In this paper,two types of frequency amplitude fomulation method are initially utilized to obtain frequency-amplitude relationship of nonlinear vibration of a punctual charge in the electric field of a charged ring.In...In this paper,two types of frequency amplitude fomulation method are initially utilized to obtain frequency-amplitude relationship of nonlinear vibration of a punctual charge in the electric field of a charged ring.In order to obtain the nonlinear natural frequency of the considered system,Reng-Gui and Geng-Cai modified methods are implemented.A table is also prepared to provide a brief review of recent development of nonlinear differential equations.The coectness of the obtained results is compared with those obtained from harmonic balance method(HBM)and energy balance method(EBM).A numerical simulation is caied out to investigate the accuracy of the used methods.In accordance with it,the relative errors of the employed approaches are numerically and analytically found based on the exact numerical solutions.It is exposed that the exerted approaches are very reliable and applicable for solving the nonlinear differential equations.展开更多
文摘In this paper,two types of frequency amplitude fomulation method are initially utilized to obtain frequency-amplitude relationship of nonlinear vibration of a punctual charge in the electric field of a charged ring.In order to obtain the nonlinear natural frequency of the considered system,Reng-Gui and Geng-Cai modified methods are implemented.A table is also prepared to provide a brief review of recent development of nonlinear differential equations.The coectness of the obtained results is compared with those obtained from harmonic balance method(HBM)and energy balance method(EBM).A numerical simulation is caied out to investigate the accuracy of the used methods.In accordance with it,the relative errors of the employed approaches are numerically and analytically found based on the exact numerical solutions.It is exposed that the exerted approaches are very reliable and applicable for solving the nonlinear differential equations.
