Quasi-static quintication method for periodic solution of strong nonlinear oscillators

Abstract

In this paper, a quasi-static quintication method for approximate periodic solution of strong nonlinear oscillators was presented. The basic idea of the method is to replace the original nonlinear oscillator with an equivalent cubic-quintic oscillator, whose stiffness constants are derived based on quasi-static equilibrium principles. The exact solution of the equivalent cubic-quintic oscillator was then applied to obtain the approximate solution to the original oscillator. The advantage of the present method is that its quintication constants (i.e. stiffness constants of the equivalent oscillator) are always in the form of elementary functions and are simpler than the corresponding constants derived by the Chebyshev quintication method. The present quintication method was verified using examples of strong nonlinear oscillators and was found to give very accurate results.

Keywords

• Nonlinear oscillator
• Cubic-quintic oscillator
• Quintication method
• Quasi-static equilibrium
• Elliptic function