A new kind of nonlinearity of inertial type caused by accelerated motion of interacting particles is described. The model deals with an ensemble of grains immersed into a vibrating fluid. First, the nonlinear vibration of two connected grains is studied. The temporal behaviours of displacement and velocity, as well as spectrum of vibration, are analysed. Numerical simulations are performed. Then an infinite chain of grains is considered and the corresponding differential-difference equation is derived. For the continuum limit the inhomogeneous nonlinear wave equation is solved and temporal profiles are calculated. A new resonant phenomenon is described and the resonant curves are constructed.