He's frequency–amplitude formulation for nonlinear oscillators using Jacobi elliptic functions
Alex Elı́as-Zúñiga, Luis Manuel Palacios-Pineda, Isaac H. Jiménez-Cedeño, Óscar Martínez-Romero, Daniel Olvera-Trejo
Abstract
In this work, the Duffing’s type analytical frequency–amplitude relationship for nonlinear oscillators is derived by using Hés formulation and Jacobi elliptic functions. Comparison of the numerical results obtained from the derived analytical expression using Jacobi elliptic functions with respect to the exact ones is performed by considering weak and strong Duffing’s nonlinear oscillators.
Topics & Concepts
Elliptic functionJacobi elliptic functionsNonlinear systemAmplitudeDuffing equationElliptic integralMathematical analysisMathematicsWork (physics)PhysicsQuantum mechanicsFractional Differential Equations SolutionsAcoustic Wave Phenomena ResearchBladed Disk Vibration Dynamics