Effects of the impactor geometrical shape on the non-linear low-velocity impact response of sandwich plate with CNTRC face sheets

In this study, non-linear low-velocity impact response of a simply supported sandwich plate with CNTRC face sheets subjected to the impactors with different geometrical shapes is investigated. It has been assumed that the sandwich plate is made up of two face sheets reinforced with CNTs graded along their thickness as X profile and a homogeneous core. In CNT-reinforced layers, a micromechanical model has been used to obtain the effective material properties and the analysis is performed in the framework of the Reddy's higher order shear deformation theory with regard to thermal effects. An analytical model is proposed to capture the response performance of the three-layer sandwich plates under different thermal environments. Through the proposed analytical study, in order to characterize the contact force between the sandwich plate and the impactors, the modified Hertz contact law is utilized. Rayleigh-Ritz method is applied to the Hamilton principle in order to find the set of equations of motion for the impactor as well as the CNTRC sandwich plate. Afterwards, the solution in the time domain is obtained based on Newmark's numerical time integration scheme. After validating the proposed approach, in order to examine the influences of various involved parameters, different parametric studies are conducted. It has been demonstrated that the variation of the initial kinetic energy as one of the parameters under study has a significant effect on the central displacement, contact force, and indentation in both conical and cylindrical impactors and the change in the radius of the cylinder has an insignificant effect on the central displacement. As well, in the case of equal masses, the cylindrical impactor causes more amount of indentation with respect to conical.