Analyses of impact motions of harmonically excited systems having rigid amplitude constraints

Two harmonically excited systems having symmetrical rigid constraints are considered. Repeated impacts usually occur in these systems due to the rigid amplitude constraints. The impact forms occurring in two systems are different, i.e., the components of one system collide with each other, and one of components of the other system collides with rigid obstacles. Dynamics of these systems are studied with special attention to Neimark–Sacker bifurcations associated with several periodic-impact motions. Period-one double-impact symmetrical motions and associated Poincaré maps of two systems are derived analytically. Stability and local bifurcations of the period-one double-impact symmetrical motions are analyzed by using the Poincaré maps. Neimark–Sacker bifurcations associated with several periodic-impact motions are found by numerical simulation, and the corresponding routes from quasi-periodic impact motions to chaos are also stated. The influence of the clearance and excitation frequency on symmetrical double-impact periodic motion and bifurcations is analyzed. Studies show that the vibratory systems having symmetrical rigid amplitude constraints may exhibit complex and rich quasi-periodic impact behavior under different system parameter conditions.