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.

在本文中，浅层夹层板被认为是由富含纳米复合材料的面板和拉胀蜂窝芯制成的，因此其泊松比为负。为了评估这种夹层板的几何非线性动态行为，考虑了各种周期性和脉冲载荷。为了求解控制非线性微分方程组，基于 Galerkin 方法进行了一种分析方法，该方法产生了一个封闭形式的运动微分方程，该方程通过四阶 Runge-Kutta 方法概念进行了数值求解。通过比较与一些特殊示例相关的结果与参考文献中其他分析和数值方法获得的相关结果，验证了所提出的分析方法的精度。验证实例的结果表明，与先前发表的论文的结果相比，所提出的方法产生的结果误差小于2%。在广泛的数值研究框架内，还评估了不同几何和机械参数对所提出的夹层板承受各种脉冲和周期性压力的动态非线性响应的影响。数值研究表明，通过使用所提出的方法，可以在不进行耗时计算的情况下对所提出的面板进行非线性动态分析。在广泛的数值研究框架内，还评估了不同几何和机械参数对所提出的夹层板承受各种脉冲和周期性压力的动态非线性响应的影响。数值研究表明，通过使用所提出的方法，可以在不进行耗时计算的情况下对所提出的面板进行非线性动态分析。在广泛的数值研究框架内，还评估了不同几何和机械参数对所提出的夹层板承受各种脉冲和周期性压力的动态非线性响应的影响。数值研究表明，通过使用所提出的方法，可以在不进行耗时计算的情况下对所提出的面板进行非线性动态分析。