The spectrum of natural oscillations of an array of micro- or nanospheres on an elastic substrate

Abstract

EREMEYEV et al. elastic shells of thickness h and radius R are attached (Fig. 1). We assume that the shells are attached to the plate (substrate) at the points x= xk, y= yk (k= 1, 2,... n). The spherical shells are considered as membranes loaded by a uniform internal hydrostatic pressure p. In the equilibrium state, the force resultants acting on the shell surface is everywhere the same: N1= N2= N= pR/2. This N value is in fact the surface tension, and the whole membrane can be considered as a spherical shell of equal ...