A unified Gram-Schmidt-Ritz formulation for vibration and active flutter control analysis of honeycomb sandwich plate with general elastic support

An admissible function constructed by orthogonal polynomials is presented to investigate the vibration and active flutter control of Honeycomb sandwich plate with general elastic support in a supersonic airflow. The control strategies based on the displacement feedback and LQR method are applied by means of pasting the piezoelectric material on the surface of the plate structure. Employing the first-order piston theory to describe the aerodynamic loads, the governing equation of plate system with the piezoelectric actuator is established based on the Hamilton principle. The mode shapes are obtained using the admissible functions, which are a set of characteristic orthogonal polynomials generated directly by employing the Gram-Schmidt process, and the general elastic constraint is modeled using the artificial spring technology. The frequency and mode shape under different boundary are calculated by Rayleigh-Ritz method. The validity of the proposed approach is confirmed by comparing the results with those obtained from FEM and literatures. The phenomenon of mode jumping is observed with the increase of the aerodynamic pressure. The study of active control shows that, the increasement of displacement feedback gain improves the critical dynamic pressure.