论文标题
线性peridenicals傅立叶乘数和特征值
Linear peridynamics Fourier multipliers and eigenvalues
论文作者
论文摘要
提供了对线性peridynynamic oberator的傅立叶乘数和特征值的表征。该分析是针对任何空间维度的各向同性均质培养基的基于州的根本动力运算符。我们就空间维度，非局部参数和材料属性为特征值提供了明确的公式。 我们遵循的方法是基于针对非局部laplacian开发的傅立叶乘数分析。线性Peridynynamic运算符的傅立叶乘数是二阶张量场，它们是通过积分表示给出的。结果表明，Peridynynamic运算符的特征值可以直接来自傅立叶乘数张量的特征值。 我们揭示了傅立叶乘数在高几幅函数方面的简单结构，该结构允许提供本特征值的积分表示以及超几何表示。这些表示形式用于显示线性perideNAgic的特征值与线性弹性弹性运算符的特征值的融合，这是在消失的非局部性的极限中的融合。此外，特征值的超几何表示用于计算线性peridensic obletors的光谱。
A characterization for the Fourier multipliers and eigenvalues of linear peridynamic operators is provided. The analysis is presented for state-based peridynamic operators for isotropic homogeneous media in any spatial dimension. We provide explicit formulas for the eigenvalues in terms of the space dimension, the nonlocal parameters, and the material properties. The approach we follow is based on the Fourier multiplier analysis developed for the nonlocal Laplacian. The Fourier multipliers of linear peridynamic operators are second-order tensor fields, which are given through integral representations. It is shown that the eigenvalues of the peridynamic operators can be derived directly from the eigenvalues of the Fourier multiplier tensors. We reveal a simple structure for the Fourier multipliers in terms of hypergeometric functions, which allows for providing integral representations as well as hypergeometric representations of the eigenvalues. These representations are utilized to show the convergence of the eigenvalues of linear peridynamics to the eigenvalues of the Navier operator of linear elasticity in the limit of vanishing nonlocality. Moreover, the hypergeometric representation of the eigenvalues is utilized to compute the spectrum of linear peridynamic operators.
