Analysis of the nonlinear differential equation of the circular sector oscillator by the global residue harmonic balance method
Junfeng Lu, Li Ma, Yi Sun
Abstract
In this paper, we apply the global residue harmonic balance method (GRHBM) for solving the nonlinear differential equation of the circular sector oscillator. The approximated solutions to the initial value problems are provided without linearization. Some remarks about the first order frequency in [Shaban M, et al. Current Applied Physics, 2010] are given. Numerical comparisons with Runge–Kutta method, the modified homotopy perturbation method and Akbari-Ganji’s method are presented to confirm the efficiency of GRHBM.
Topics & Concepts
Harmonic balanceNonlinear systemHarmonic oscillatorBalance (ability)Differential equationPhysicsBalance equationMathematical analysisResidue (chemistry)MathematicsMechanicsChemistryQuantum mechanicsBiochemistryPhysical medicine and rehabilitationMedicineMarkov modelMarkov chainStatisticsFractional Differential Equations SolutionsBladed Disk Vibration DynamicsVibration and Dynamic Analysis