A necessary big step up in the modern water wave theories and their widespread application in ocean engineering is how to obtain 6-wave resonance conditions and to prove it. In the light of the existing forms and char...A necessary big step up in the modern water wave theories and their widespread application in ocean engineering is how to obtain 6-wave resonance conditions and to prove it. In the light of the existing forms and characteristics of 3-wave, 4-wave and 5-wave resonance conditions, the 6-wave resonance conditions are proposed and proved for currently a maximum wave-wave resonance interactions of the ocean surface gravity waves in deep water, which will be indispensable to both the Kolmogorov spectrum of the corresponding universal wave turbulence and a synthetic 4-5-6-wave resonant model for the ocean surface gravity waves.展开更多
In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of ne...In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.展开更多
Harmonic nonlinear ultrasound can offer high sensitivity for residual stress measurements;however,it cannot be used for local stress measurements at a point in space and exhibits nonlinear distortions in the experimen...Harmonic nonlinear ultrasound can offer high sensitivity for residual stress measurements;however,it cannot be used for local stress measurements at a point in space and exhibits nonlinear distortions in the experimental system.This paper presents a feasibility study on the measurement of residual stress in a metal plate using a nonlinear Lamb wave-mixing technique.The resonant conditions for two Lamb waves to generate a mixing frequency wave are obtained via theoretical analysis.Finite element simulations are performed to investigate the nonlinear interactions between the two Lamb waves.Results show that two incident A0 waves interact in regions of material nonlinearity and generate a rightward S0 wave at the sum frequency.Residual stress measurement experiments are conducted on steel plate specimens using the collinear Lamb wave-mixing technique.By setting different delays for two transmitters,the generated sum-frequency component at different spatial locations is measured.Experimental results show that the spatial distribution of the amplitude of the sum-frequency component agrees well with the spatial distribution of the residual stress measured using X-rays.The proposed collinear Lamb wave-mixing method is effective for measuring the distribution of residual stress in metal plates.展开更多
The paper deals a fractional functional boundary value problems with integral boundary conditions. Besed on the coincidence degree theory, some existence criteria of solutions at resonance are established.
The degenerated homoclinic bifurcation for high dimensional system is considered. The existence, uniqueness, and incoexistence of the 1-homclinic orbit and 1-periodic orbit near Г are studied under the nonresonant c...The degenerated homoclinic bifurcation for high dimensional system is considered. The existence, uniqueness, and incoexistence of the 1-homclinic orbit and 1-periodic orbit near Г are studied under the nonresonant condition. Complicated bifurcation pattern is described under the resonant condition.展开更多
In this paper,three-dimensional finite-element modeling is conducted to investigate the nonlinear interactions between Lamb waves and microcracks.The simulation research focuses on the influence of microcrack orientat...In this paper,three-dimensional finite-element modeling is conducted to investigate the nonlinear interactions between Lamb waves and microcracks.The simulation research focuses on the influence of microcrack orientation on the propagation direction of generated sum-frequency Lamb waves.The simulation results show that the resonant conditions based on classical nonlinear theory are valid for such interactions,leading to the generation of transmitted and reflected sum-frequency SO waves(SFSWs).Moreover,the propagation directions of these two SFSWs exhibit different trends with respect to the orientations of microcracks.The transmitted SFSW can be used to detect microcracks,whereas the reflected one can be used to measure their orientations.展开更多
The homoclinic bifurcations under resonant conditions are considered in the ho- moclinic manifold consisting of a series of homoclinic orbits for the fourth-dimensional system.The existence,coexistence and uniqueness ...The homoclinic bifurcations under resonant conditions are considered in the ho- moclinic manifold consisting of a series of homoclinic orbits for the fourth-dimensional system.The existence,coexistence and uniqueness of 1-homoclinic orbit,1-periodic orbit and 2-fold 1-periodic orbit are obtained under resonant condition,the correspon- ding bifurcation surfaces and existing regions are also given.展开更多
An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare als...An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare also evaluated.AMS(MOS) Subject classifications 34B15展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11772180)the State Key Laboratory of Ocean Engineering of China(Grant No.1503)
文摘A necessary big step up in the modern water wave theories and their widespread application in ocean engineering is how to obtain 6-wave resonance conditions and to prove it. In the light of the existing forms and characteristics of 3-wave, 4-wave and 5-wave resonance conditions, the 6-wave resonance conditions are proposed and proved for currently a maximum wave-wave resonance interactions of the ocean surface gravity waves in deep water, which will be indispensable to both the Kolmogorov spectrum of the corresponding universal wave turbulence and a synthetic 4-5-6-wave resonant model for the ocean surface gravity waves.
基金Projects Supported by the Science Fund of the Chinese Academy of Sciences
文摘In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.
基金National Natural Science Foundation of China(Grant Nos.11972053,12274012)。
文摘Harmonic nonlinear ultrasound can offer high sensitivity for residual stress measurements;however,it cannot be used for local stress measurements at a point in space and exhibits nonlinear distortions in the experimental system.This paper presents a feasibility study on the measurement of residual stress in a metal plate using a nonlinear Lamb wave-mixing technique.The resonant conditions for two Lamb waves to generate a mixing frequency wave are obtained via theoretical analysis.Finite element simulations are performed to investigate the nonlinear interactions between the two Lamb waves.Results show that two incident A0 waves interact in regions of material nonlinearity and generate a rightward S0 wave at the sum frequency.Residual stress measurement experiments are conducted on steel plate specimens using the collinear Lamb wave-mixing technique.By setting different delays for two transmitters,the generated sum-frequency component at different spatial locations is measured.Experimental results show that the spatial distribution of the amplitude of the sum-frequency component agrees well with the spatial distribution of the residual stress measured using X-rays.The proposed collinear Lamb wave-mixing method is effective for measuring the distribution of residual stress in metal plates.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘The paper deals a fractional functional boundary value problems with integral boundary conditions. Besed on the coincidence degree theory, some existence criteria of solutions at resonance are established.
基金National Natural Science Foundation of China!(No. 19771037)
文摘The degenerated homoclinic bifurcation for high dimensional system is considered. The existence, uniqueness, and incoexistence of the 1-homclinic orbit and 1-periodic orbit near Г are studied under the nonresonant condition. Complicated bifurcation pattern is described under the resonant condition.
基金supported by the National Key Research and Development Program of China(Grant No.2016YFF0203002)National Natural Science Foundation of China(Grant Nos.11572010,11572011).
文摘In this paper,three-dimensional finite-element modeling is conducted to investigate the nonlinear interactions between Lamb waves and microcracks.The simulation research focuses on the influence of microcrack orientation on the propagation direction of generated sum-frequency Lamb waves.The simulation results show that the resonant conditions based on classical nonlinear theory are valid for such interactions,leading to the generation of transmitted and reflected sum-frequency SO waves(SFSWs).Moreover,the propagation directions of these two SFSWs exhibit different trends with respect to the orientations of microcracks.The transmitted SFSW can be used to detect microcracks,whereas the reflected one can be used to measure their orientations.
文摘The homoclinic bifurcations under resonant conditions are considered in the ho- moclinic manifold consisting of a series of homoclinic orbits for the fourth-dimensional system.The existence,coexistence and uniqueness of 1-homoclinic orbit,1-periodic orbit and 2-fold 1-periodic orbit are obtained under resonant condition,the correspon- ding bifurcation surfaces and existing regions are also given.
文摘An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare also evaluated.AMS(MOS) Subject classifications 34B15
