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ISSN 1028-3358, 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.
 

Summary: ISSN 1028-3358, 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.
268
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 1-fold 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

  

Source: Argatov, Ivan Ivanovich - Institute for Problems in Mechanical Engineering, Russian Academy of Sciences

 

Collections: Mathematics; Engineering