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A unified three-dimensional method for vibration analysis of the frequency-dependent sandwich shallow shells with general boundary conditions

机译:具有一般边界条件的频率相关夹层浅壳振动的统一三维方法

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In this paper, we present an accurate three-dimensional formulation for the vibrations of the laminated and sandwich shallow shells. The sandwich structure is characterized by a thick viscoelastic core and two thin composite faces. Frequency dependent viscoelastic models are introduced in the sandwiches. Without any change in solution procedure, the formulation makes it quite easy to change the boundary conditions. The solution can be obtained by means of Rayleigh–Ritz process combined with the three-dimensional modified Fourier series which are actually assumed displacement functions. These functions, without need to meet the boundary conditions in advance, take the form of the three-dimensional Fourier series with several closed-form auxiliary functions which are supplemented to deal with the discontinuities at the boundaries in terms of displacements and its derivatives. Besides, only three assumed displacement variables are employed in the formulation which effectively reduces the computation cost. The reliability and accuracy of the method are demonstrated by numerical comparisons and examples with the constant viscoelastic models as well as the frequency dependent ones. Modal analysis and parametric studies are conducted to examine the influences of the boundary condition, dimension, lamination scheme, temperature and frequency dependence of the materials.
机译:在本文中,我们为层压和夹层浅壳的振动提供了精确的三维公式。夹层结构的特征是厚的粘弹性芯和两个薄的复合面。三明治中引入了频率相关的粘弹性模型。在求解过程中无需任何更改,该公式使更改边界条件变得非常容易。可以通过将Rayleigh-Ritz过程与三维修改的Fourier级数相结合来获得该解,这实际上是假定的位移函数。这些函数不需要预先满足边界条件,而是采用三维傅里叶级数的形式,并带有几个封闭形式的辅助函数,这些函数被补充以处理位移及其导数方面的边界处的不连续性。此外,公式中仅采用了三个假设的位移变量,有效地降低了计算成本。通过数值比较和实例,恒定粘弹性模型以及频率相关模型,证明了该方法的可靠性和准确性。进行了模态分析和参数研究,以检查材料的边界条件,尺寸,层压方案,温度和频率依赖性的影响。

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