پرویز ملک زاده

The nonlinear free vibration of sandwich skew plates with auxetic core and multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) face sheets supported by elastic point supports using a meshfree radial point interpolation method (RPIM). The nonlinear motion equations are developed based on the higher-order shear deformation theory (HSDT) in conjunction with von K´arma´ n geometric nonlinearity assumptions. The harmonic balance method and the direct iteration technique are employed to carry out the variations of nonlinear frequencies against the plate vibration amplitude. The approach is validated by displaying its convergence rate and comparing the obtained solutions with those reported in literature in the limit cases. Subsequently, the impact of point support stiffness, different GPLs distribution patterns of the face sheets and auxetic core layer parameters on the nonlinear to linear frequency ratios of the sandwich skew plates with auxetic core and FG-GPLRC face sheets are carried out. The results show that a fundamental interaction between the linear and nonlinear vibrational modes is observed. As an observable phenomenon, a “mode redistribution” or “sudden decrease of non-linear stiffness” is found when the fundamental nonlinear frequency approach to the second linear frequency a mode redistribution is occurred.