A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points
A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points
复制标题
具有夹紧点的薄板模态消除和振动限制的边界积分方程方法
DOI：
10.1007/s10444-017-9580-6
复制
发表时间：
2017
影响因子：
1.7
通讯作者：
Laura J. Wendelberger
中科院分区：
文献类型：
--
作者：
A. Lindsay;B. Quaife;Laura J. Wendelberger
我们考虑具有一组离散夹紧点的薄弹性板振动模式的双拉普拉斯特征值问题。开发了一种高阶边界积分方程方法，用于在存在多种二维几何形状的多个局部缺陷的情况下对这些模式进行有效的数值确定。这些缺陷导致特征函数具有弱奇点，可以通过将解分解为格林函数加上平滑正则部分的叠加来解决。该方法应用于各种规则和不规则域，观察到两个关键现象。首先，仔细放置夹紧点可以完全消除特定的特征值，并提出一种操纵刚体振动特性的策略，以便消除不需要的频率。其次，板的夹紧会导致域的划分，从而使振动模式很大程度上限制在某些空间区域。这种数值方法为调整薄弹性板的振动特性提供了一种精密工具。
We consider the bi-Laplacian eigenvalue problem for the modes of vibration of a thin elastic plate with a discrete set of clamped points. A high-order boundary integral equation method is developed for efficient numerical determination of these modes in the presence of multiple localized defects for a wide range of two-dimensional geometries. The defects result in eigenfunctions with a weak singularity that is resolved by decomposing the solution as a superposition of Green’s functions plus a smooth regular part. This method is applied to a variety of regular and irregular domains and two key phenomena are observed. First, careful placement of clamping points can entirely eliminate particular eigenvalues and suggests a strategy for manipulating the vibrational characteristics of rigid bodies so that undesirable frequencies are removed. Second, clamping of the plate can result in partitioning of the domain so that vibrational modes are largely confined to certain spatial regions. This numerical method gives a precision tool for tuning the vibrational characteristics of thin elastic plates.
穿孔板和膜的渐近分析第 2 部分：大孔的静态和动态问题
影响因子：
3.6
作者：
Andrianov I.V;Danishevs’kyy V.V;Kalamkarov A.L.
通讯作者：
Kalamkarov A.L.