A variable-structure system, consisting of a thin horizontal elastic plate, loaded by a heavy layer of granular material is considered. The system is excited by prescribed vertical vibrations of the plate boundaries. An essentially nonlinear vibrational rheological model with unilateral constraints is proposed for simulation of the layer behavior. During the coupled motion stages the layer dynamic response on the interface between plate and granular layer is described by the Volterra integro-operator relationship with nonlinear isochronic force-displacement characteristic. The governing set of equations includes the plate dynamics differential equation, an integro-differential equation of the layer dynamics, and also appropriate boundary and initial conditions. Due to utilization of the Galerkin method and Kroosh approximation, the initial set is reduced to the set of nonlinear differential equations. The latter is integrated numerically. Model identification is carried out by the computer processing of the experimental bending strain histories. Influence of the excitation parameters, height of the layer, and damping on the bending strains is analyzed. Adequate simulation of the layer behavior for one-period modes is achieved with regard to the motion periodicity, the values of the strain peaks, the critical time points and the duration of the main time stages. Analysis of numerical phase trajectories and Poincaré sections predicts transition to stochastic vibration modes and the existence of stable two-period limit cycles, when the maximum forcing acceleration is increased above 3g.