Bending and twisting vibration control of flexible structures using piezoelectric materials

A number of thin structural elements such as plates, shells, beams, and panels experience both bending and twisting vibration in response to external loadings. To control the vibration and reject disturbances, structural excitation is produced by actuators according to a control law. Of primary importance is the ability to actuate all types of vibration observed (bending, twisting, in-plane, etc.), since observed modes that cannot be actuated can lead to instability. In this paper, possible ways to actuate both bending and twisting are discussed, including structural coupling through the use of orthotropic materials, orthotropic actuators, external masses or stores attached to the structure, and directionally attached piezoelectrics. The importance of having sensors with suitable material symmetry is reviewed. Examples are given on how to excite plate bending and twisting as well as on how to suppress vibration in a beam with structural and/or mass coupling that links bending and twisting.