Determining material stiffness using piezoelectric bimorphs

The dynamic behavior of homogeneous, elastic piezoelectric bimorphs clamped at one end were determined in the case where the tip of the other end of the bimorph was constrained by a Hookean spring of stiffness k. It was found that the frequency at which the bimorph resonated increased by an amount related to k when compared to the case where the end was free. Therefore, a cantilever bimorph provides a technique to assess stiffness of a material by a simple measurement of the resonant frequency. Since the bimorph behavior scales with its geometry, the device can be designed specifically for mechanical measurement of microscopic systems such as living cells and molecules.