Convergence of thin vibrating rods to a linear beam equation
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...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Physik 2022-08, Vol.73 (4), Article 166 |
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| container_title | Zeitschrift für angewandte Mathematik und Physik |
| container_volume | 73 |
| creator | Abels, Helmut Ameismeier, Tobias |
| description | 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. |
| doi_str_mv | 10.1007/s00033-022-01803-y |
| format | Article |
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| subjects | Approximation Asymptotic series Convergence Engineering Euler-Bernoulli beams Exact solutions Mathematical analysis Mathematical Methods in Physics Theoretical and Applied Mechanics Wave equations |
| title | Convergence of thin vibrating rods to a linear beam equation |
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