165Friction-Induced Instabilities and Vibrations
6.4.3.9 Discussion
As described in the previous section, Nosonovsky and Adams (2004) mod-
eled roughness of the surfaces by a periodic wavy surface on one of the bod-
ies. The contact occurs at periodically spaced contact regions on the peaks
of the wavy asperities. The length of the contact regions is known from the
solution of the steady-state problem; then the stability of sliding was ana-
lyzed. The overall solution was sought in the form of a superposition of the
steady-state solution and small vibrations. Using a Fourier series representa-
tion for the vibration modes, the dynamic problem was reduced to a singular
integral equation for determining the eigenvectors (modes) and eigenvalues
(