The Lagrange interpolation for He’s frequency formulation
Yue Shen
Abstract
Nonlinear oscillators arise everywhere in engineering, and though there are many analytical methods available, a fast and accurate estimation of the frequency–amplitude relationship is much needed in practical applications. He’s frequency formulation meets this requirement, but the local points are chosen randomly. In this paper, the Gaussian interpolation points are adopted, making He’s method more mathematically rigorous and physically reliable. The cubic-quintic Duffing equation is used for comparison, and an excellent result is obtained.
Topics & Concepts
Interpolation (computer graphics)Quintic functionDuffing equationApplied mathematicsBilinear interpolationNonlinear systemMathematicsAmplitudeGaussianMathematical analysisComputer scienceCalculus (dental)PhysicsArtificial intelligenceStatisticsOpticsMotion (physics)DentistryQuantum mechanicsMedicineFractional Differential Equations SolutionsAcoustic Wave Phenomena ResearchProbabilistic and Robust Engineering Design