Cycle response characteristics research on a class of piecewise nonlinear elastic and damping double constraint system

Abstract

Piecewise nonlinear constraint exists in various fields and it always affects the stability of a system. In order to realize the dynamic characteristic of the system constrained by these nonlinearity, we consider two kinds of typical piecewise nonlinear constraints under the dynamic conditions, and establish a dynamic model with double piecewise nonlinear constraint of elasticity and damping, according to the generalized dissipation Lagrange principle. An average method is used to solve the amplitude and frequency response of the system under a periodic external incentive. By a numerical simulation, we compare the time domain responses under different piecewise nonlinear elastic constraints. The results show that the stronger the piecewise nonlinear elastic constraint, the more obvious the piecewise nonlinear damping constraint is. We also compare the bifurcation responses under different piecewise nonlinear damping constraints, the results show that the chaos state will emerge in an enlarged scope with the increase of the piecewise nonlinear damping coefficient, and threaten the stability of the system. The dynamic evolution process of the system is shown by the phase diagrams and Poincaré sections under the corresponding constraint conditions. By comparing the amplitude-frequency characteristics of the system under different constraint conditions, we obtain the response characteristic of the system and its change rule with the piecewise nonlinear constraints. By comparing and analyzing the amplitude-frequency characteristics under the piecewise nonlinear elastic and piecewise nonlinear damping constraint, we obtain the law of system stability influenced by different nonlinear factors, and the interaction relationship between the two piecewise nonlinear constraints.