Nonlinear Thermal Effect on Free Vibration of FG Rectangular Mindlin Nanoplate of Bilinearly Varying Thickness Via Eringen's Nonlocal Theory

Purpose The present paper studies the effect of nonlinear temperature profile across the thickness on free vibration of functionally graded nonuniform rectangular Mindlin nanoplate using Eringen's nonlocal theory. The nonuniformity in the cross-section of the plate is assumed to arise due to bilinear variation of thickness. The mechanical properties of plate material are taken to be temperature-dependent and graded in thickness direction according to a power-law function. Methods The governing equations of motion for the present model have been derived using Hamilton's energy principle. The frequency equations for three different combinations of clamped and simply-supported boundary conditions have been obtained employing the generalized differential quadrature method. The frequency equations have been solved numerically for frequency parameter in the first three modes of vibration using software MATLAB. Results It results show that stiffness of the plate increases with increasing values of slenderness ratio, aspect ratio while decreases with increasing values of temperature difference. Further, the plate's stiffness increases as plate changes from thinner to thicker at the outer edges. Three-dimensional plate configurations have also been plotted. Conclusion It has been observed that the cross-sectional nonuniformity has significant effects on the temperature-dependent vibration characteristics of functionally graded nanoplate which is considerably affected by other plate parameters.