Experimental study of the nonlinear dynamics of a smooth and discontinuous oscillator with different smoothness parameters and initial values

Abstract

The dynamic response of a nonlinear system is very sensitive to initial conditions. Both the irrational nonlinearity and the large displacement of a smooth and discontinuous (SD) oscillator have been studied in this paper. An experimental study has been conducted on a model of the SD oscillator with different initial conditions and smoothness parameters. Experimental results indicate that tiny variation in the initial displacement will lead to different kinds of vibrations, and the system exhibits a wide range of nonlinear dynamical phenomena with the change of smoothness parameters. All experimental results are in good conformity with numerical simulation results.