Fundamental Frequency of Tapered Plates by Differential Quadrature

Abstract

In this paper, a differential quadrature method is presented for computation of the fundamental frequency of a thin rectangular isotropic elastic plate with variable thickness. In this method, a partial derivative of a function with respect to a space variable at a discrete point is approximated as a weighted linear sum of the function values at all discrete points in the region of that variable. The weighting coefficients are treated as the unknowns. Applying this concept to each partial derivative of the free vibration differential equation of motion of the plate gives a set of linear simultaneous equations, which are solved for the unknown weightage coefficients by accounting for the boundary conditions. The method is used to evaluate the fundamental frequency of linearly tapered plates with simply supported, fully clamped, and mixed boundary conditions. Results are compared with existing solutions available from other analytical and numerical methods. The method presented gives accurate results and is computationally efficient.