Experimental Study of a Symmetrical Piecewise Base-Excited Oscillator

Abstract

This paper presents an experimental study on a base-excited piecewise linear oscillator with symmetrical flexible constrains of high stiffness ratio (above 20). The details of the adopted design of the oscillator, the experimental setup, and calibration procedure are briefly discussed. The regions of chaotic motion predicted theoretically were confirmed by the experimental results arranged into bifurcation diagrams. Clearance, stiffness ratio, amplitude, and frequency of the external force were used as branching parameters. The discussion of the system dynamics is based on bifurcation diagrams and Lissajous curves. The investigated system tends to be periodic for large clearances and chaotic for small ones. This picture is reversed for the amplitude of the forcing changes, where periodic motion occurred for small values and chaos dominated for larger forcing. The same behavior is observed for increasing frequency ratio where, for values below the natural frequency, the most interesting dynamics occurs. For the investigated parameter values, the stiffness ratio variation produces only periodic motion.

Study of a piecewise linear dynamic system with negative and positive stiffness

“…The method of a Poincaré section and the resultant return map were used to investigate the periodic orbits and local bifurcations. Wiercigroch and Sin studied the system dynamics of a base-excited piecewise linear oscillator with all positive stiffnesses [2]. Experimental and numerical results were arranged into bifurcation diagrams and Lissajous curves, compared, and analyzed.…”

Dynamical analysis of a single degree-of-freedom impact oscillator with impulse excitation

“…The calculation of the spectrum of Lyapunov exponents for impactvibrating systems with rigid constraints was given in detail by Jin et al 20 Yue and Xie 21 developed a method of calculating the Lyapunov exponents in vibro-impact systems with symmetric rigid constraints. Moreover, other scholars [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] studied different impact oscillators and found some typical different phenomena.…”

Chaotic vibrations in a damage oscillator with crack closure effect

“…It has to be pointed out that these material sources of nonlinearities are mainly investigated from a theoretical point of view, and very few papers have been devoted to the experimental evidence of chaos in these nonsmooth oscillators. [Wiercigroch and Sin 1988] can be cited for extensive experimental investigations on nonsmooth oscillators with piecewise linear restoring forces. [Ing et al 2008] is also an experimental contribution on an impact oscillator with a one-sided elastic constraint.…”