根据Catmull-Clark分区表面对Piizower Kirchhoff-love Shells的振动分析 (Vibration Analysis of Piezoelectric Kirchhoff-Love Shells based on Catmull-Clark Subdivision Surfaces)

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.

翻译：演示了用于分析花电贝壳自由振动的等离子测量 Galerkin 方法。贝壳运动学专门针对极微变形, 并遵循Kirchhoff- love 假设。几何和物理场均使用 Catmull- Clark 亚形基基基基基基点提供所需的 C1 连续分解方法。它为Kirchhoff- Love 理论提供了所需的 C1 连续分解方法。派电材料的晶体结构是使用厌异结构关系来描述的。 Hamilton 的变异原则应用到动态分析中, 以得出调节方形的微弱形式。结合的叶值问题是通过在没有外部负荷的情况下考虑调振动问题来形成的。纯弹性案件的配方是使用球状的薄壳基准加以验证的。随后, 将分析并评估反向异形异体曲线曲线板的振动模式。最后, 将分析并评估出一个顶层声标结构结构的CAD模型的二等值分析。最后, 展示了拟议地质处理方法的能力。