Vibration of a cantillever beam with extended tip mass and axial load subject to piezoeletric control

Abstract

The effect of piezoelectric control on the frequencies of a cantilever beam with an extended tip mass and axial load is studied. Rotatory inertia of the tip mass as well as the stiffness of piezo layers are taken into account and an analytical solution of the problem is obtained by eigenfunction expansions. Displacement feedback control is implemented by bonding ceramic piezoelectric layers on the top and bottom surfaces of the beam. It is noted that the strains caused by the activated piezoelectric layers manifest themselves as moments at the boundary conditions at the free end. Numerical results indicate that the fundamental frequency of the cantilever beam is effectively modified by piezoelectric control. For a beam with extended tip mass and axial load there is a significant reduction in the fundamental frequency. The reduction in the fundamental frequency is limited under certain end conditions. When the tip mass and axial load are large, the changes in frequency becomes insignificant. The results are useful for the design of vibrating cantilever beams with tip mass and under constant axial load.