The article entitled “Mathematical modeling and solution of nonlinear vibration problem of laminated plates with CNT originating layers interacting with two-parameter elastic foundation” based on the studies conducted by Department of Mathematics members Prof. Dr. Semra Ahmetolan and her PHD student, Mahmure Avey, was published in the Journal of the Brazilian Society of Mechanical Sciences and Engineering.

This study extends the first-order shear deformation plate theory (FOPT) proposed by Ambartsumyan to heterogeneous laminated nanocomposite plates, addressing the nonlinear vibration problem analytically and incorporating an elastic medium. The Pasternak-type elastic foundation model (PT-EF) is utilized as the elastic medium model. Mathematical models for laminated rectangular plates with CNT originating layers on the PT-EF are established, and the stress-strain relationships and motion equations are derived as nonlinear partial differential equations (PDEs) within FOPT. Through the application of Galerkin's method, these equations are reduced to a nonlinear ordinary differential equation (NL-ODE) that includes second- and third-order nonlinear terms. The NL-ODE is solved using the semi-inverse method, yielding a nonlinear frequency-amplitude relationship for laminated plates with CNT originating layers on the PT-EF within FOPT. Numerical analyses are conducted to compare the accuracy of the obtained formulas with existing literature results.

https://link.springer.com/article/10.1007/s40430-023-04016-0