Free Vibration of Rectangular Plates with Porosity Distributions under Complex Boundary Constraints

Free vibration of rectangular plates with three kinds of porosity distributions and different boundary constraints has been performed by means of a semianalytical method. The distribution of porous varies along the thickness of the plate, in which the mechanical properties are defined by open-cell metal foam. Regardless of boundary conditions, displacement admissible functions are represented by combination of standard cosine Fourier series and auxiliary sine series. The kinetic energy and potential energy of plates are also expressed on the basis of first-order shear deformation theory (FSDT) and displacement admissible functions. Finally, the coefficients in the Fourier series which determine natural frequencies and modal shape are derived by means of the Rayleigh-Ritz method. Convergence and dependability of the current method are verified by comparing with the results of FEM and related literatures. In addition, some new results considering geometry parameters under classical and elastic boundary constraints are listed. The effects of geometry parameters, material parameters, and boundary constraints have been discussed in detail.