Oscillator with Time-Variable Degree of Nonlinearity: Theory and Application in Aging of Polymer Composite Structure

Abstract

In this paper, a new type of one-degree-of-freedom pure nonlinear oscillator with a time variable degree of nonlinearity is introduced. Namely, the degree of the nonlinearity in the restitution force is not a constant but a ‘slow time’ variable function. The mathematical model is a second-order nonlinear differential equation with time-variable parameters. An approximate solving procedure based on the method of time-variable amplitude, frequency and phase is developed. It is found that the vibration properties depend on initial conditions and the degree of time-variable function. The theoretical results are tested on almost linear, cubic and high-degree nonlinear oscillators. According to theoretical considerations, the process of aging in fiber-reinforced polymer composite structure is investigated. It is found that the amplitude and the frequency of vibration of the reinforced polymer structure decrease over time. The result is in good agreement with already published experimental data. The additional conclusion of the research is that the oscillator model suggested in the paper is suitable for the prediction of mechanic properties of the polymer structure in aging and also in similar destructive processes.