Free vibration characteristics of concentric stiffened rectangular plates determined based on spectral Tchebyshev technique

Abstract

In this paper, a two-dimensional spectral Tchebyshev (2D-ST) technique is developed to solve the free vibration problem of the concentric stiffened rectangular plate (CSRP) under arbitrary boundary conditions. According to this technique, the variables of the x and y axes are all selected Gauss-Lobatto sampling points for discretization, while the Tchebyshev polynomials are used to perform spectral expansion on the displacement functions of the structure. The CSRP is regarded as a coupling connection of ribs and plates of different thicknesses. By setting artificial springs to deal with the continuity and arbitrary boundary requirements, the unified fundamental differential equations of CSRP are derived from the combined framework of first-order shear deformation theory (FSDT) and Hamilton's principle. The free vibration characteristic equations in matrix form of CSRP are obtained by solving the differential equation, and the convergence of the solution is evaluated. Based on the comparison of various calculation examples with other methods and experiment, it is fully proved that the present solution has the advantages of fast convergence speed and high solution accuracy. Finally, this paper further focuses on how the geometric parameters of ribs influence the free vibration characteristics of the CSRP to implement the parametric studies.