DETERMINE THE SOLUTIONS IN A SINGLE-DEGREE-OF-FREEDOM NONLINEAR SYSTEM AND APPLYING THE WEIGHTED AVERAGE METHOD

Abstract

This paper proposes the determination of the solution of a single-degree-of-freedom nonlinear system. The contents of the paper are to calculate the natural frequencies of the nonlinear system using three methods.  They are the method of direct integration of the differential equation, the method based directly on the numerical calculation results and the method of using the weighted average function. This paper used the least square criterion to evaluate the error between the numerical methods and the proposed methods. The results obtained are the exact natural frequencies and the frequencies according to the proposed methods. Along with the frequency calculation results, the paper also obtained the solutions as approximate analytical expressions. From obtained results, it can be seen that the errors between the solutions according to the numerical method and the solution according to the proposed methods are very small. The weighted average method to determine the solution of the nonlinear differential equation revealed that this is an approach with many advantages. The weighted average method can be easy to apply to the calculation and obtain results with high reliability.