Natural vibration and aeroelastic stability of shallow shells with passive electric circuit

Abstract

This article presents the results of study of natural vibration and aeroelastic stability of isotropic shallow cylindrical shells interacting with a supersonic gas flow. The examined systems are equipped with piezoelectric elements which are located on the inner surface of the structure, and can be connected to a passive electric circuit. The mathematical formulation of the problem is based on the variational principle of virtual displacements taking into account the work of inertia forces, aerodynamic pressure and electric field. The solution is developed in a three-dimensional formulation using the mode-superposition technique and finite element method. The non-classical problem on complex eigenvalues is solved using the Muller method. The validity of the obtained results is confirmed by solution convergence with increase of the nodal unknowns and by comparison with the literature. The influence of the piezoelectric element location on the frequency and critical pressure of the gas flow leading to the onset of flutter instability is analyzed at different combinations of kinematic boundary conditions. The applicability of shunt R and RL-circuits for controlling the aeroelastic stability boundary and the damping rate of free vibration in the subcritical region are evaluated. The methodology described in this paper allows obtaining higher damping ratios and provides the smallest difference between the natural vibration frequencies of the shell and the electric circuit, compared to solutions based on the known analytical expressions.