Flexural Vibrations and Resonance of Piezoelectric Cantilevers with a Nonpiezoelectric Extension

A piezoelectric cantilever (PEC) is a flexural transducer consisting of a piezoelectric layer [e.g., lead zirconate titanate (PZT)] bonded to a nonpiezoelectric layer (e.g., stainless steel). A PEC with a thin nonpiezoelectric extension has two distinctive sections, each with a different thickness, different axial density, and elastic-modulus profiles and has been increasingly used as an in-situ biosensor. It has the advantages of dipping only the nonpiezoelectric extension part in an aqueous solution without electrically insulating the piezoelectric section as well as serving as the bonding pad for receptor immobilization. In this study, we examined the effect of the thin nonpiezoelectric extension on the flexural resonance spectrum and resonance vibration waveforms of PEC; in particular, how the length ratio between the piezoelectric section and the nonpiezoelectric extension section affects the resonance frequencies and resonance peak intensities of PEC. Theoretical resonance frequencies and resonance vibration waveforms were obtained using an analytical transcendental equation we derived by solving the flexural wave equation. Both experimental and theoretical results showed that the two-section structure distorted the flexural vibration waveforms from those of PEC without an extension. As a result, the higher-mode resonance peaks of PEC with a nonpiezoelectric extension could be higher than the first resonance peak due to the two-section structure. With PEC that has a piezoelectric section of 0.25-mm thick PZT bonded to 0.07 mm thick stainless steel of various length l
₁
and a 0.07-mm thick nonpiezoelectric extension of length I
₂
, we showed that the first-mode-to-second-mode resonance peak intensity ratio had a maximum of 5.6 at I
₁
/I
₂
= 0.75 and the first-mode- to-second-mode resonance frequency ratio a minimum of 2.2 at I
₁
/I
₂
= 1.8. These findings will undoubtedly help optimize the design and perf