An elastic beam system formulated by partial
differential equations with initial and boundary conditions is investigated in
this paper. An evolution equation corresponding with the beam system
is established in an appropriate Hilbert space. The spectral analysis and semigroup
generation of the system operator of the beam system are discussed. Finally, a
variable structural control is proposed and a significant result that the
solution of the system is exponentially stable under a variable structural
control with some appropriate conditions is obtained.