Nonlinear Modeling and Experimental Analysis of Vertically Aligned Carbon Nanotube Pads Under Uniaxial Compressive Loading

There have been a variety of attempts to model the quasi-static and high energy impact dynamics of vertically aligned carbon nanotube (VACNT) pads. However, very little work has focused on identifying the behavior at the midlevel frequencies that may occur in materials handling or vibration suppression applications. Moreover, the existing models are predominantly very complex, and yet provide only a very rough approximation of the bulk behavior. While several of the existing models make attempts at ascribing physical relevance, an adequate first principles approach has yet to be demonstrated. In this work, a close-fitting continuous model of these midfrequency dynamics is developed utilizing a combination of phenomenological- and identification-based methodologies. First, a set of specially fabricated carbon nanotube pads are preconditioned and subjected to various position-controlled compression experiments. The measured position and force responses are used to develop load–displacement curves, from which several characteristic features are identified. Based on these observations, a preliminary version of the proposed model is introduced. This simplified model is then systematically refined in order to demonstrate completely both the modeling approach and parameter identification scheme. The accuracy of the model is demonstrated through a comparison between the modeled and experimental responses including a normalized vector correlation of >0.998 across all sets of sinusoidal experimental data. A brief analysis utilizing a Lyapunov linearization approach follows, as well as a discussion of the advantages and limitations of the final model.