The stiffening effects on the natural frequencies of laminated beams
with piezoelectric actuators are investigated theoretically. A simple
two-dimensional model is developed and the closed-form solutions are
obtained. The applied voltage, the center locations and lengths of actuators,boundary conditions are discussed in order to piezoelectrically tune the natural frequencies effectively and efficiently. The results reveal that the piezoelectric actuators with positive voltage applied should be placed in regions of high shear to increase natural frequencies. The piezoelectric actuators with negative voltage applied should be placed in regions of high bending to decrease natural frequencies.