Analysis and design of doubly curved piezoelectric strip-actuated aperture antennas

Aperture antennas that have the ability to change their reflector shape through the use of piezoelectric actuators have been studied. The results show that those antennas can exhibit beam steering and beam shaping in the far field. However, many of the previous studies have been confined to cylindrical shape antennas. This study examines the use of “doubly curved” antenna structures to achieve better performance in controlling an antenna´s coverage area. The spherical antenna is modeled as a shallow spherical shelf with a small hole at the apex for mounting. Following Reissner´s (1959) approach, a stress function is introduced and two governing equations are derived in terms of the stress function and the axial deflection. Next, the surface deflections are evaluated from the calculated stress function and the axial deflection. As actuators, four lead-zirconate-titanate (PZT) thunder actuators are attached along the meridians separated by 90°, respectively. The forces developed by the actuators are expanded in a Fourier series and fed into the governing equations as boundary conditions at the outer edge. Finally, the deflection versus applied voltage is calculated analytically and its effect on the far-field-radiation is given