Flutter characteristics and free vibrations of rectangular functionally graded porous plates

This paper investigates the flutter characteristics and free vibrations of porous functionally graded plates using the analytical and Rayleigh-Ritz methods. The analytical methods can be employed for the solution of six of 21 arbitrary boundary conditions (the combinations of clamped, simply supported and free). The influence of five various models of porosity is studied, including different variations of stiffness/density along the thickness and/or length of a plate. The analysis is carried out for the classical (CPT) and first order transverse shear deformation (FSDT) theory. For CPT analytical solutions the effects of porosity are characterized by two simple correction factors that shows a very good agreement with the numerical Rayleigh-Ritz method. Parametric studies illustrate the possibility of increasing natural frequencies as well as flutter critical aerodynamic pressures and the necessity of implementing the optimization techniques to find the best solutions from the engineering point of view. The solutions are valid for thin and moderately thick porous FGM plates although the proposed methodology of computations can be easily adopted to the application of different approximations of 2D displacement distributions (see Appendix).