Abstract
In this paper, the hinge in the articulated structure is studied, the gap hinge is described as a nonlinear bilateral constraint, and the equivalent modeling and analysis of the hinge connection collision vibration are carried out based on the Lankarani–Nikravesh nonlinear contact force model. With the help of the method of nonlinear system dynamics analysis research, the Poincaré mapping of hinge joint collision vibration is constructed, the bifurcation diagram of the system with different parameters is solved, and the variation law of the system motion and the influence of parameters are analyzed by combining the time response diagram, phase diagram, Poincaré cross section diagram, and spectrum diagram of the typical motion of the system. The simulation results show that the system moves in a single degree of freedom and varies with parameters with multiplicative period bifurcation and rubbing edge bifurcation leading to chaos; the system’s periodic motion has shock state mutation and mirror jump transformation.
Highlights
E focus of this paper will be on the description of the mechanical behavior of the hinge gap and contact interface
For the system with clearance, the trajectory in the phase space of the system is different from that of the smooth nonlinear system because of the clearance constraint: the trajectory passes through the constrained boundary, the dynamic formulas of the system switch, the smoothness of the trajectory is destroyed, and the contact may cause singularity. e construction of Poincaremapping for systems with gaps involves two different methods of mapping cross sections in phase space [34]:the fixed phase section and the constraint boundary determined by the Poincaresections
By comparing the bifurcation diagrams under different frequencies with the decrease of damping ratio, the system experienced a jump mutation from single period motion to chaos through period-doubling bifurcation. e excitation frequency makes the bifurcation diagram shift as a whole; the period-doubling window at the small damping end is compressed when the frequency increases. e results show that the large damping of the structure accelerates the energy dissipation of the impact vibration and makes the motion response of the structure tend to be stable
Summary
Equivalent Modeling of Hinge Connection Impact Vibration. The hinge is composed of a double ear bar, a single ear bar, a pin shaft, and a shaft sleeve, and the elastic thin wall is used to simulate the bar connection constraints. The elastic thin wall is simplified into linear spring and linear damping, the double ear bar and single ear bar are defined as concentrated masses, and the clearance contact of the hinge is treated as a nonlinear bilateral constraint. When the oscillator moves to the nonlinear constraint boundary, a contact
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