We extend the Melnikov method to non-smooth dynamical systems to study the global behavior near a non-smooth homoclinic orbit under small time-periodic perturbations. The definition and an explicit expression for the ...We extend the Melnikov method to non-smooth dynamical systems to study the global behavior near a non-smooth homoclinic orbit under small time-periodic perturbations. The definition and an explicit expression for the extended Melnikov function are given and applied to determine the appearance of transversal homoclinic orbits and chaos. In addition to the standard integral part, the extended Melnikov function contains an extra term which reflects the change of the vector field at the discontinuity. An example is discussed to illustrate the results.展开更多
Non-Hamiltonian systems containing degenerate fixed points obtained from twodegrees of freedom near-integrable Hamiltonian systems through non-canonicaltransformations are dealt with in this paper. Two criteria .for d...Non-Hamiltonian systems containing degenerate fixed points obtained from twodegrees of freedom near-integrable Hamiltonian systems through non-canonicaltransformations are dealt with in this paper. Two criteria .for determining theexistence of transversal homoclinic and heteroclinic orbits are presented. By exploitingthese criteria the existence of the transversal homoclinic orbits and so, of thetransversal homoclinic tangle .phenomenon in the near-integrable circular planarrestricted three-body problem with sufficiently small mass ratio of the two primaries isproven. Under some assumptions, the existence of the transversal heleroclinic orbits isproven. The global qualitative phase diagram is also illustrated.展开更多
Hydro-pneumatic near-zero frequency(NZF)vibration isolators have better performance at isolating vibration with low frequencies and heavy loadings when the nonlinear fluidic damping is introduced and the pressurized g...Hydro-pneumatic near-zero frequency(NZF)vibration isolators have better performance at isolating vibration with low frequencies and heavy loadings when the nonlinear fluidic damping is introduced and the pressurized gas pressure is properly adjusted.The nonlinear characteristics of such devices make their corresponding dynamic research involve chaotic dynamics.Chaos may bring negative influence and disorder to the structure and low-frequency working efficiency of isolators,which makes it necessary to clarify and control the threshold ranges for chaos generation in advance.In this work,the chaotic characteristics for a class of hydro-pneumatic NZF vibration isolators under dry friction,harmonic,and environmental noise excitations are analyzed by the analytical and numerical methods.The parameter ranges for the generation of chaos are obtained by the classical and random Melnikov methods.The chaotic characteristics and thresholds of the parameters in the systems with or without noise excitation are discussed and described.The analytical solutions and the influence of noise and harmonic excitation about chaos are tested and further analyzed through many numerical simulations.The results show that chaos in the system can be induced or inhibited with the adjustment of the magnitudes of harmonic excitation and noise intensity.展开更多
The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break...The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.展开更多
基金Supported by the National Natural Science Foundation of China(No.10071030)
文摘We extend the Melnikov method to non-smooth dynamical systems to study the global behavior near a non-smooth homoclinic orbit under small time-periodic perturbations. The definition and an explicit expression for the extended Melnikov function are given and applied to determine the appearance of transversal homoclinic orbits and chaos. In addition to the standard integral part, the extended Melnikov function contains an extra term which reflects the change of the vector field at the discontinuity. An example is discussed to illustrate the results.
文摘Non-Hamiltonian systems containing degenerate fixed points obtained from twodegrees of freedom near-integrable Hamiltonian systems through non-canonicaltransformations are dealt with in this paper. Two criteria .for determining theexistence of transversal homoclinic and heteroclinic orbits are presented. By exploitingthese criteria the existence of the transversal homoclinic orbits and so, of thetransversal homoclinic tangle .phenomenon in the near-integrable circular planarrestricted three-body problem with sufficiently small mass ratio of the two primaries isproven. Under some assumptions, the existence of the transversal heleroclinic orbits isproven. The global qualitative phase diagram is also illustrated.
基金Project supported by the National Natural Science Foundation of China(Nos.12172340 and12411530068)the Shenzhen Science and Technology Program(No.JCYJ20240813114012016)+2 种基金the High-Level Talent Introduction Plan of Guangzhou Citythe Fundamental Research Funds for the Central Universities-China University of Geosciences(Wuhan)(No.G1323524005)the Young Top-Notch Talent Cultivation Program of Hubei Province。
文摘Hydro-pneumatic near-zero frequency(NZF)vibration isolators have better performance at isolating vibration with low frequencies and heavy loadings when the nonlinear fluidic damping is introduced and the pressurized gas pressure is properly adjusted.The nonlinear characteristics of such devices make their corresponding dynamic research involve chaotic dynamics.Chaos may bring negative influence and disorder to the structure and low-frequency working efficiency of isolators,which makes it necessary to clarify and control the threshold ranges for chaos generation in advance.In this work,the chaotic characteristics for a class of hydro-pneumatic NZF vibration isolators under dry friction,harmonic,and environmental noise excitations are analyzed by the analytical and numerical methods.The parameter ranges for the generation of chaos are obtained by the classical and random Melnikov methods.The chaotic characteristics and thresholds of the parameters in the systems with or without noise excitation are discussed and described.The analytical solutions and the influence of noise and harmonic excitation about chaos are tested and further analyzed through many numerical simulations.The results show that chaos in the system can be induced or inhibited with the adjustment of the magnitudes of harmonic excitation and noise intensity.
基金support from the National Natural Science Foundation of China(Nos.12102242 and 12172086)the Educational Foundation of Liaoning Province(No.JYTQN2023261)the Key R&D Program of Shandong Province of China(No.2022SFGC0801).
文摘The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.
