Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonl...Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange＇s equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov＇s method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.展开更多
In this paper, studied are the dynamics of a moored buoy near the surface subjected to wave excitation. According to the physical structure, submersible buoy moored by tethered line is modeled firstly. Then from the d...In this paper, studied are the dynamics of a moored buoy near the surface subjected to wave excitation. According to the physical structure, submersible buoy moored by tethered line is modeled firstly. Then from the differential equations, the natural frequencies are estimated by neglecting the coupling between tangential and normal direction. By use of numerical integration method, solutions are obtained. On this basis, strange attractors and bifurcation phenomena are obtained by applying Poineare map, phase plots and bifurcation diagram, showing the existence of the chaotic response in this system when wave steepness is high enough.展开更多
The beer game model is a typical paradigm used to study complex dynamics behaviours in production–distribution systems. The model, however, does not accord with current practical supply chain system models in discret...The beer game model is a typical paradigm used to study complex dynamics behaviours in production–distribution systems. The model, however, does not accord with current practical supply chain system models in discrete?type manufacturing industry, which are generally composed of retailers, distributors, manufacturers with internal sup?ply chain, and suppliers. To describe how ordering policies influence the complex dynamics behaviour modes and operating cost in a general discrete?type manufacturing industry supply chain system, a high dimension piecewise?linear dynamics model is built for the supply chain system. Five kinds of ordering policy combination are considered. The distribution of both the largest Lyapunov exponent of e ective inventory and average operating cost per cycle is obtained by simulation in a policy space. The simulation shows that for the general discrete?type manufacturing industry supply chain system, the upper chaotic corners emerge besides the lower chaotic corners in the policy space expressing the distribution of system behaviour mode, and that the ordering policies at each supply chain node as well as their combination have very significant e ect on the topology of the distribution of both system behaviour mode and operating cost in the policy space. We find that chaos is not always corresponding to high cost, and the "chaos amplification" is not completely relevant to the "cost amplification".展开更多
The constitutive behavior of microcrystals remains mysterious since very little,or no information regarding plastic deformation in the measured stress-strain curve is available due to plastic instability.Furthermore,t...The constitutive behavior of microcrystals remains mysterious since very little,or no information regarding plastic deformation in the measured stress-strain curve is available due to plastic instability.Furthermore,the measured stress-strain curves vary greatly under different control modes,while constitutive behavior should remain unaffected by test methods.Beyond these reasons,probing the real constitutive behavior of microcrystals has long been a challenge because the nonlinear dynamical behaviors of micromechanical testing systems are unclear.Here,we perform and carefully analyze the experiments on singlecrystal aluminum micropillars under displacement control and load control.To interpret these experimental results,a lumpedparameter physical model based on the principle of micromechanical testing is developed,which can directly relate nonlinear dynamics of the micromechanical testing system to the constitutive behavior of microcrystals.This reveals that some stages of the measured stress-strain curve attributed to the control algorithm are not related to constitutive behavior.By solving the nonlinear dynamics of the micromechanical testing system,intense plastic instability(large strain burst)starting from the equilibrium state is attributed to the strain-softening stage of microcrystals.Parametric studies are also performed to reduce the influence of plastic instability on the measured responses.This study provides critical insights for developing various constitutive models and designing a reliable micromechanical testing system.展开更多
The nonlinear modal coupling in a T-shaped piezoelectric resonator,when the former two natural frequencies are away from 1:2,is studied.Experimentally sweeping up the exciting frequency shows that the horizontal beam ...The nonlinear modal coupling in a T-shaped piezoelectric resonator,when the former two natural frequencies are away from 1:2,is studied.Experimentally sweeping up the exciting frequency shows that the horizontal beam exhibits a nonlinear hardening behavior.The first primary resonance of the vertical beam,owing to modal coupling,exhibits an abrupt amplitude increase,namely the Hopf bifurcation.The frequency comb phenomenon induced by modal coupling is measured experimentally.A Duffing-Mathieu coupled model is theoretically introduced to derive the conditions of the modal coupling and frequency comb phenomenon.The results demonstrate that the modal coupling results from nonlinear stiffness hardening and is strictly dependent on the loading range and sweeping form of the driving voltage and the frequency of the piezoelectric patches.展开更多
基金supported by National Key Technologies R&D Program of the 10th Five-year Plan of China (Grant No. ZZ02-13B-02-03-1)Hebei Provincial Natural Science Foundation of China (Grant No. F2008000882)Hebei Provincial Education Office Scientific Research Projects of China (Grant No. ZH2007102, 2007496)
文摘Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange＇s equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov＇s method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.
