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- W4376279969 abstract "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 by Alali and Albin (Applicable Analysis 2526–2546, 1). 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." @default.
- W4376279969 created "2023-05-13" @default.
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- W4376279969 date "2023-05-12" @default.
- W4376279969 modified "2023-10-17" @default.
- W4376279969 title "Linear Peridynamics Fourier Multipliers and Eigenvalues" @default.
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- W4376279969 doi "https://doi.org/10.1007/s42102-023-00102-y" @default.
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