Response of an impacting Hertzian contact to an order-2 subharmonic excitation : Theory and experiments

In this paper, the response of a normally excited preloaded Hertzian contact is investigated in order to analyse the subharmonic resonance of order 2. The nonlinearity associated with contact losses is included. The method of multiple scales is used to obtain the non-trivial steady-state solutions, their stability, and the frequency–response curves. To this end, a third-order Taylor series of the elastic Hertzian contact force is introduced over the displacement interval where the system remains in contact. A classical time integration method is also used in conjunction with a shooting method to take into account losses of contact. The theoretical results show that the subharmonic resonance constitutes a precursor of dynamic responses characterised by loss of contact, and consequently, the resonance establishes over a wide frequency range. Finally, experimental validations are also presented in this paper. To this end, a specific test rig is used. It corresponds to a double sphere–plane contact preloaded by the weight of a moving mass. Experimental results show good agreements with theoretical ones.