Global bifurcation and circuit simulation of a soft-impacting system

Considering that the dynamic analysis of mechanical systems with clearance needs to compile complex calculation programs, and high-precision numerical simulation is limited by computer performance. Dynamics of a two-degree-of-freedom system with soft impact are revealed from the perspective of equivalent circuit simulation in this paper. By using bifurcation diagrams and phase diagrams based on Poincaré mapping, as well as Lyapunov exponents, the mechanism of single-period multi-impact <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>1-</mml:mtext> <mml:mi>p</mml:mi> </mml:math> - <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> motion and chattering impact under low-frequency conditions was revealed. In the MultiSim14.0 environment, a circuit diagram equivalent to the mathematical model of the system is designed by using the addition circuit, integration circuit, and inverter circuit composed of operational amplifiers, resistors, and capacitors. The nonlinear module is realized by the saturation characteristics of the operational amplifier. It is found that the output waveform of the virtual oscilloscope has a very good agreement with that obtained from the numerical simulation. Equivalent circuit test method not only has fast operation speed and less time consumption, but also can realize real-time dynamic adjustment of parameters, which provides a reference method for the dynamic research of mechanical system with clearance.