Vibration response of FG-CNTRC plate resting on non-homogeneous elastic foundation via a closed-form dynamic stiffness formulation

Abstract

In this work, a closed-form dynamic stiffness matrix has been formulated to study the influence of various configurations of non-homogeneous elastic foundation on the free vibration characteristics of carbon nanotube-reinforced functionally graded (FG-CNTRC) plate. The plate kinematic variables are defined based on the first order shear deformation theory. Through the application of Hamilton’s principle, frequency dependent dynamic stiffness (DS) matrix is formulated for a Levy type plate element supported on the Winkler-Pasternak foundation. Appropriate assembly of these DS matrices leads to the formation of global dynamic stiffness matrix, for the non-homogeneously supported plate, which is finally solved using the well-established Wittrick–Williams algorithm to compute the mode shapes and natural frequencies to a desired accuracy. Thus, the present work exploits the applicability of the dynamic stiffness method (DSM) for the free vibration study of the FG-CNTRC plate supported by partial and non-homogeneous elastic foundations. A comparative study is also carried out to ascertain the exactness and the computational efficiency of the dynamic stiffness method. Results from the parametric studies show that the non-homogeneous supports greatly influence the frequency as well as the modeshape of the plate. It is observed that the Pasternak parameter has a profound effect on the response of the plates as compared to that of the Winkler parameter. Effect of different CNT distributions on the frequency behavior are also discussed in detail. It can be emphasized that the new set of DSM computed results reported in the paper for diverse plate configurations may serve as reference results for the future research studies.