Application of Adaptation HAM for Nonlinear Oscillator Typified as A Mass Attached to A Stretched Elastic Wire - Bataineh, A. Sami (Communications in Mathematics and Applications, 2017)
This paper applies the adaptation of homotopy analysis method (AHAM) for the first time to obtained the periodic solutions for the oscillation of a mass attached to a stretched elastic wire. The AHAM approach can be applied directly to the governing equation without rewrite it in a form that does not contain the square-root expression. More precisely, with the help of the homotopy polynomials procedure the nonlinear term of the problem can be decompose as a series of polynomials to overcomes the difficulty arising in calculating complicated integrals. A comparative study between AHAM and other existing solutions obtained by several authors is conducted to demonstrate the simplicity and the efficiency of AHAM. The approximate frequency and periodic solution for both small and large amplitude of oscillations show a good agreement with the numerical solution.
Keywords: Homotopy analysis method; Homotopy polynomials; Nonlinear oscillation; Periodic solutions