Vibrational frequencies of FG-GPLRC viscoelastic rectangular plate subjected to different temperature loadings based on higher-order shear deformation theory and utilizing GDQ procedure

In this study, the effect of nonlinear temperature gradient on the natural frequencies of functionally graded graphene platelets reinforced composite (FG-GPLRC) viscoelastic plate embedded in the visco-Pasternak foundation is examined on the basis of higher-order shear deformation theory (HSDT) numerically and analytically. By performing Hamilton's principle, the governing equations of the system are obtained. And also, the viscoelastic properties of the structure are modeled based on the appropriate Kelvin-Voigt viscoelasticity model. Afterward, the deflection problem of the system as a function of time is solved according to the fourth-order Runge-Kutta numerical manner. Also, in order to obtain the numerical results, the generalized differential quadrature method (GDQM) is applied as a high accuracy numerical method. For validation, the calculated numerical results are compared with those reported in the engineering literature. Furthermore, to demonstrate the effects of various parameters on the response of the system, such as various patterns of temperature rise, the stiffness of the foundation, damper, and viscoelasticity constants, weight fraction, and distribution patterns of GPLs, a comprehensive parametric study is done. According to the results, an increment in the temperature difference leads to an increase in the absolute value of sensitivity for various distributions of temperature. Ascending the nonlinearity of the temperature distribution soars the rigidity of the system; consequently, contrary to the dimensionless vibrational frequency lessens the transverse displacement of the structure.