  We consider a single electron transistor where the central island can
oscillate. It has been shown that for weak coupling of the elastic and electric
degrees of freedom the position of the island fluctuates with a small variation
of the current through the device. In this paper we consider the strong
coupling limit. We show that the system undergoes a static mechanical
instability that is responsible for the opening of a gap in the current voltage
characteristics even at the degeneracy point. We provide an analytical
description of the transition point. We also discuss how the mechanical nature
of the suppression of the current can be probed experimentally by a slow
modulation of the gate voltage.
