TY  - JOUR
AU  - Cluni, Federico
AU  - Gusella, Vittorio
AU  - Mugnai, Dimitri
AU  - Lippi, Edoardo Proietti
AU  - Pucci, Patrizia
PY  - 2025
TI  - Modal characteristics and evolutive response of a bar in peridynamics involving a mixed operator
JO  - AIMS Mathematics
SP  - 9435
EP  - 9461
VL  - 10
IS  - 4
AB  - The paper first gives a rigorous proof of existence and highlights proprieties of the eigenvalues and eigenfunctions for a bounded body with peridynamical Dirichlet boundary conditions. In particular, the mechanical behavior of the body is described by mixed local and nonlocal operators where, for the latter, the regional fractional Laplacian is used. The dynamics of the1-dimensional case is thereafter analyzed. More precisely, the previous results are applied to analyze the evolutionary problem which corresponds to free oscillations of a bar taking also into account the damping effects. A peculiar numerical approach is finally proposed to solve both the eigenvalue problem and the time evolution problem. Comparisons with classical local models and super- and sub-critical behaviors are highlighted.
UR  - https://doi.org/10.3934/math.2025436
DO  - 10.3934/math.2025436