Modeling, analysis, and control of MFC sandwiched laminate panel flutter with general layups and arbitrary boundary conditions

In this paper, a new solution approach based on Lagrange multipliers is developed for aeroelastic panel flutter analysis of rectangular composite plates sandwiched by two Macro Fiber Composites (MFCs). The smart panel has general stacking sequences and subjected to the elastic edge restraints. By utilizing the assumed mode technique, the displacements and electric potentials are expanded using formerly determined mode shapes. Afterward, the potential and kinetic energies of the problem are achieved and by employing the Lagrange equation, the discretized equations of the motion are obtained. The supersonic aerodynamic load is modeled through the well-known piston theory and included within the equations by means of the non-conservative force term of the Lagrange equation. Deriving the equations is more simplified thanks to the orthogonality of the Legendre polynomials. Finally, the input voltage of the MFC actuator is determined through the proportional or velocity feedback control algorithms based on the sensor output. The capability and credibility of the proposed approach are confirmed by comparing the results with those achieved by the FEM. The method is used to investigate the effects of MFCs orientations on the panel flutter boundaries of smart plates.