Abstract
We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of mass density inhomogeneity is the same as the order of stiffness inhomogeneity, with heavier part being softer. The limit problem for high frequency approximations depends nonlinearly on the spectral parameter. The quantization of the spectral semiaxis is applied in order to get a close approximations of eigenvalues as well as eigenfunctions for the prime problem under perturbation.
| Original language | English |
|---|---|
| Pages (from-to) | 1860-1867 |
| Number of pages | 8 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 234 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 15 Jul 2010 |
| Event | 8th International Conference on Mathematical and Numerical Aspects of Waves - Reading, UK United Kingdom Duration: 23 Jul 2007 → 27 Jul 2007 |
Keywords
- quantization
- WKB method
- eigenfunction approximation
- mass perturbation
- stiff problem
- high frequency