Modeling the effect of elastic point contact on dynamic response

We present a general, theoretical model describing the three-dimensional elastic behavior of point contacts. We provide a prescription for employing the model in a variety of physical systems and describe in detail how the model enables the use of lower-dimensional dynamic models while including approximate three-dimensional behavior of elastic point contacts. We conduct a series of experiments to validate the model for extensional and cantilever oscillators, and find good agreement between our measurements and the predictions of the model. We observe that the phenomenological effects of elastic point contacts can be significant and believe that our model will be useful to a broad range of research and engineering disciplines.