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Global/local analytical and numerical free vibration analysis of sandwich columns

机译：三明治柱的全球/局部分析和数值自由振动分析

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摘要

Sandwich structures are increasingly applied in many industrial fields of application, due to their lightweight combined with favorable mechanical properties. Despite this, such structures are subject to specific failure modes, such as buckling or vibratory resonance. In both cases, due to the presence of thin and stiff skins, global but also local modes may be of great interest when dimensioning such composite structures, which makes it impossible to use classical models. In this paper, the free vibration problem of classical sandwich columns (with homogeneous core materials) is investigated, using special kinematic models, so as to deal with both global and local eigenmodes in an effective and precise way. First, the problem is addressed analytically, where the two faces are represented by Euler-Bernoulli beams and the core material is considered as a 2D continuous solid, in small strain elasticity. Then, an enriched 1D finite element formulation is developed, so as to handle efficiently more general configurations encountered in practice. The homogeneous core layer is here described using hyperbolic functions, in accordance with the modal displacement fields obtained analytically. The present analytical and numerical solutions (natural frequencies and vibration modes) are contrasted against each other and compared to 2D reference numerical results.
机译：夹层结构越来越多地应用于许多工业应用领域，因为它们的轻质与有利的机械性能相结合。尽管如此，这种结构受特定的故障模式，例如屈曲或振动共振。在这两种情况下，由于存在薄且僵硬的皮肤，全局但也可能在尺寸尺寸方面可能具有很大的兴趣，这使得不可能使用经典模型。在本文中，研究了特殊运动学模型的古典夹心柱（具有均匀核心材料）的自由振动问题，以便以有效和精确的方式处理全球和局部特征模。首先，在分析上解决问题，其中两个面由Euler-Bernoulli光束表示，并且芯材被认为是2D连续固体，其小应变弹性。然后，开发了富集的1D有限元制剂，以便在实践中有效地处理更大的一般配置。根据分析获得的模态位移场，使用双曲函数描述均匀核心层。本分析和数值解决方案（自然频率和振动模式）相互置向，并与2D参考数值结果相比。

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