Analysis of free vibration characteristics of porous rectangular plates with variable thickness

Porous solid structures have attracted much attention because they are widely used in national defense, military industry, machinery, civil engineering and other fields. In this paper, the problem of free vibration of a porous rectangular plate with variable thickness is investigated. Firstly, given the two distribution modes of the porous rectangular plate along the thickness direction, the dimensionless governing differential equations for the free vibration of the porous rectangular plate are derived using the classical plate theory and the Hamiltonian variational principle. Then, the dimensionless governing differential equations of motion and boundary conditions are derived by converting them into algebraic equations through the differential transformation method (DTM). The dimensionless natural frequencies of the porous rectangular plate are solved by iterative convergence method through MATLAB programming. Finally, numerical examples are given to analyze the influence of different parameters on the vibration frequency of porous rectangular plates with different porosity distributions under different boundary conditions. Numerical examples show that the method has fast convergence speed and high accuracy. In addition, some novel results are presented in this paper, which can be used for reference in the following research on the vibration mechanical behavior of graded porous rectangular plates with variable thickness.