Purpose

Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates mostly undergo a variety of dynamic loads, which may sometimes result in large-amplitude vibration. Additionally, initial stresses and geometric imperfections are widespread in this type of structure. Furthermore, it is universally known that initial stresses and geometric imperfections may affect mechanical behavior of structures severely, particularly in dynamic analysis. Thus, the purpose of this paper is to study the stress variation rule of a stiffened plate during large-amplitude vibration considering initial stresses and geometric imperfections.

Design/methodology/approach

The initial stresses are represented in the form of initial bending moments applying to the stiffened plate, while the initial geometric imperfections are considered by means of trigonometric series, and they are assumed existing in the plate along the z-direction exclusively. Then, the dynamic equilibrium equations of the stiffened plate are established using Lagrange’s equation as well as aforementioned conditions. The nonlinear differential equations of motion are simplified as a two-degree-of-freedom system by considering 1:2 and 1:3 internal resonances, respectively, and the multiscale method is applied to solve the equations.

Findings

The influence of initial stresses on the plate, stresses during internal resonance is remarkable, while that is moderate for initial geometric imperfections. (Upon considering the existence of initial stresses or geometric imperfections, the stresses of motivated modes are less than the primary mode for both and internal resonances). The influence of bidirectional initial stresses on the plate’s stresses during internal resonance is more remarkable than that of unidirectional initial stresses. The coupled vibration in 1%3A2 internal resonance is fiercer than that in internal resonance.

Originality/value

Stiffened plates are widely used in engineering structures. However, as a type of thin-walled structure, stiffened plates vibrate with large amplitude in most cases owning to their complicated operation circumstance. In addition, stiffened plates usually contain initial stresses and geometric imperfections, which may result in the variation of their mechanical behavior, especially dynamical behavior. Based on the above consideration, this paper studies the nonlinear dynamical behavior of stiffened plates with initial stresses and geometrical imperfections under different internal resonances, which is the originality of this work. Furthermore, the research findings can provide references for engineering design and application.

中文翻译：

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考虑不同共振条件的具有初始应力和几何缺陷的加筋板非线性振动的动态应力分析

目的

加筋板已广泛用于土木，海洋，航空航天工程中。作为一种在复杂环境中运行的薄壁结构，加劲板通常会承受各种动态载荷，有时可能会导致大振幅振动。另外，初始应力和几何缺陷在这种类型的结构中很普遍。此外，众所周知，初始应力和几何缺陷会严重影响结构的机械性能，特别是在动态分析中。因此，本文的目的是研究考虑初始应力和几何缺陷的大振幅振动过程中加劲板的应力变化规律。

设计/方法/方法

初始应力以施加到加劲板上的初始弯矩的形式表示，而初始几何缺陷是通过三角级数考虑的，并且假定它们仅沿z方向存在于板中。然后，利用拉格朗日方程和上述条件建立加劲板的动平衡方程。通过分别考虑1：2和1：3内部共振，将非线性非线性运动方程简化为两自由度系统，并应用多尺度方法求解这些方程。

发现

初始应力对板的影响，内部共振时的应力是显着的，而对于初始几何缺陷来说是中等的。（考虑到初始应力或几何缺陷的存在，对于内部共振和内部共振，激励模式的应力都小于主要模式）。在内部共振期间，双向初始应力对板应力的影响比单向初始应力的影响更为显着。1％3A2内部共振的耦合振动比内部共振的耦合振动更剧烈。

创意/价值

加筋板广泛用于工程结构。然而，作为薄壁结构的一种类型，由于操作环境复杂，加劲板在大多数情况下振动幅度大。此外，加劲板通常会包含初始应力和几何缺陷，这可能会导致其机械行为（尤其是动力学行为）发生变化。基于上述考虑，本文研究了在不同内部共振条件下具有初始应力和几何缺陷的加筋板的非线性动力学行为，这是这项工作的独创性。此外，研究成果可为工程设计和应用提供参考。