Abels, Helmut and Ameismeier, Tobias (2022) Convergence of thin vibrating rods to a linear beam equation. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 73 (4): 166. ISSN 0044-2275, 1420-9039
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We show that solutions for a specifically scaled nonlinear wave equation of nonlinear elasticity converge to solutions of a linear Euler-Bernoulli beam system. We construct an approximation of the solution, using a suitable asymptotic expansion ansatz based upon solutions to the one-dimensional beam equation. Following this, we derive the existence of appropriately scaled initial data and can bound the difference between the analytical solution and the approximating sequence.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | BENDING-TORSION THEORY; NONLINEAR ELASTICITY; INEXTENSIBLE RODS; CURVED RODS; LIMIT; DERIVATION; MODELS; Wave equation; Nonlinear elasticity; Thin rods; Dimension reduction |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Nov 2023 07:55 |
| Last Modified: | 07 Nov 2023 07:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56636 |
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