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Vibration Analysis of Piezoelectric Kirchhoff-Love Shells based on Catmull-Clark Subdivision Surfaces
arXiv - CS - Computational Engineering, Finance, and Science Pub Date : 2021-05-06 , DOI: arxiv-2105.09288
Zhaowei Liu, Andrew McBride, Prashant Saxena, Luca Heltai, Yilin Qu, Paul Steinmann

An isogeometric Galerkin approach for analysing the free vibrations of piezoelectric shells is presented. The shell kinematics is specialised to infinitesimal deformations and follow the Kirchhoff-Love hypothesis. Both the geometry and physical fields are discretised using Catmull-Clark subdivision bases. It provides the required C1 continuous discretisation for the Kirchhoff-Love theory. The crystalline structure of piezoelectric materials is described using an anisotropic constitutive relation. Hamilton's variational principle is applied to the dynamic analysis to derive the weak form of the governing equations. The coupled eigenvalue problem is formulated by considering the problem of harmonic vibration in the absence of external load. The formulation for the purely elastic case is verified using a spherical thin shell benchmark. Thereafter, the piezoelectric effect and vibration modes of a transverse isotropic curved plate are analysed and evaluated for the Scordelis-Lo roof problem. Finally, the eigenvalue analysis of a CAD model of a piezoelectric speaker shell structure showcases the ability of the proposed method to handle complex geometries.

中文翻译:

基于Catmull-Clark细分曲面的压电基尔霍夫-洛夫壳的振动分析

提出了一种等几何Galerkin方法,用于分析压电壳体的自由振动。壳运动学专门研究微小变形,并遵循基尔霍夫-洛夫(Kirchhoff-Love)假设。几何和物理场都使用Catmull-Clark细分基进行离散。它为Kirchhoff-Love理论提供了所需的C1连续离散化。使用各向异性本构关系描述压电材料的晶体结构。将汉密尔顿的变分原理应用于动力学分析,以得出控制方程的弱形式。耦合特征值问题是通过考虑在没有外部负载的情况下的谐波振动问题来制定的。使用球形薄壳基准对纯弹性表壳的配方进行了验证。之后,分析和评估了横观各向同性弯曲板的压电效应和振动模式,以解决Scordelis-Lo屋顶问题。最后,压电扬声器外壳结构的CAD模型的特征值分析显示了所提出的方法处理复杂几何形状的能力。
更新日期:2021-05-20
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