Analytic solutions for fundamental eigenfrequencies of optical actuators in six directions of motion

Perhaps, this is the ®rst paper that derives analytic solutions for the fundamental eigenfrequencies in all six directions of motion in optical actuators. The speci®c analysis is conducted for actuators suspended by four cantilevered beams having rectangular bends near the beam ends. While some existing reports consider only one or two translational motions, the present paper considers all six motions including rotational motions. The well-known Castigliano theorem is employed for the prediction of sti€ness in the six directions of motion. The use of simple, approximate deformed shapes for all directions is newly proposed in this work. The correct deformed shapes play a crucial role in the analysis. The validity of the present results is veri®ed by comparison with ®nite element results. As a practical application of the present approach, an optimal suspension beam sizing problem is considered