The closed form solutions of the stationary random response of a single‐degree‐of‐freedom vibro‐impact system with clearance are formulated in this paper. The Hertz contact law from elasticity is used to model the contact phenomena between the mass and constraint during vibration. The excitation is assumed to be a stationary white Gaussian process with zero mean. Through solving the time‐independent Fokker‐Planck equation, the stationary responses are obtained analytically. The effects of contact stiffness and clearance on the response are discussed probabilistically. It is found that, when the clearance is about twice the square root of the mean square response of the corresponding linear system, the contact phenomena are almost negligible.
All Science Journal Classification (ASJC) codes
- Geotechnical Engineering and Engineering Geology
- Earth and Planetary Sciences (miscellaneous)