Periodically forced system with symmetric motion limiting constraints: Dynamic characteristics and equivalent electronic circuit realization

A two-degree-of-freedom periodically-forced system with symmetric motion limiting constraints is considered in this paper. The incidence relation between dynamics and constraint parameters (clearance and constraint stiffness) is studied and some novel results are obtained by double-parameter simulation analysis. The fundamental group of impact motions having the excitation period and differing by the number of impacts is given special consideration for analyzing low frequency vibration characteristics of the system. Dynamics of the system are studied with emphasis on the mutual transition characteristics between neighboring regions of fundamental impact motions. An electronic circuit is designed for physical implementation of dynamics of the periodically-forced system with symmetric constraints. The non-linear terms of the system are replaced by using an absolute-value function and can be fully implemented with simple electronic elements (resistors and operational amplifiers). The electronic circuit is realized and studied. The oscilloscope outputs of electrical waveforms of various non-smooth oscillations, generated by the circuit itself, are experimentally observed. A good agreement among the numerical results of the mechanical model, the electronic design simulation of the circuit and the real oscilloscope outputs of hardware implementation is confirmed.