Free vibration of electroelastic thin-walled structures under static load

The mathematical formulation and finite element algorithm for solving the problem of free vibration of electroelastic plates and shells under static load are considered. In modeling, the curvilinear surface of a thin-walled structure is represented as a set of flat segments. In each of them, the physical relations of the classical laminated plate theory and the theory of electroelasticity, written for a plane stress state, are fulfilled. The strains are determined using nonlinear equations, which are linearized with respect to the state with a small deviation from the initial equilibrium position caused by static forces. As an examples, we consider a rectangular plate and a circular cylindrical shell with a piezoelectric element under the action of the uniform pressure. The validity of the solution is confirmed by comparing the normal displacement and natural frequencies of vibration with experimental data and results obtained with the use of commercial finite element software.