Nonlinear Frequency Responses of Functionally Graded Carbon Nanotube-Reinforced Sandwich Curved Panel Under Uniform Temperature Field

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Abstract
The higher-order kinematic theory in conjunction with Green–Lagrange strain field has been incorporated to compute the nonlinear frequency parameter of the curved (single/doubly) graded (functionally) sandwich panel structure numerically via finite element technique. The current sandwich panel model is derived assuming the functionally graded carbon nanotube face sheets and isotropic (epoxy) core. The current mathematical model is generic in nature, i.e., the grading configurations of the face sheets and sandwich construction including the different geometrical shapes can be achieved easily. The governing equation of the sandwich structure is obtained and the subsequent weak form derived with the help of the isoparametric finite element method. The nonlinear solutions are computed via an original computer code using a robust numerical method (direct iterative method). The consistency and the accuracy of the current finite element solutions are established by executing different types of numerical examples. Also, the concurrence of current numerical solution is established by comparing the results with the available benchmark solutions. Finally, the effect of various design parameters on the nonlinear natural frequency values have been computed under the uniform temperature environment and the inferences provided in detail.

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