Vibrations of a damageable string. (English) Zbl 1297.74053
Botelho, Fernanda (ed.) et al., Fluids and waves. Recent trends in applied analysis. Research conference, May 11–13, 2006, The University of Memphis, Memphis, TN, USA. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4247-8/pbk). Contemporary Mathematics 440, 1-13 (2007).
Summary: This work models and numerically simulates the vibrations of a string when the evolution of its material damage is taken into account. The model consists of the hyperbolic equation of motion coupled with a parabolic inclusion which gives the evolution of damage. The existence of a unique weak solution is established to a regularized and truncated problem. The evolution of the system is numerically simulated, using an explicit finite differences scheme. The simulation provides insight into the conditions and manner under which complete damage occurs.
For the entire collection see [Zbl 1121.76002].
For the entire collection see [Zbl 1121.76002].
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K05 | Strings |
| 74R05 | Brittle damage |
| 74H20 | Existence of solutions of dynamical problems in solid mechanics |
| 74S20 | Finite difference methods applied to problems in solid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
