Discontinuous Dynamic Analysis of a Class of 2-DOF Oscillators With Strong Nonlinearity Under a Periodic Excitation

Starting from the car suspension system, nonlinear characteristics of a class two-degree-of-freedom oscillators with strong nonlinearity under periodic excitation are discussed by switching theory flow in discontinuous dynamical systems. Based on forces and different motions two masses, phase plane each mass is composed stick domain, nonstick domain (or free domain) separation boundary absolute relative coordinates, respectively. The swithching criteria between conditions grazing motion regions developed via G-functions control laws. mapping dynamics used to give four-dimensional transformation set mapping, for explored. In addition, motions, kinds this system comparison velocities, accelerations responses) masses force simulated numerically. results show that stability comfort vehicle can be improved adjusting force, which generated unit or exerted external excitation. For further investigating influence parameters behaviors, bifurcation scenarios varying driving frequency amplitude also developed, provide useful information parameter selection vibration systems clearance optimal design This paper has important reference value practical applications other industries machinery elastic impacts.