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Oscillation of a Punch Moving on the Free Surface of an Elastic Half Space

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Abstract

The contact problem concerning oscillation of a circular rigid punch, moving uniformly at sub-Rayleigh speed along the surface of an elastic half space, is investigated using a three-dimensional formulation. “Slow” motion of the punch is considered, which implies that the characteristic time for the external loading is much larger than the time interval necessary for shear waves to propagate across the punch. An asymptotic solution for the vertical oscillation of the punch is given. It is shown that the vertical displacement of the punch can approximately be described by the equation of dynamics for a system of one degree of freedom with viscous friction. The dependence of the coefficients for effective viscosity and stiffness, occurring in this equation, on the speed of the punch and Poisson ratio of the half space, is investigated. The solution for the non-stationary problem concerning a suddenly applied moving point load is also obtained, correcting and extending the result known so far.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering RAS, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russia

    S. N. Gavrilov

  2. Faculty of Information Technology and Systems, Dept. of Appl. Math. Analysis, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    G. C. Herman

  3. Shell International E & P, Rijswijk, The Netherlands

    G. C. Herman

Authors
  1. S. N. Gavrilov
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  2. G. C. Herman
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Correspondence to S. N. Gavrilov.

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Mathematics Subject Classifications (2000)

74H10, 74J05, 74M15.

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Gavrilov, S.N., Herman, G.C. Oscillation of a Punch Moving on the Free Surface of an Elastic Half Space. J Elasticity 75, 247–265 (2004). https://doi.org/10.1007/s10659-004-5902-2

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  • DOI: https://doi.org/10.1007/s10659-004-5902-2

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