### ASA 127th Meeting M.I.T. 1994 June 6-10

## 5pSA9. Resonance oscillations of infinite and finite elastic structures
with inclusions.

**A. K. Abramian
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V. L. Andreyev
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D. A. Indejtchev
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*Acad. of Sci. of Russia, St. Petersburg
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Inst. for Problems of Mech. Eng., Bolshoy 61 V.O., St. Petersburg 199178,
Russia
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It has been found that by the type of a system operator and type of
inclusions the discrete spectrum may lie above the cutoff frequency of the
continuous spectrum as well as below it. It is shown that the standing modes
located in the inclusions region are caused by the trapping modes effect.
Necessary and sufficient conditions for low-and high-frequency trapping modes
were found. The discrete spectrum shifts to the continuous spectrum axis and
initiation of high-frequency trapping modes is accompanied by a phenomenon of
traveling waves damping. Special attention is paid at the advance of vibration
through hydroelastic systems. Despite this, the problem of the effect of
symmetry of a structure on the initiation of high-frequency trapping modes is
studied. Some natural frequencies of finite structures are equal to discrete
frequencies of the similar infinite structures. A peculiarity of the emergence
of these frequencies of the finite structures is that the frequencies are
multiples of two (in case of one-dimensional structures).