This paper investigates the dynamic snap-through buckling of classical and non-classical curved beams subjected to a suddenly applied step load. The small scale effect prevalent in non-classical beams, viz, micro and nanobeam, is modeled using the nonlocal elasticity approach. The formulation accounts for moderately large deflection and rotation. The governing equilibrium equations are derived using the dynamic version of the principle of virtual work and are subsequently simplified in terms of the generalized displacements for the development of a nonlocal nonlinear finite element model. The spatial domain comprises of 3-noded higher-order curved beam elements based on shear flexible theory associated with sine function. The nonlinear governing equations are solved using the incremental stiffness matrices and by adopting direct time integration method. The critical dynamic buckling load is identified by the smallest load at which there is a sudden rise in the amplitude of vibration. The efficacy of model here is compared against the available analytical studies for the local and nonlocal beams. A detailed study is made to highlight the effects of the geometric parameter, initial condition, nonlocal parameter, load duration, and boundary conditions on the dynamic stability of both classical and non-classical curved beams. The nature and degree of participation of various eigen modes accountable for the dynamic snap-through behavior are examined a posteriori using the modal expansion approach. Some interesting observations made here are valuable for the optimal design of such structural members against fatigue and instability.

本文研究了承受突然施加的阶跃载荷的经典和非经典弯曲梁的动态捕捉屈曲。小尺度效应普遍存在于非经典光束中，即使用非局部弹性方法对微米束和纳米束进行建模。该公式说明了较大的偏转和旋转。控制平衡方程是使用虚拟功原理的动态形式导出的，随后根据用于生成非局部非线性有限元模型的广义位移进行了简化。空间域由基于与正弦函数相关的剪切挠性理论的3节点高阶弯曲梁单元组成。使用增量刚度矩阵并采用直接时间积分方法来求解非线性控制方程。临界动态屈曲载荷由振动振幅突然升高的最小载荷确定。将模型的功效与本地和非本地光束的可用分析研究进行比较。进行了详细的研究，以突出几何参数，初始条件，非局部参数，载荷持续时间和边界条件对经典和非经典弯曲梁的动力稳定性的影响。检查负责动态捕捉行为的各种本征模式的性质和参与程度使用模态展开方法的后验。此处所做的一些有趣的观察对于此类结构构件抗疲劳和不稳定性的最佳设计非常有价值。