Dynamics and SC-CNN circuit implementation of a periodically forced non-smooth mechanical system

Abstract

A two-degree-of-freedom periodically forced system with multiple motion limiting constraints is considered. The incidence relation between dynamics and key parameters (clearance, constraint stiffness and forcing frequency) is numerically studied by selecting different values of constraint stiffness and finely scanning the (forcing frequency, clearance)–parameter plane. Two cases, associated with the non-prepressing and prepressing constraints, are considered in the research. The fundamental group of impact motions with an excitation period and the different impact number is studied with emphasis on the generation mechanism. The complicated and regular transition characteristics between adjacent fundamental impact motions are analyzed by their existence domains and bifurcation boundaries in the (forcing frequency, clearance)–parameter plane. The influence of the constraint parameters on multiformity and transitional characters of periodic–impact motions of the system is studied in relatively large parameter spaces. An electronic circuit in the framework of state-controlled cellular neural network (SC-CNN) is designed for experimental verification of dynamic mechanical behaviors of the non-smooth system driven by periodical exciting forces. Real electronic circuit, based on four SC-CNN cells, is made by using printed circuit board, and the oscilloscope output of phase portraits of electrical waveforms generated by the circuit itself is 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. The results fully show that the modeling method using the strategy based on SC-CNN is suitable for the modeling of the periodically forced systems with multiple motion limiting constraints. The high availability and reliability of the electronic circuit, based on the SC-CNN framework, are verified by the contrast analyses.