Application of dynamic stiffness method for accurate free vibration analysis of sigmoid and exponential functionally graded rectangular plates. (November 2019) - Kumar, Subodh; Jana, Prasun
Highlights: The dynamic stiffness method is applied for the free vibration analysis of FGM plates with sigmoid and exponential property variations. The dynamic stiffness matrix is developed by obtaining a closed form (Levy type) solution of the governing differential equation. Through the application of Wittrick-Williams algorithm, accurate natural frequencies are computed by ensuring that no frequencies are missed within a range of frequencies of the plate. For the first time in the literature, free vibration behaviour of stepped thickness FGM plates are studied. New sets of accurate frequency results for the FGM plates are reported which can be referred as benchmark results for comparison purposes in the future. Abstract: In this work, the dynamic stiffness method (DSM) is implemented to investigate free vibration behaviour of thin rectangular functionally graded material (FGM) plate with the sigmoid (S-FGM) and exponential (E-FGM) property variations along its thickness direction. Both uniform and stepped thickness FGM plates are considered in this study. Classical plate theory in conjunction with the physical neutral surface of the FGM plate is utilized to obtain the governing differential equation of motion including the effect of rotary inertia. Considering Levy type plates, the dynamic stiffness matrix is developed through the application of displacement and force boundary conditions at the appropriate edges. The well-known Wittrick-Williams algorithm is employed to solve this dynamic stiffness matrix in order to compute the natural frequencies of the plate with reasonably high accuracy. It is shown upon comparison with the existing literature that the DSM frequency results are most accurate and can be referred to judge the accuracy of several other numerical solutions applied to thin S-FGM and E-FGM plates. This study also highlights some insufficiently accurate published results and points out the possible reasons for this inaccuracy. Finally, this study reports a set of new results by changing different plate parameters which will be useful in the design of both uniform and stepped FGM plates under considerations. Graphical abstract: Image, graphical abstract