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### Analytical Modeling of Proof-Mass Piezoelectric Wafer Active Sensor for Symmetric Lamb Waves Tuning

#### Abstract

This paper presents theoretical work on proof-mass piezoelectric actuator for tuning the symmetric modes of Lamb wave. In the first part of this study, a simplified three bar piezo-resonator was modeled using the resonator theory. Three bar resonator model includes a piezoelectric wafer active sensor (PWAS) in the center and two isotropic elastic bars bonded on both sides of the PWAS. The following assumptions were made for the three-bar piezo-resonator model. First, the geometry and the cross-section area of all three bars were the same although they have different materials and different lengths. Second, the two isotropic bars were assumed to be perfectly bonded to the PWAS on the interfaces. The three bar piezoresonator model was used to obtain the resonance frequencies for the normal mode expansion method. Essentially, this model was to build the basis for the proof-mass PWAS (PM-PWAS). The study was followed by proof-mass analysis to investigate desired control objectives (such as tuning of axial wave modes) using the correlation between a proof-mass transducer and structural dynamic properties in the substrate structure. The PM-PWAS transducer is configured with a PWAS actuator and proof-mass on top. Proof masses shift system resonance towards optimal frequency point. PM-PWAS transducer attached to an isotropic elastic plate was analytically modeled. A parametric study to indicate effect of the proof-mass size change on mode shapes in relation with frequency response function amplitudes at resonance frequencies. The paper ends with summary, conclusions, and suggestions for future work.