Abstract: This paper deals with the vibration of the beam with an attached constrained damping layer. Firstly, in the displacement modeling,the transverse shear effect of the attachment on the beam structure is considered,and its displacement is treated as the composition of the base movement and its relative motion to the base. Then,the vibration equaiton and the boundary conditions are given. Through the natural vibration analysis of a simply supported beam with the attached constrained viscoelastic damping layer, the interaction between the axial vibration, the transverse shear vibration and the bending vibration si discussed. Finally,an effective fomula of complex bending rigidity is derived according to the solution in the simply supported state. It is proved by the numerical examples that this formula possesses higher computational precision than the others.

Key words: constrained damping layer, vibration of beam, viscoelast icity