periodic solutions of the duffing harmonic oscillator by he's energy balance method

Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...

Nonlinear oscillator with discontinuity by generalized harmonic balance method

A generalized harmonic balance method is used to calculate the periodic solutions of a nonlinear oscillator with discontinuities for which the elastic force term is proportional to sgn(x). This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have rational form. This approach gives us not only a truly periodic solution but also the fr...

An explicit approximate solution to the Duffing- harmonic oscillator by a cubication method

Solution of strongly nonlinear oscillator problem arising in Plasma Physics with Newton Harmonic Balance Method

In this paper, Newton Harmonic Balance Method (NHBM) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. Periodic solution is analytically verified and consequently the relation between the Natural Frequency and the amplitude is obtained in an ana...

Numerical Solution of the Controlled Harmonic Oscillator by Homotopy Perturbation Method

‎The controlled harmonic oscillator with retarded damping‎, ‎is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems‎. ‎In this paper‎, ‎to solve this problem‎, ‎we presented an analytical method‎. ‎This approach is based on the homotopy perturbation method‎. ‎The solution procedure becomes easier‎, ‎simpler and mor...

Periodic solutions for some strongly nonlinear oscillations by He's energy balance method

In this paper, applying He’s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy. Keywords—He’s energy balance method; Periodic solution; Nonlinear oscillator; Discontinuous; Fracti...