Abstract
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.
Highlights
For the construction and design of the lightweight systems, the weight saving is one of the major considerations
The solution procedure of active flutter control is divided into two steps, first obtaining the frequency and mode of the plate based on the Rayleigh-Ritz method, in which the boundary support is formulated by the artificial spring
The validity of the equivalent plate theory is verified by Paik tests [1], which gives the elasticity modulus and thickness of plate according to the equal principle of stiffness and density, making the honeycomb sandwich plate equivalent to an isotropic plate
Summary
For the construction and design of the lightweight systems, the weight saving is one of the major considerations. The research on the vibration and flutter problem of the plate structure with general elastic support is rarely found. A UNIFIED GRAM-SCHMIDT-RITZ FORMULATION FOR VIBRATION AND ACTIVE FLUTTER CONTROL ANALYSIS OF HONEYCOMB SANDWICH PLATE WITH GENERAL ELASTIC SUPPORT. The free vibration of composite laminated shells under elastic boundary was studied by Jin [9] using Rayleigh-Ritz procedure, in which the displacements were expressed by a Fourier cosine series and the effects of boundary restraining stiffness on the frequency were illustrated. Lin [13, 14] presented an admissible function to investigate the vibration and flutter problem of laminated plate and FGM cylindrical shells with arbitrary boundaries. The solution procedure of active flutter control is divided into two steps, first obtaining the frequency and mode of the plate based on the Rayleigh-Ritz method, in which the boundary support is formulated by the artificial spring. The effects of displacement feedback gain on the critical dynamic pressure and response are highlighted
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