Vibrational characteristics of a FG-GPLRC viscoelastic thick annular plate using fourth-order Runge-Kutta and GDQ methods

This is the first research on the vibrational analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) viscoelastic annular plate within the framework of higher order shear deformation theory (HSDT). Hamilton's principle is employed to establish governing equations of motion within the framework of HSDT. In this article, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Generalized differential quadrature method is applied to obtain numerical solution. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of viscoelasticity coefficient, weight fraction, boundary conditions, and distribution patterns of GPLs on the frequency response of the structure. The results revealed that applying locating more square shaped GPLs in the vicinity of the top and bottom surface results into the highest natural frequency. Another important consequence is that FG-GPLRC structure with FG-V, FG-A, and UD patterns have similar effect on the natural frequency of the GPLRC annular plate while FG-X has the best stability and natural frequency. A useful suggestion of this research is that, increasing the value of the length to thickness ratio of GPL not only decreases the central deflection of the structure through time, but also causes to decrease real time domain changes for the FG-GPLRC viscoelastic annular plate.