Modal Analysis Of Stepped Beams With Piezoelectric Materials

A stepped beam model is developed to predict analytically the natural frequencies and mode shapes of a uniform flexible beam with surface bonded piezoelectric materials. The stepped portion includes the inertia and stiffness of the piezoelectric material and bonding layer, and the shear deformation and rotary inertia of the beam are also considered. By using the analytical modal solution, the stepped beam model is further extended to investigate its modal parameter changes under piezoelectric actuation. It is shown that for a length ratio of 16·67 and thickness ratio of four between the beam and piezoelectric material, the first natural frequency can be increased by as much as 5% compared with that of a uniform beam model. In addition, there exists a generalized stiffness from piezoelectric actuation, and it can be either positive or negative, depending on the locations of the piezoelectric actuators. The analytical predictions are verified by experiments.