On the problems of controllability and uncontrollability for some mechanical systems described by the equations of vibrations of plates and beams with integral memory

Abstract

Controllability problems for some models of plates and beams with integral memory are considered. The vibrational equation of the plate contains an Abelian kernel in the integral term, and the vibrational equation of the beam contains a continuous kernel consisting of a finite sum of decreasing exponential functions. It is proved that by controlling the whole domain, the first system cannot be driven to a state of rest, and for the second system, controllability to rest is possible.