Damping of Hydroelastic Vibrations of the Plate Using Shunted Piezoelectric Element. Part I: Numerical Model

In this work, we investigate the possibility of using a piezoelectric element connected to an external electric RL-circuit for passive vibrations damping of a cantilevered plate interacting with a quiescent fluid. The behavior of piezoelectric elements is described by the equations of electrodynamics of deformable electroelastic media within the framework of quasi-static approximation. The motion of an ideal fluid in the case of small perturbations is considered in the framework of acoustic approximation. Small strains in a thin plate are determined using the Reisner–Mindlin theory. A mathematical formulation of the problem of electroelasticity elastic body with external electric circuits is based on the Lagrange variational principle, which includes the expression for hydrodynamic pressure. The acoustics equations together with the boundary conditions and the impermeability condition are converted to a weak form using the Bubnov–Galerkin method. The numerical implementation of the problem is carried out using an original approach, which is based on the ANSYS finite element package integrated with the program that implements the algorithm for solving the non-classical eigenvalue problem by the Muller method. This allows us to evaluate the values of the parameters of the external RL-circuit, which could provide the most effective damping of vibrations at a certain frequency.