We deal with an initial-boundary value problem describing the perpendicular vibrations of an anisotropic viscoelastic plate free on its boundary and with a rigid inner obstacle. A weak formulation of the problem is in the form of the hyperbolic variational inequality. We solve the problem using the discretizing the time variable. The elliptic variational inequalities for every time level are uniquely solved. We derive the a priori estimates and the convergence of the sequence of segment line functions to a variational solution of the considered problem.

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