Design guidelines on piezoelectric transducers properties for multilayer structures hybrid damping: analytical predictions and experimental comparisons

Multilayer cantilever beams using two stiff skins and a viscoelastic core are known to be efficient passive damping solutions (<i>Ross et al., structural damping, 1959</i>). Combining such a structure with an active damping solution using a piezoelectric transducer to couple mechanical vibration energy and electrical energy can lead to hybrid damping capability or resonance frequency tuning in a limited frequency band. A frequency dependent equivalent dynamic model of a sandwich structure was first theorized by J.L. Guyader et al. (journal of sound and vibration, 1978) and updated to anisotropic multilayer plates by F. Marchetti et al. (<i>journal of sound and vibration, 2020</i>). The resulting frequency-dependent stiffness of the equivalent structures highly influences the optimal electromechanical coupling coefficient of the entire structure. An analytical model has been established from the works of F. Marchetti and a spring-mass model analogy is applied to a cantilever beam instrumented with a piezoceramic transducer in order to predict the coupling coefficient associated with the first vibration mode of the beam. The theoretical predictions are compared to measurements obtained on different mechanically and electrically stimulated cantilever beams made with various materials configurations, transducer configurations and resonance frequencies. This model is used to optimize the electromechanical coupling coefficient for a given sandwich beam thus defining design rules of the piezoelectric transducer configuration in order to optimize damping or tuning.