In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called t...In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called the Krylov-Bogoliubov-Mitropolsky(KBM)method and the multiple scales method(MSM).All mentioned methods are applied to obtain some accurate and stable approximations to the proposed problem without decoupling the original problem.All obtained approximations are discussed graphically using different numerical values to the relevant parameters.Moreover,all obtained approximate solutions are compared with the 4thorder Runge-Kutta(RK4)numerical approximation.The maximum residual distance error(MRDE)is also estimated,in order to verify the high accuracy of the obtained analytic approximations.展开更多
In this paper, we studied a method of averaging which decide a uniform validsolution for nonlinear equationand got the ,modified forms for KB ,method (Krylov-Bogoliubov method)and KBMmethod (Krytov-Bogoliubov-Mitropol...In this paper, we studied a method of averaging which decide a uniform validsolution for nonlinear equationand got the ,modified forms for KB ,method (Krylov-Bogoliubov method)and KBMmethod (Krytov-Bogoliubov-Mitropolski method). Through the comparison of two examples with the method of multiple scales it can be shown that the modifies averaging methods here are uniformly valid and thereby the applied area of the methodof averaging are extended.展开更多
The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this met...The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this method is limited to dealing with the system with strong nonlinearity.In this paper we present a procedure to study the resonance solutions of the system with strong nonlinearities by employing the homotopy analysis technique to extend the KBM method to the strong nonlinear systems,and we also analyze the truncation error of the procedure.Applied to a given example,the procedure shows the efficiencies in studying bifurcation.展开更多
The dynamic model of a pedestal looseness rotor system is built and the dynamics of the system near the resonance region is analyzed using the KBM method. Then the asymptotic method to study a dynamic system with slow...The dynamic model of a pedestal looseness rotor system is built and the dynamics of the system near the resonance region is analyzed using the KBM method. Then the asymptotic method to study a dynamic system with slow-changing parameters is used to study the starting and braking course of the system. Finally, the analytical results are proved by experiment. The results can be used in the inspecting and fault diagnosis of a rotor system of this type.展开更多
This article examines a fifth order critically damped nonlinearsystem in the case of small equal eigenvalues and tries to find out an asymptotic solution. This paper suggests that the solutions obtained by the perturb...This article examines a fifth order critically damped nonlinearsystem in the case of small equal eigenvalues and tries to find out an asymptotic solution. This paper suggests that the solutions obtained by the perturbation techniques based on modified Krylov-Bogoliubov-Mitropoloskii (KBM) method is consistent with the numerical solutions obtained by the fourth order Runge-Kutta method.展开更多
基金the Deputyship for Research&Innovation,Ministry of Education in Saudi Arabia for funding this research work through the project number RI-44-0143
文摘In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called the Krylov-Bogoliubov-Mitropolsky(KBM)method and the multiple scales method(MSM).All mentioned methods are applied to obtain some accurate and stable approximations to the proposed problem without decoupling the original problem.All obtained approximations are discussed graphically using different numerical values to the relevant parameters.Moreover,all obtained approximate solutions are compared with the 4thorder Runge-Kutta(RK4)numerical approximation.The maximum residual distance error(MRDE)is also estimated,in order to verify the high accuracy of the obtained analytic approximations.
文摘In this paper, we studied a method of averaging which decide a uniform validsolution for nonlinear equationand got the ,modified forms for KB ,method (Krylov-Bogoliubov method)and KBMmethod (Krytov-Bogoliubov-Mitropolski method). Through the comparison of two examples with the method of multiple scales it can be shown that the modifies averaging methods here are uniformly valid and thereby the applied area of the methodof averaging are extended.
基金supported by the National Natural Science Foundation of China (Grant No.10632040)
文摘The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this method is limited to dealing with the system with strong nonlinearity.In this paper we present a procedure to study the resonance solutions of the system with strong nonlinearities by employing the homotopy analysis technique to extend the KBM method to the strong nonlinear systems,and we also analyze the truncation error of the procedure.Applied to a given example,the procedure shows the efficiencies in studying bifurcation.
文摘The dynamic model of a pedestal looseness rotor system is built and the dynamics of the system near the resonance region is analyzed using the KBM method. Then the asymptotic method to study a dynamic system with slow-changing parameters is used to study the starting and braking course of the system. Finally, the analytical results are proved by experiment. The results can be used in the inspecting and fault diagnosis of a rotor system of this type.
文摘This article examines a fifth order critically damped nonlinearsystem in the case of small equal eigenvalues and tries to find out an asymptotic solution. This paper suggests that the solutions obtained by the perturbation techniques based on modified Krylov-Bogoliubov-Mitropoloskii (KBM) method is consistent with the numerical solutions obtained by the fourth order Runge-Kutta method.
