Global Optimal Design of Nanomechanical Resonators

Novel nanomechanical resonators with high mass sensitivities are designed in an optimal manner. We are concerned with a nanomechanical resonator with step changes in cross section and determine its geometry so as to maximize its mass sensitivity. Since the mass sensitivity is proportional to the fundamental frequency, we decide the geometric shape so as to maximize the fundamental frequency. In particular, we design a cantilever resonator with a single discontinuity in its cross sectional area. As the design space of this design problem is decided by the volume of the resonator, we synthesize it for various prescribed volume constraints. The fundamental frequency is estimated based on the Euler-Bernoulli beam theory. We discovered that there is a unique global optimal solution of this design problem that does not depend on the given volume constraints. The mass sensitivity of optimally designed cantilever resonators is 1.9193 times greater than that of conventional uniform beam type resonators that are designed for the same volume. Consequently, the mass sensitivity of a nanomechanical uniform resonator of constant volume can always be enhanced without regard to its global size by modifying its geometry following the optimal design proposed in this paper.