Nonlinear dynamic stability analysis of axial impact loaded structures via the nonlocal strain gradient theory

In engineering applications, there has been an overwhelming tendency towards portability, miniaturization, and integration in recent years. To link the intrinsic size dependency feature of the small-scale structure with its structural stability, the nonlocal strain gradient theory, which captures the size effect in a more general size-dependent continuum-based model, is introduced to explore the nonlinear dynamic stability behaviour of nanoplates. Four types of axial impact loading configurations, namely, sinusoidal, exponential, rectangular, and damping, are considered. Some practical factors, such as Winkler-Pasternak elastic foundation and damping, are taken into account in the analysis. The equations of motion for the size-dependent initially imperfect plate are derived in the framework of the first-order shear deformation plate theory in conjunction with the Von Karman nonlinear terms. Then the Airy stress function corresponding to simply supported nanoplate is introduced; then, by applying the Galerkin method, the obtained differential equations are addressed by the fourth-order Runge-Kutta algorithm. Subsequently, the specific value of the critical dynamic buckling load is determined by the Volmir criterion. Organic solar cells (OSCs), a type of emerging solar-to-electrical energy conversion nanodevice, are used as an illustrative example within the existing framework. The effects of size dependency in conjunction with the pulse load configuration, the initial imperfection, the elastic foundation, as well as the damping ratio on the nonlinear dynamic buckling behaviour of the OSC are thoroughly investigated. (c) 2022 Elsevier Inc. All rights reserved.