 
Summary: ISSN 10283358, Doklady Physics, 2006, Vol. 51, No. 5, pp. 268271. © Pleiades Publishing, Inc., 2006.
Original Russian Text © I.I. Argatov, 2006, published in Doklady Akademii Nauk, 2006, Vol. 408, No. 2, pp. 188191.
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The asymptotic solution to the problem is con
structed under the assumption that the contact pressure
under the punch base is slightly varied during the time
of travel of the Rayleigh wave along the distance equal
to the diameter of the contact area. It is assumed that,
during the motion, the contact area is fixed and there is
no friction under the punch base. The construction of
terms of the asymptotic expansion for the contact pres
sure is reduced to the solution of the integral equation
for a quasistatic contact problem.
STATEMENT OF THE PROBLEM
Let 0 < be a small parameter. The contact area
is obtained from domain 1 through 1fold contrac
tion, i.e., = {(x1, x2): 1(x1, x2) 1}. The idea of
extended coordinates x = 1(x1, x2) is widely
exploited in the method of matched asymptotic expan
sions [1]. We require that the diameter of domain 1
