Modal control of piezolaminated anisotropic rectangular plates. I - Modal transducer theory

Selective modal transducers are developed for piezolaminated anisotropic plate systems that are capable of sensing and exciting any specified set of vibrational modes according to a specified set of modal participation factors. Transduction of selected modes is accomplished through combining the effect of three piezolaminate pairs whose piezoelectric fields are varied spatially. Each coupled pair contains a single layer located anywhere strictly above the reference plane, which is complemented by a second layer colocated below the reference plane. Piezoelectric constitutive properties associated with each layer in a given couple must be identical, whereas the constitutive properties of all three couples must be uniquely different. If all selective modal transducer layers are formed from the same stock material, the stock material must be piezoelectrically biaxial and the skew angles of all couples must be unique. Individual actuator inputs must be proportional to a common control function or, conversely, the sensed output must be a weighted sum of the measurements acquired by individual layers. An algorithm is presented that dictates how the piezoelectric field strength of each selective modal transducer layer must be varied spatially and is an explicit function of piezoelectric constants, mode shapes, and designer-chosen modal participation factors. Selective modal transducers for orthotropic systems are shown to require three piezolaminate layers rather than three coupled pairs.

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