基于Catmull-Clark细分曲面的压电Kirchhoff-Love壳振动分析
Vibration Analysis of Piezoelectric Kirchhoff-Love Shells based on Catmull-Clark Subdivision Surfaces
摘要：
本文提出了一种分析压电壳体自由振动的等几何伽辽金方法。壳运动学是专门为无穷小的变形，并遵循基尔霍夫-洛夫假设。几何和物理领域的离散使用Catmull-Clark细分基地。它提供了所需的C1连续离散的基尔霍夫-爱理论。利用各向异性本构关系描述压电材料的晶体结构。应用Hamilton的变分原理进行动力分析，导出了控制方程的弱形式。通过考虑无外载荷时的简谐振动问题，建立了耦合本征值问题。纯弹性的情况下，使用球形薄壳基准验证的配方。然后，对横观各向同性曲板的压电效应和振动模式进行了分析和评价。最后，一个压电扬声器外壳结构的CAD模型的特征值分析展示了所提出的方法来处理复杂的几何形状的能力。
英文摘要：
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.
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