Dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative

Abstract

In this paper, the dynamic response of a piecewise linear single-degree-of-freedom oscillator with fractional-order derivative is studied. First, a mathematical model of the single-degree-of-freedom system is established, and the approximate steady-state solution associated with the amplitude-frequency equation is obtained based on the averaging method. Then, the amplitude-frequency response equations are used for stability analysis, and the stability condition is founded. To validate the correctness and precision, the approximate solutions determined by the analytical method are compared with the solutions based on the numerical integration method. It is found that the approximate solutions and the numerical solutions are in excellent agreement. Finally, the effects of system parameters, such as fractional-order coefficient, order, clearance, and piecewise stiffness, on the complex dynamical behaviors of the piecewise linear singledegree-of-freedom oscillator are studied. The results show that the system parameters not only influence resonance amplitude and resonance frequency but also affect the size of the unstable region.

Experimental Modelling and Amplitude-Frequency Response Analysis of a Piecewise Linear Vibration System

“…15 shows the experiment-based relative displacement time history of the proof mass for = 10 Hz, which is validated by the numerical simulation shown in Fig. 16 Using the experimental data in Fig. 18 Fig.…”

“…For the forced vibration of an oscillator with piecewise linear asymmetrical damping, Silveira et al [15] obtained the exact analytical solutions by joining the solutions for the compression and expansion phases and the approximate solutions by the HIB method. Wang et al [16] studied the effect of the system parameters on the dynamical behaviours of a piecewise linear SDOF oscillator with fractional-order derivative by the averaging method.…”