A finite element framework is established to study the nonlinear dynamic instability of stiffened plates subjected to in-plane harmonic patch loading. An eight-noded isoparametric degenerated shell element and a three-noded curved beam element are used to model the skin and the stiffener, respectively. The Green–Lagrange strain displacement relationship is adopted to formulate the system matrices for the plate and the stiffener, adopting the total Lagrangian approach. The Bolotin method is adopted to trace the boundaries of linear dynamic instability region. The Incremental Harmonic Balance (IHB) method is used to investigate the nonlinear instability behavior of stiffened plates. The effect of varying loading patches along with the number of stiffeners in unidirectional ( x-directional and y-directional) and bidirectional ( x as well as y-directional) stiffened plates on the nonlinear frequency response is studied. It is observed that the cross-stiffened plates with the higher number of stiffeners are dynamically more stable than the unidirectional stiffened plates. Moreover, the stiffened plates with smaller loading patches are dynamically more stable than those with larger loading patches.

中文翻译：

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单向和双向加筋复合材料板的谐波面内贴片载荷引起的非线性动态失稳

建立了有限元框架来研究面内谐波贴片载荷作用下加筋板的非线性动态失稳。八节点等参简并壳单元和三节点曲梁单元分别用于对蒙皮和加劲肋进行建模。采用格林-拉格朗日应变位移关系来制定板和加强筋的系统矩阵，采用全拉格朗日方法。采用Bolotin方法追踪线性动态不稳定区域的边界。增量谐波平衡（IHB）方法用于研究加筋板的非线性失稳行为。研究了不同载荷补片以及单向（x 方向和 y 方向）和双向（x 以及 y 方向）加筋板中加劲肋的数量对非线性频率响应的影响。据观察，具有较多加强筋的交叉加强板比单向加强板动态更稳定。此外，具有较小加载补片的加劲板比具有较大加载补片的加劲板动态更稳定。