An asymptotic model of vibroadhesion

A compliantly fixed hemispherical indenter in adhesive contact with an elastic sample firmly bonded to a rigid base is considered under the assumption that the rigid base undergoes small-amplitude high-frequency normal (vertical) oscillations. A general law of the rate-dependent JKR-type adhesion is assumed, which relates the work of adhesion to the contact front velocity. Using the Bogoliubov averaging approach in combination with the method of harmonic balance, the leading-order asymptotic model is constructed for steady-state vibrations. The effective work of adhesion is evaluated in implicit form. A quasi-static approximation for the pull-off force is derived. The case of rigid fixation of the indenter is considered in detail.