Mathematical modeling of vibration devices

Mathematical models of vibration devices designed to intensify technological processes are considered. Mathematical models are initial-boundary-value problems for coupled systems of partial differential equations for hydrodynamic functions and deformation functions of elastic elements. We examine the dynamics and dynamic stability of elastic elements. The study of dynamics is based of the Bubnov–Galerkin method. The study of dynamical stability is based on the construction of positive definite Lyapunov-type functionals.