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Coupled Vibrations of Viscoelastic Three-Layer Composite Plates. 2. Numerical Experiments
Vestnik St. Petersburg University, Mathematics Pub Date : 2021-03-16 , DOI: 10.1134/s106345412101009x
V. M. Ryabov , B. A. Yartsev , L. V. Parshina

Abstract

The results of the numerical studies of the influence of the reinforcement orientation of rigid layers and relative thickness of a soft isotropic viscoelastic polymer layer on the values of natural frequencies and loss factors of the coupled vibrations of symmetric and asymmetric unsupported three-layer rectangular composite plates are discussed. It is shown that in a symmetric three-layer plate, a flexural and torsion interaction arises generating mutual transformations of the natural forms of the coupled vibration modes if at least one of its natural forms in the plate directions is characterized by an even number of quarter-wavelengths, and another natural form is characterized by an odd number of quarter-wavelengths. A flexural–flexural interaction arises in an asymmetric unsupported three-layer plate and generates mutual transformations of the natural forms of coupled vibration modes in two mutually orthogonal planes if both natural forms are characterized by either an even or an odd number of quarter-wavelengths in the main directions of the plate. It has been found that each mode of the natural vibrations of the three-layer plates corresponds to the effective relative thickness of the soft isotropic viscoelastic polymer layer.



中文翻译:

粘弹性三层复合板的耦合振动。2.数值实验

摘要

刚性层的增强方向和软的各向同性粘弹性聚合物层的相对厚度对对称和不对称无支撑三层矩形复合板耦合振动的固有频率和损耗因子的影响的数值研究结果讨论。结果表明,在对称的三层板中,如果至少一种在板方向上的自然形式的特征是偶数个四分之一,那么就会产生挠曲和扭转相互作用,从而产生耦合振动模态的自然形式的相互转换。 -波长,另一自然形式的特征是奇数个四分之一波长。挠曲-挠曲相互作用在不对称的无支撑三层板中产生,并且如果两个自然形式的特征是偶数或奇数个四分之一波长的特征,则会在两个相互正交的平面中产生耦合振动模式的自然形式的相互转换。板的主要方向。已经发现,三层板的固有振动的每种模式对应于软的各向同性粘弹性聚合物层的有效相对厚度。

更新日期:2021-03-16
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