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Perturbation of eigenvalues in thermoelasticity and vibration of systems with concentrated masses. (English) Zbl 0542.73006
Trends and applications of pure mathematics to mechanics, Symp., Palaiseau/France 1983, Lect. Notes Phys. 195, 346-368 (1984).
[For the entire collection see Zbl 0533.00030.]
The paper examines two problems depending on a small parameter \(\epsilon\). The first problem involves vibrations of a bounded thermoelastic body with \(\epsilon\) denoting the thermal conductivity. For \(\epsilon =0\) the spectrum consists of purely imaginary eigenvalues. The second problem concerns a three dimensional wave equation with density distribution depending on \(\epsilon\). As \(\epsilon \to 0\), the arising vibrations are associated with small eigenvalues.
Reviewer: J.L.Nowinski

MSC:
74F05 Thermal effects in solid mechanics
74A15 Thermodynamics in solid mechanics
74J99 Waves in solid mechanics