APPLICATION OF HE’S FREQUENCY FORMULA TO NONLINEAR OSCILLATORS WITH GENERALIZED INITIAL CONDITIONS
Jiangang Zhang, Qing-Ru Song, Jianqiang Zhang, Fang Wang
Abstract
This paper focuses on the vibration periodic property of Duffing oscillator with generalized initial conditions. Firstly, the undamped case is solved by Ji-Huan He’s frequency formulation; Secondly, the formulation is extended to the damped case. Numerical verification shows that the frequency formulation is mathematically simple and physically insightful and practically applicable. This paper paves a novel way for engineers to use the formulation to study nonlinear vibration system with ease and reliability.
Topics & Concepts
Duffing equationNonlinear systemSimple (philosophy)Property (philosophy)VibrationReliability (semiconductor)Control theory (sociology)MathematicsApplied mathematicsMathematical analysisComputer sciencePhysicsAcousticsEpistemologyQuantum mechanicsPower (physics)PhilosophyControl (management)Artificial intelligenceVibration and Dynamic AnalysisMagnetic Bearings and Levitation DynamicsStructural Health Monitoring Techniques