DYNAMIC BEHAVIOR OF CROSS-PLY LAMINATED BEAMS WITH PIEZOELECTRIC LAYERS

The dynamic behavior of cross-ply non-symmetric composite beams, havin g uniform piezoelectric layers is analysed. A first-order Timoshenko t ype analysis is applied to obtain the equations of motion, which inclu de shear deformation, rotary inertia, bending-stretching coupling term s and induced axial strains caused by the piezoelectric material. Usin g the principle of virtual work, the coupled equations of motion and t he relevant boundary conditions are obtained. For a laminated beam hav ing uniform piezoelectric layers the induced strains appear only in th e boundary conditions yielding time dependent ones. Therefore, a speci al procedure involving orthogonality of the coupled Timoshenko type na tural vibrational modes of the beam is applied to help understanding o f the dynamic behavior of the non-symmetric laminated beam and to inve stigate the influence of the induced strains (by the piezoelectric lay ers) on the dynamic behavior while keeping an 'open-loop' control. Typ ical types of laminates and piezoelectric materials are used to calcul ate natural frequencies and mode shapes. Numerical results for various parameters of laminated beams are presented to stress the better appl icability and suitability of the present approach to the analysis of d ynamic behavior of laminated composite beams with piezoelectric layers .