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, a theoretical treatment of the stability behavior of the zero solution of nonlinear damped oscillator in the vectorial case is investigated. We study the sufficient conditions for the boundedness of sol...In this paper, a theoretical treatment of the stability behavior of the zero solution of nonlinear damped oscillator in the vectorial case is investigated. We study the sufficient conditions for the boundedness of solution of the nonlinear damped vectorial oscillator and the conditions for the stability of the zero solution to be uniformly stable as well as asymptotically stable.展开更多
In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example...In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.展开更多
The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
The purpose is to design the control method for a single-degree-of-freedom(SDOF)exponentially damped oscillator.Based on the Lyapunov stability theory,sliding mode control and adaptive sliding mode control have been p...The purpose is to design the control method for a single-degree-of-freedom(SDOF)exponentially damped oscillator.Based on the Lyapunov stability theory,sliding mode control and adaptive sliding mode control have been proposed.Sliding control laws and adaptive sliding laws are designed for exponentially damped oscillator respectively in cases that the bound of the external exciting force is known or unknown.The viability and effectiveness of the above control designs have been validated by numerical simulations.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, a theoretical treatment of the stability behavior of the zero solution of nonlinear damped oscillator in the vectorial case is investigated. We study the sufficient conditions for the boundedness of solution of the nonlinear damped vectorial oscillator and the conditions for the stability of the zero solution to be uniformly stable as well as asymptotically stable.
文摘In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.
文摘The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
基金National Natural Science Foundation of China(No.11802338)
文摘The purpose is to design the control method for a single-degree-of-freedom(SDOF)exponentially damped oscillator.Based on the Lyapunov stability theory,sliding mode control and adaptive sliding mode control have been proposed.Sliding control laws and adaptive sliding laws are designed for exponentially damped oscillator respectively in cases that the bound of the external exciting force is known or unknown.The viability and effectiveness of the above control designs have been validated by numerical simulations.
