Static and dynamic stabilities of a microbeam actuated by a piezoelectric voltage

In this paper, flutter and divergence instabilities of a cantilever, a clamped–clamped, and a cantilever with intermediate simply-support microbeam sandwiched by piezoelectric layers have been studied. By presenting a mathematical formulation and numerical solution, critical piezoelectric force for avoiding of the instability in a cantilever microbeam has been calculated and validated by known buckling capacity of Beck column. By applying a similar mathematical analysis it has been introduced a critical piezoelectric voltage for a clamped–clamped microbeam. It has been shown that for cantilever microbeams, increasing of the follower piezoelectric force leads to: first flutter and then divergence instabilities whereas in the clamped–clamped microbeams only divergence instability can be occurred. Also effects of the intermediate simply support position on the critical piezoelectric voltage of a cantilever microbeam have been investigated. It has been shown that for case when the intermediate simply support is near to the fixed end of the cantilever increasing of the follower piezoelectric force leads to flutter instability but for case when the intermediate simply support is near to the free end of the cantilever it leads to divergence instability.