Free vibration of sigmoid functionally graded plates using the dynamic stiffness method and the Wittrick-Williams algorithm

Abstract

In this paper, the free vibration characteristics of Sigmoid Functionally Graded Material (S-FGM) Levy-type plates are investigated by developing the Dynamic Stiffness Method (DSM) through the application of the Wittrick-Williams algorithm, as solution technique. Kirchoff-Love Plate Theory (KLPT) and Hamilton principle are utilised to derive the governing equation of motion and associated natural boundary conditions. Based on two power-law distribution functions, the material properties are gradually varied along the thickness direction. Using the proposed theory, a substantial number of numerical examples showing the natural vibration characteristics of plates made of sigmoid functionally graded material are illustrated to demonstrate the accuracy of the method. Some numerical results are compared with published results and found to be in excellent agreement. An extensive investigation is carried out and the results are examined and discussed in detail. The variations of material properties such as the Young’s modulus ratio and density ratio are seen to affect the natural frequencies of S-FGM plates significantly. The proposed method is not only accurate but also, quite simple and straightforward to compute the natural frequencies and mode shapes of S-FGM plates. The results presented can be used as benchmark solution for further investigation of FGM plates.