The energy balance to nonlinear oscillations via Jacobi collocation method

Abstract

This study develops the energy balance based on Jacobi collocation method for accurate prediction of conservative nonlinear oscillator models with a single collocation point. The node points are taken as the roots of Jacobi orthogonal polynomials. Several examples are included to demonstrate the applicability and accuracy of the proposed algorithm, and some comparisons are made with the existing results. The method is suitable and the approximate frequencies are valid for small as well as large amplitudes of oscillation. Excellent agreement with exact ones is presented for the first order approximation.

Keywords

• Orthogonal collocation
• Energy balance method
• Nonlinear oscillation
• Accurate prediction
• Jacobi polynomial