Parameter Sensitivity Analysis of Piezoelectrically-Actuated Flexural/Torsional Vibrating Beams

A numerical parameter sensitivity analysis is performed on the bending and torsional vibrations of a flexural-torsional vibrating beam gyroscope model. The gyroscope analyzed in this work is comprised of a rotating cantilever beam with a point-mass attached to its free end and a piezoelectric actuator fixed to a portion of its length. The governing equations of motion are derived using extended Hamilton’s principle and the steady-state magnitude response of the system is obtained through frequency domain methods. A sensitivity analysis is then carried out for the parameters including rotational speed of the base, the length of the beam, the location of the piezoelectric patch, and the location of the added point mass along the beam’s length. It is observed that, in the region surrounding specific configurations, small variations in the rotation rate, beam length and the location of the piezoelectric patch will result in significant changes to the amplitudes of the coupled vibrations and produce peaks in the sensitivity curves. Further, the amplitude of vibration tends to increase as the location of the added point-mass is moved closer to the free end. Generally, the bending modes are more sensitive to all of these parameter variations than are the torsional modes.