The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO...The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.展开更多
In this paper, a new analytical method for vibration analysis of a cracked simply supported beam is investigated. By considering a nonlinear model for the fatigue crack, the governing equation of motion of the cracked...In this paper, a new analytical method for vibration analysis of a cracked simply supported beam is investigated. By considering a nonlinear model for the fatigue crack, the governing equation of motion of the cracked beam is solved using perturbation method. The solution of the governing equation reveals the superhaxmonics of the fundamental frequency due to the nonlinear effects in the dynamic response of the cracked beam. Furthermore, considering such a solution, an explicit expression is also derived for the system damping changes due to the changes in the crack parameters, geometric dimensions and mechanical properties of the cracked beam. The results show that an increase in the crack severity and approaching the crack location to the middle of the beam increase the system damping. In order to validate the results, changes in the fundamental frequency ratios against the fatigue crack severities are compared with those of experimental results available in the literature. Also, a comparison is made between the free response of the cracked beam with a given crack depth and location obtained by the proposed analytical solution and that of the numerical method. The results of the proposed method agree with the experimental and numerical results.展开更多
The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many pri...The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many prior studies presented, but, more important, with involutecontact ratio (ICR) as well. The ICR embodies its impact on the spur gear's dynamic performancethrough changing the proportion of tooth stiffness when there are n+1 teeth in contact to toothstiffness when there are n teeth in contact. A couple of curves about impact of ICR on the gear'sdynamic performance are presented, and they clearly demonstrate that the model can accuratelydescribe the effects of ICR on dynamic transmission error. Finally, some conclusions useful toreduce vibration and noise of gear-pair are proposed.展开更多
The transient flow mathematical model of arbitrary shaped heterogeneous reservoirs with impermeability barrier is proposed in this paper. In order to establish this model, the perturbation method is employed and the s...The transient flow mathematical model of arbitrary shaped heterogeneous reservoirs with impermeability barrier is proposed in this paper. In order to establish this model, the perturbation method is employed and the solution of model is expanded into a series in powers of perturbation parameter. By using the Boundary Element Method (BEM) and Duhamel principle, wellbore pressure with effects of skins and wellbore storage is obtained. The type curves are plotted and analyzed considering effects of heterogeneity, arbitrary shape and impermeable barriers. Finally, the results obtained by perturbation boundary element method is compared with the analytical solution and is available for the transient pressure analysis of arbitrary shaped reservoirs.展开更多
This paper uses the weakly nonlinear method and perturbation method to deal with the quasi-geostrophic vorticity equation,and the modified Korteweg-de Vries（mKdV） equations describing the evolution of the amplitude ...This paper uses the weakly nonlinear method and perturbation method to deal with the quasi-geostrophic vorticity equation,and the modified Korteweg-de Vries（mKdV） equations describing the evolution of the amplitude of solitary Rossby waves as the change of Rossby parameter β（у） with latitude у is obtained.展开更多
The combined effects of the system rotation (Coriolis force) and curvature (centrifugal force) on the flow in rotating curved circular pipe with small curvature are examined by perturbation method. A second order per...The combined effects of the system rotation (Coriolis force) and curvature (centrifugal force) on the flow in rotating curved circular pipe with small curvature are examined by perturbation method. A second order perturbation solution is presented. The secondary flow structure and the primary axial velocity distributions are studied in detail. The loops of the secondary flow are more complex than those in a curved pipe without rotation or a rotating straight pipe. Its numbers depend on the body force ratio F which represents the ratio of the Coriolis to the centrifugal force. The maximum of the axial velocity is pushed to either outer bend or inner bend, which is also determined by F. The results are confirmed by the results of other authors who studied the same problem by different methods.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 40676016 and 10471039)the State KeyProgram for Basic Research of China (Grant Nos 2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences (Grant No KZCX3-SW-221)in partly by E-Institutes of Shanghai Municipal Education Commission (Grant NoN.E03004)the Natural Science Foundation of Zhejiang Province,China (Grant No Y606268)
文摘The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.
文摘In this paper, a new analytical method for vibration analysis of a cracked simply supported beam is investigated. By considering a nonlinear model for the fatigue crack, the governing equation of motion of the cracked beam is solved using perturbation method. The solution of the governing equation reveals the superhaxmonics of the fundamental frequency due to the nonlinear effects in the dynamic response of the cracked beam. Furthermore, considering such a solution, an explicit expression is also derived for the system damping changes due to the changes in the crack parameters, geometric dimensions and mechanical properties of the cracked beam. The results show that an increase in the crack severity and approaching the crack location to the middle of the beam increase the system damping. In order to validate the results, changes in the fundamental frequency ratios against the fatigue crack severities are compared with those of experimental results available in the literature. Also, a comparison is made between the free response of the cracked beam with a given crack depth and location obtained by the proposed analytical solution and that of the numerical method. The results of the proposed method agree with the experimental and numerical results.
文摘The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many prior studies presented, but, more important, with involutecontact ratio (ICR) as well. The ICR embodies its impact on the spur gear's dynamic performancethrough changing the proportion of tooth stiffness when there are n+1 teeth in contact to toothstiffness when there are n teeth in contact. A couple of curves about impact of ICR on the gear'sdynamic performance are presented, and they clearly demonstrate that the model can accuratelydescribe the effects of ICR on dynamic transmission error. Finally, some conclusions useful toreduce vibration and noise of gear-pair are proposed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos: 50174011 10172028) the Science Tech. Research Program of Heilongjiang Provincial Education Department (Grant No: 10531032).
文摘The transient flow mathematical model of arbitrary shaped heterogeneous reservoirs with impermeability barrier is proposed in this paper. In order to establish this model, the perturbation method is employed and the solution of model is expanded into a series in powers of perturbation parameter. By using the Boundary Element Method (BEM) and Duhamel principle, wellbore pressure with effects of skins and wellbore storage is obtained. The type curves are plotted and analyzed considering effects of heterogeneity, arbitrary shape and impermeable barriers. Finally, the results obtained by perturbation boundary element method is compared with the analytical solution and is available for the transient pressure analysis of arbitrary shaped reservoirs.
基金Project supported by the Educational Department of Inner Mongolia (NJZY:08005)Open Fund of the Key Laboratory of Ocean Circulation and Waves,Chinese Academy of Sciences (Grant No KLOCAW0805)
文摘This paper uses the weakly nonlinear method and perturbation method to deal with the quasi-geostrophic vorticity equation,and the modified Korteweg-de Vries（mKdV） equations describing the evolution of the amplitude of solitary Rossby waves as the change of Rossby parameter β（у） with latitude у is obtained.
文摘The combined effects of the system rotation (Coriolis force) and curvature (centrifugal force) on the flow in rotating curved circular pipe with small curvature are examined by perturbation method. A second order perturbation solution is presented. The secondary flow structure and the primary axial velocity distributions are studied in detail. The loops of the secondary flow are more complex than those in a curved pipe without rotation or a rotating straight pipe. Its numbers depend on the body force ratio F which represents the ratio of the Coriolis to the centrifugal force. The maximum of the axial velocity is pushed to either outer bend or inner bend, which is also determined by F. The results are confirmed by the results of other authors who studied the same problem by different methods.
