Free Vibration of Tapered Mindlin Plates Using Basic Displacement Functions

Introducing the concept of basic displacement functions (BDFs) in plate elements, a novel method is proposed to calculate new shape functions of tapered Mindlin plates for the free vibration analysis using BDFs. The BDFs are obtained from dynamic deformations of an arbitrary point in tapered Mindlin plate using Ritz method and substituting boundary equations of Clamped–Clamped–Free–Free plate in them. It is shown that exact shape functions and consequently structural matrices could be derived from BDFs. Unlike current shape functions used in FE method, the new shape functions take thickness variation and eigenfrequencies of the plates into account. So, higher accuracy and more rapid convergence could be expected with fewer elements. To verify the competency of the present shape functions, the results of several numerical examples are compared with those in the literature. It is shown that these shape functions derived from BDFs have quite satisfactory accuracy and low computational cost.