Transient behavior of a few dies on an elastic half-space


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An asymptotic approach to dynamic interaction between a few distant dies and an elastic half-space is proposed. The transient motion of the dies under low-frequency vertical load is under consideration. The explicit expression for the fundamental singular solution of Lamb's problem is used to derive the boundary integral equation of contact. Then this equation is asymptotically simplified and solved numerically in combination with equations of motion of the dies.

Equations obtained in the asymptotic limit describe both the die-medium dynamic interaction and the interaction between dies through the elastic medium. These equations take into account the energy dissipation phenomenon associated with energy transfer deep into the medium by outgoing elastic waves, of so called geometrical damping.

Equations proposed are asymptotically correct within the corresponding range of parameters, as such improving the state-of-the-art.
Original languageEnglish
Pages (from-to)185-195
Number of pages11
JournalActa Mechanica
Issue number3-4
Publication statusPublished - Sept 2000

Bibliographical note

The study has been supported by the Russian Foundation of Basic Research through Grant No. 99-01-00694.


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