Sanchez-Palencia, E. 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 Cited in 4 ReviewsCited in 35 Documents MSC: 74F05 Thermal effects in solid mechanics 74A15 Thermodynamics in solid mechanics 74J99 Waves in solid mechanics Keywords:perturbation of eigenvalues; systems with concentrated masses; two problems depending on a small parameter; vibrations of a bounded thermoelastic body; three dimensional wave equation Citations:Zbl 0533.00030 PDFBibTeX XML