In this paper the shallow sandwich panels are considered to be made of the nanocomposite enriched face-sheets and the auxetic honeycomb core so that its Poisson's ratio is negative. In order to evaluate the geometrical nonlinear dynamic behavior of such sandwich panels, various periodic and impulsive loadings are considered. For the sake of solving the governing nonlinear differential equations system, an analytical approach on the basis of the Galerkin method is conducted which yields a closed form differential equation of motion which is numerically solved by the fourth-order Runge–Kutta method concept. The precision of the proposed analytical method is approved using comparison of the results related to some special examples and the relevant ones achieved by the other analytical and numerical methods in the references. The results of verification examples showed that the proposed method yields to the results with errors of less than 2% comparing to the results of previously published papers. The influences of different geometrical and mechanical parameters on the dynamic nonlinear responses of the proposed sandwich panels undergoing the various impulsive and periodic pressures are also evaluated in the framework of wide range of numerical study. The numerical studies revealed that by using the proposed method, performing the nonlinear dynamic analysis of the proposed panels without time-consuming computations is possible.
