Improved passive shunt vibration control of smart piezo-elastic beams using modal piezoelectric transducers with shaped electrodes

Modal control and spatial filtering technologies for mitigation of vibration and/or structural acoustics radiation may be achieved through the use of distributed modal piezoelectric transducers with properly shaped electrodes. This approach filters out undesirable and uncontrollable modes over the bandwidth of interest in order to increase the robustness and stability of the controlled structural system, and may also yield higher values of the generalized modal electromechanical coupling coefficient, which is an important design parameter for achieving efficient passive shunt damping design. In this paper the improvements in passive shunt damping performance when using modal piezoelectric transducers with shaped electrodes are investigated for a two-layered resonant-shunted piezo-elastic smart beam structure. An electromechanical one-dimensional equivalent single-layer Euler-Bernoulli analytical model of two-layered smart piezo-elastic beams with arbitrary spatially shaped electrodes is established for modal and uniform electrode designs. The model is verified and validated by comparison with a one-dimensional discrete-layer (layerwise) finite element model, the damping performance of the shunted smart beam with shaped electrodes is investigated and assessed in terms of the generalized electromechanical coupling coefficient and frequency responses obtained when considering uniform and modally shaped electrodes and the underlying improved performance and advantages are assessed and discussed.