基金supported by the Key Program of National Natural Science Foundation of China (Grant No.50739004) the Shandong Province Key Lab of Ocean Engineering in Ocean University of China
文摘In this paper, studied are the dynamics of a moored buoy near the surface subjected to wave excitation. According to the physical structure, submersible buoy moored by tethered line is modeled firstly. Then from the differential equations, the natural frequencies are estimated by neglecting the coupling between tangential and normal direction. By use of numerical integration method, solutions are obtained. On this basis, strange attractors and bifurcation phenomena are obtained by applying Poineare map, phase plots and bifurcation diagram, showing the existence of the chaotic response in this system when wave steepness is high enough.
基金Supported by National Natural Science Foundation of China(Grant No.11072192)Shaanxi Provincial Industrial Technology Research Projects of China(Grant No.2015GY118)
文摘The beer game model is a typical paradigm used to study complex dynamics behaviours in production–distribution systems. The model, however, does not accord with current practical supply chain system models in discrete?type manufacturing industry, which are generally composed of retailers, distributors, manufacturers with internal sup?ply chain, and suppliers. To describe how ordering policies influence the complex dynamics behaviour modes and operating cost in a general discrete?type manufacturing industry supply chain system, a high dimension piecewise?linear dynamics model is built for the supply chain system. Five kinds of ordering policy combination are considered. The distribution of both the largest Lyapunov exponent of e ective inventory and average operating cost per cycle is obtained by simulation in a policy space. The simulation shows that for the general discrete?type manufacturing industry supply chain system, the upper chaotic corners emerge besides the lower chaotic corners in the policy space expressing the distribution of system behaviour mode, and that the ordering policies at each supply chain node as well as their combination have very significant e ect on the topology of the distribution of both system behaviour mode and operating cost in the policy space. We find that chaos is not always corresponding to high cost, and the "chaos amplification" is not completely relevant to the "cost amplification".
基金supported by the National Natural Science Foundation of China(Grant Nos.51731009,12102216,and 11972205)the Fundamental Research Funds for the Central Universities(Grant No.2020XZZX005-02)the China Postdoctoral Science Foundation(Grant Nos.2021M691796,and 2021T140379).
文摘The constitutive behavior of microcrystals remains mysterious since very little,or no information regarding plastic deformation in the measured stress-strain curve is available due to plastic instability.Furthermore,the measured stress-strain curves vary greatly under different control modes,while constitutive behavior should remain unaffected by test methods.Beyond these reasons,probing the real constitutive behavior of microcrystals has long been a challenge because the nonlinear dynamical behaviors of micromechanical testing systems are unclear.Here,we perform and carefully analyze the experiments on singlecrystal aluminum micropillars under displacement control and load control.To interpret these experimental results,a lumpedparameter physical model based on the principle of micromechanical testing is developed,which can directly relate nonlinear dynamics of the micromechanical testing system to the constitutive behavior of microcrystals.This reveals that some stages of the measured stress-strain curve attributed to the control algorithm are not related to constitutive behavior.By solving the nonlinear dynamics of the micromechanical testing system,intense plastic instability(large strain burst)starting from the equilibrium state is attributed to the strain-softening stage of microcrystals.Parametric studies are also performed to reduce the influence of plastic instability on the measured responses.This study provides critical insights for developing various constitutive models and designing a reliable micromechanical testing system.
基金supported by the National Natural Science Foundation of China(No.11902182)the Program of Shanghai Academic/Technology Research Leader of China(No.19XD1421600)+2 种基金the China Postdoctoral Science Foundation(No.2019M651485)the Natural Science Foundation of Shandong Province of China(No.ZR2019BA001)the Natural Science Foundation of Tianjin of China(No.20JCQNJC01070)。
文摘The nonlinear modal coupling in a T-shaped piezoelectric resonator,when the former two natural frequencies are away from 1:2,is studied.Experimentally sweeping up the exciting frequency shows that the horizontal beam exhibits a nonlinear hardening behavior.The first primary resonance of the vertical beam,owing to modal coupling,exhibits an abrupt amplitude increase,namely the Hopf bifurcation.The frequency comb phenomenon induced by modal coupling is measured experimentally.A Duffing-Mathieu coupled model is theoretically introduced to derive the conditions of the modal coupling and frequency comb phenomenon.The results demonstrate that the modal coupling results from nonlinear stiffness hardening and is strictly dependent on the loading range and sweeping form of the driving voltage and the frequency of the piezoelectric patches.
