Quantitative determination of material viscoelasticity using a piezoelectric cantilever bimorph beam

The objective of this paper is to formulate the governing equation of a cantilever bimorph beam associated with a tip mass in contact with a viscoelastic material, which is modeled by a stiffness and a damper in parallel. From the eigenvalue problem, we can obtain the resonant frequencies as functions of the tip mass and material stiffness. The relation between the spectrum and material damping is established by the half-power bandwidth. It is found that the resonant frequencies increase as the material stiffness increases or the tip mass decreases, and the spectrum decreases by increasing the damping. From the analytic results, a cantilever could provide a technique to assess material viscoelasticity by simple measurements of the resonant frequency and the spectrum. Since the cantilever's behavior scales with its geometry, the device can be designed specifically for mechanical measurement of a microscopic system such as living cells and biomaterials.