A new cubication method is proposed for periodic solution of nonlinear Hamiltonian oscillators. The method is formulated based on quasi-static equilibrium of the original oscillator and the undamped cubic Duffing oscillator. The cubication constants derived from the present cubication method are always based on elementary functions and are simpler than the constants derived by other cubication methods. The present method was verified using three common examples of strongly nonlinear oscillators and was found to give reasonably accurate results. The method can be used to introduce nonlinear oscillators in relevant undergraduate physics and mechanics courses.
Big-AlaboA.Continuous piecewise linearization method for approximate periodic solution of the relativistic oscillator.Int J Mech Eng Educ. 2020; 48: 178–194.
7.
KovacicICveticaninLZukovicM, et al.
Jacobi elliptic functions: a review of nonlinear oscillatory application problems. J Sound Vib2016;
380: 1–36.
8.
Bravo YutseSMartin SanchezA.A weighted mean-square method of “cubication” for nonlinear oscillators. J Sound Vib1989;
134: 423–433.
9.
Bravo YutseS.“Cubication” for nonlinear oscillators using the principle of harmonic balance. Int J Non-Linear Mech1990;
27: 347–356.
10.
Elıas-ZunigaAMartınez-RomeroO.Accurate solutions of conservative nonlinear oscillators by the enhanced cubication method.Math Probl Eng2013: 1–9. Article 842423. DOI:10.1155/2013/842423
11.
Elias-ZunigaA. “Quintication” method to obtain approximate analytical solutions of non-linear oscillators. Appl Math Comput2014;
243: 849–855.
12.
Big-AlaboA.Periodic solutions of Duffing-type oscillators using continuous piecewise linearization method. Mech Eng Res2018;
8: 41–52.
13.
HeJH.Preliminary report on the energy balance for nonlinear oscillations. Mech Res Commun2002;
29: 107–111.
