Impact interactions between two vibration systems under random excitation

The exact stationary solutions of the random response of two special vibration systems with impact interactions are formulated in this paper. Between the two systems, the Hertz contact law is used to model the contact process during vibration. A clearance is also introduced. The excitation is assumed to be a stationary white Gaussian process with zero mean and acting on the two systems independently. By assuming the ratio of the excitation and damping parameter of each system to be the same, the exact solutions can be found through solving the time‐independent Fokker‐Planck equation. The effects of contact stiffness, clearance and the system properties on the response are discussed probabilistically. From this study, it is found that, under some cases, the contact phenomena still play an important role on the response even when the clearance is larger than three times the root mean square response of the corresponding linear systems.