The effect of elastic point contact and mechanical resonators

摘要

We present a novel analytical treatment of nearfield elasticity effects in mechanical resonator systems, which shows that local strain fields near a point contact can be accounted for by introducing a spring-like contact impedance at appropriate interfaces. We demonstrate via experiment that such effects can cause significant shifts in resonant frequency, and predict that the local displacements give rise to an additional dissipation mechanism which can be significant. The mathematical expressions we obtain are simple enough as to be easily included in traditional engineering models that are typically used to approximate the results one would obtain via true three-dimensional elasticity theory calculations. The effects we describe are scale invariant; we briefly discuss potentially relevant biological, nanomechanical, and large-scale systems.