A stepped beam model is developed to predict analytically the natural frequencies and mode shapes at different piezoelectric sensor/actuator locations. The modal solution obtained by including the inertia and stiffness of the surface-bonded piezoelectric materials is applied to investigate the interaction of structure vibration and piezoelectric actuation under closed circuit condition. It is shown that a generalized stiffness from electromechanical coupling is induced by the interaction. The generalized stiffness is a function of structure mode shapes and piezoelectric sensor/actuator locations, thus either softening or stiffening system stiffness is achievable in closed circuit condition. All analytical predictions are validated by modal testing.
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