This study presents a semi-analytical solution of the nonlinear dynamic response, shock spectrum, and dynamic buckling of a simply supported imperfect plate under various types of in-plane pulse forces. Here, the plate is modelled based on higher-order shear deformation theory (HSDT) considering the von-Kármán geometric nonlinearity. The governing nonlinear partial differential equations (NLPDEs) of the imperfect plates are developed via Hamilton’s principle. Using Galerkin’s method, the NLPDEs are converted into sets of nonlinear algebraic equations (NLAEs) for static stability problems and nonlinear ordinary differential equations (NLODEs) for dynamic problems. The critical buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the plate is evaluated using nonlinear static stability analysis based on the yield stress failure criterion. The dynamic response and shock spectrum of the plates are plotted via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the yield stress failure criterion. Dynamic load factor (DLF) is the ratio of dynamic failure load to static failure load. Based on the pulse duration time, the pulse forces are divided into three categories known as impulsive, dynamic, and quasi-static. In the case of impulsive, dynamic, and quasi-static loading regimes, DLF > 1, DLF < 1, and DLF \(\approx\) 1, respectively. The results obtained from the current works will help in the appropriate design of the imperfect plates against dynamic buckling.

这项研究提出了在各种类型的平面内脉冲力作用下，简单支撑的非理想板的非线性动力响应，冲击谱和动态屈曲的半解析解。在这里，考虑到von-Kármán几何非线性，基于高阶剪切变形理论（HSDT）对板进行建模。不完全板的控制非线性偏微分方程（NLPDEs）是根据汉密尔顿原理建立的。使用Galerkin方法，将NLPDE转换为针对静态稳定性问题的非线性代数方程组（NLAE）和针对动态问题的非线性常微分方程组（NLODE）。板的临界屈曲载荷是通过相关的特征值问题获得的。基于屈服应力破坏准则，使用非线性静态稳定性分析评估板的静态破坏载荷。板的动态响应和冲击光谱是通过Newmark方法绘制的。基于屈服应力破坏准则，使用Newmark方法评估板的动态破坏载荷。动态负载因子（DLF）是动态故障负载与静态故障负载的比率。根据脉冲持续时间，将脉冲力分为三类，即脉冲，动态和准静态。在脉冲，动态和准静态载荷情况下，DLF> 1，DLF <1，DLF 基于屈服应力破坏准则，使用Newmark方法评估板的动态破坏载荷。动态负载因子（DLF）是动态故障负载与静态故障负载的比率。根据脉冲持续时间，将脉冲力分为三类，即脉冲，动态和准静态。在脉冲，动态和准静态载荷情况下，DLF> 1，DLF <1，DLF 基于屈服应力破坏准则，使用Newmark方法评估板的动态破坏载荷。动态负载因子（DLF）是动态故障负载与静态故障负载的比率。根据脉冲持续时间，将脉冲力分为三类，即脉冲，动态和准静态。在脉冲，动态和准静态载荷情况下，DLF> 1，DLF <1，DLF\（\ approx \） 1。从当前工作中获得的结果将有助于对不完善的板进行适当的设计以防止动态屈曲。