Abstract
A new kind of nonlinearity of inertial type caused by accelerated motionof interacting particles is described. The model deals with an ensembleof grains immersed into a vibrating fluid. First, the nonlinearvibration of two connected grains is studied. The temporal behaviours ofdisplacement and velocity, as well as spectrum of vibration, areanalysed. Numerical simulations are performed. Then an infinite chain ofgrains is considered and the corresponding differential-differenceequation is derived. For the continuum limit the inhomogeneous nonlinearwave equation is solved and temporal profiles are calculated. A newresonant phenomenon is described and the resonant curves areconstructed.
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