IOP PUBLISHING SMART MATERIALS AND STRUCTURES Smart Mater. Struct. 16 (2007) 1043–1049 doi:10.1088/0964-1726/16/4/012 A material rigidity effect of a bimorph piezoelectric actuator Dong-chan Lee 1,2,3 , Deok-won Yun 1 and Chang-soo Han 1,3 1 Department of Mechanical Engineering, Hanyang University, Sa-1 dong, Sangnok-gu, Ansan, Kyeonggi-do 425-791, Korea 2 CAE Consulting Team, SPACE Solution, Korea E-mail: dclee@engspace.com and cshan@hanyang.ac.kr Received 4 August 2006, in final form 25 April 2007 Published 5 June 2007 Online at stacks.iop.org/SMS/16/1043 Abstract This paper presents the numerical modeling of a piezoelectric actuator used to avoid the limitation of the lock-in region in a ring resonator. Ring resonators have proved suitable for use as inertial sensors for navigation, guidance and attitude controls. However, their accuracy has been limited by the lock-in region due to frequency coupling between two counter-propagating waves at low rotation rates. This coupling introduces no phase difference, and no angular increment is detected. The problem can be overcome by mechanically dithering the ring resonator. Mechanically, the vibro-elastic bimorph piezoelectric actuator has been used as a control but is influenced by piezoelectric rigidity effects. To more accurately predict the dithering frequency of a mechanical dither, numerical modeling of a piezoelectric actuator includes the piezoelectric rigidity effect of the actuator, which occurs in both the static and dynamic behaviors of composite plates having piezoelectric layers symmetrically bonded to the top and bottom surfaces. (Some figures in this article are in colour only in the electronic version) 1. Introduction Ring lasers have been investigated in order to ascertain their suitability for use as rotation rate sensors. When there is an applied rotation about the axis normal to the plane of rotation, the operation of a gyroscope depends on the phase difference for beams traveling in opposite directions within a closed path. However, the accuracy of gyroscopes has been limited by the lock-in region due to the fact that at low rotation rates of gyroscope the frequency coupling mechanism arises from backscattering of the mirrors. This effect gives no phase difference and hence no detect of angular increment. In other words, this reduces the angular sensitivities to the electrical and mechanical disturbances, such as low frequency noise components, in the optical measurement. It is important to minimize the transition period of the lock-in region in the beam traveling path. A good laser gyro consists of mirrors with low backscatter in conjunction with a stable gas discharge, a suitable dither drive and a stabilized resonator cavity length in order to avoid temperature effects. Under the temperature 3 Authors to whom any correspondence should be addressed. effects, a change of the beam path geometry increases the lock- in threshold. It is very important to stabilize the beam path geometry during the operations. By using the piezoelectric mirror, it was possible to change the beam path geometry inside the laser cavity with extreme precision [1, 2]. After avoiding of the lock-in effect [3–5], the interests involved in the development design of ring resonator began to concentrate on the practical solution of stabilizing the beam path [6–10]. The purpose of the mechanical dithering is to suppress the dead band, oscillate the block about the rotation axis, and add an external rotation rate. The following describes the design considerations. The systematic considerations for the gyroscope; • Structural resonant frequency • Peak angular amplitude and peak dither rate • Mechanical properties of piezoelectric actuator material (choice of material) • Driving technique • Inertia of dithered components. 0964-1726/07/041043+07$30.00 © 2007 IOP Publishing Ltd Printed in the UK 1043