  Response of a normally excited preloaded Hertzian contact is investigated in
order to analyze 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.
