Abstract
Starting from the car suspension system, the nonlinear characteristics of a class of two-degree-of-freedom oscillators with strong nonlinearity under a periodic excitation are discussed by the switching theory of flow in discontinuous dynamical systems. Based on the discontinuous forces and different motions of the two masses, the phase plane of each mass is composed of stick domain, nonstick domain (or free domain) and separation boundary in absolute and relative coordinates, respectively. The swithching criteria between the stick and nonstick motions and the conditions of grazing motion in two different regions are developed via the G-functions and switching control laws. The mapping dynamics theory is used to give the four-dimensional transformation set and four-dimensional mapping, and the conditions for periodic motions are explored. In addition, the stick motions, two kinds of grazing motions, periodic motions for this system and a comparison of the velocities, accelerations (or forces responses) of the two masses under the two conditions of control force are simulated numerically. The results show that the stability and comfort of the vehicle can be improved by adjusting the control force, which is generated by the control unit of system or exerted by the external excitation. For further investigating the influence of system parameters on dynamical behaviors, the stick and grazing bifurcation scenarios varying with driving frequency or amplitude are also developed, which can provide useful information for parameter selection of vibration systems with clearance and the optimal design of vehicle suspension systems. This paper also has important reference value for practical applications in other industries or machinery with elastic impacts.
Highlights
Vehicle vibration is an important factor that affects the ride comfort, stability and life of automobile parts, and serious car vibration can affect the speed of the car and generate noise
It is a significant work to study the dynamical behaviors of such discontinuous dynamical systems
Activated by a simplified system for the active suspension system of vehicles, the aim of the work described in this paper is to investigate the dynamics of a class of 2-DOF oscillators with strong nonlinearity under a periodic excitation by the flow switching theory in discontinuous dynamical systems, which can describe the dynamic behavior of lots of mechanical components, for instance rotating members of robots and vibration dampers and so on. [1]–[13] highlighted the different technological processes used for suspension system control or focused on the method of optimal design for passive, semi-active and active vehicle suspension systems, for example sliding mode control, constrained multiobjective evolutionary search, fuzzy control and genetic algorithm etc
Summary
Vehicle vibration is an important factor that affects the ride comfort, stability and life of automobile parts, and serious car vibration can affect the speed of the car and generate noise. Activated by a simplified system for the active suspension system of vehicles, the aim of the work described in this paper is to investigate the dynamics of a class of 2-DOF oscillators with strong nonlinearity under a periodic excitation by the flow switching theory in discontinuous dynamical systems, which can describe the dynamic behavior of lots of mechanical components, for instance rotating members of robots and vibration dampers and so on. The comparison of the velocities and accelerations (or forces responses) for the two masses under the two conditions of control force, and the stick and grazing bifurcation scenarios varying with driving frequency or amplitude are further carried out to better demonstrate the dynamical behaviors in such system
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