborhood of some point on the discontinuous curve is studied.An efficient algorithm for constructing the point itself and an asymptotic representation of arbitrary-order accuracy to the solution is proposed.For sufficiently small parameter values,the existence theorem is proved by the technique of matching asymptotic expansions.An example is given to show the effectiveness of their method. 展开更多
关键词 Reaction-Diffusion-Advection equation Internal layer Asymptotic method piecewise-smooth dynamical system
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Subharmonic resonance of single-degree-of-freedom piecewise-smooth nonlinear oscillator
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作者 Jiangchuan Niu Wenjing Zhang +1 位作者 Yongjun Shen Shaopu Yang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2020年第5期1109-1118,I0003,共11页
Take the single degree of freedom nonlinear oscillator with clearance under harmonic excitation as an example,the 1/3 subharmonic resonance of piecewise-smooth nonlinear oscillator is investigated.The approximate anal... Take the single degree of freedom nonlinear oscillator with clearance under harmonic excitation as an example,the 1/3 subharmonic resonance of piecewise-smooth nonlinear oscillator is investigated.The approximate analytical solution of 1/3 subharmonic resonance of the single-degree-of-freedom piecewise-smooth nonlinear oscillator is presented.By changing the solving process of Krylov-Bogoliubov-Mitropolsky(KBM)asymptotic method for subharmonic resonance of smooth nonlinear system,the classical KBM method is extended to piecewise-smooth nonlinear system.The existence conditions of 1/3 subharmonic resonance steady-state solution are achieved,and the stability of the subharmonic resonance steady-statesolution is also analyzed.It is found that the clearance affects the amplitude-frequency response of subharmonic resonance in the form of equivalent negative stiffness.Through a demonstration example,the accuracy of approximate analytical solution is verified by numerical solution,and they have good consistency.Based on the approximate analytical solution,the infuences of clearance on the critical frequency and amplitude-frequency response of 1/3 subharmonic resonance are analyzed in detail.The analysis results show that the KBM method is an effective analytical method for solving the subharmonic resonance of piecewise-smooth nonlinear system.And it provides an effective reference for the study of subharmonicr esonance of other piecewise-smooth systems. 展开更多
关键词 Subharmonic resonance piecewise-smooth system Approximate analytical solution Asymptotic method
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Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation
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作者 Qian Yang Mingkang Ni 《Science China Mathematics》 SCIE CSCD 2022年第2期291-308,共18页
A piecewise-smooth second-order singularly perturbed differential equation whose right-hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a new class of problems in the case ... A piecewise-smooth second-order singularly perturbed differential equation whose right-hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a new class of problems in the case where the degenerate equation has a multiple root on the left-hand side of the curve which separates the domain and an isolated root on the right-hand side of that curve. The asymptotics of a solution with an internal layer near a point on the discontinuous curve and the transition point is constructed. The method to construct the internal layer function is proposed. The behavior of the solution in the internal layer consisting of four zones essentially differs from the case of isolated roots. For sufficiently small parameter values, the existence of a smooth solution with an internal layer from the multiple root of the degenerate equation to the isolated root in the neighborhood of a point on the discontinuous curve is proved. The method can be shown to be effective in the given example. 展开更多
关键词 reaction-diffusion equation multizonal internal layer asymptotic method piecewise-smooth dynamical system
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Analytic Solution to Nonlinear Dynamical System of Dragon Washbasin
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作者 贾启芬 李芳 +2 位作者 于雯 刘习军 王大钧 《Transactions of Tianjin University》 EI CAS 2004年第3期190-194,共5页
Based on phase-plane orbit analysis, the mathematical model of piecewise-smooth systems of multi-degree-of-freedom under the mode coordinate is established. Approximate analytical solution under the physical coordinat... Based on phase-plane orbit analysis, the mathematical model of piecewise-smooth systems of multi-degree-of-freedom under the mode coordinate is established. Approximate analytical solution under the physical coordinate of multi-degree-of-freedom self-excited vibration induced by dry friction of piecewise-smooth nonlinear systems is derived by means of average method, the results of which agree with those of the numerical solution. An effective and reliable analytical method investigating piecewise-smooth nonlinear systems of multi-degree-of-freedom has been given. Furthermore, this paper qualitatively analyses the curves about stationary amplitude versus rubbing velocity of hands and versus natural frequency of hands, and about angular frequency versus rubbing velocity of hands. The results provide a theoretical basis for identifying parameters of the system and the analysis of steady region. 展开更多
关键词 dry friction nonlinear vibration piecewise-smooth self-excited vibration average method
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