Uncertainty analysis for wave dispersion behavior of carbon nanotubes embedded in Pasternak-type elastic medium

At nano-scale, the molecular defects and manufacturing tolerances of carbon nanotubes (CNTs) both would introduce inevitable uncertainties. In this paper, a theoretical framework based on interval analysis method is presented to study the wave-dispersion behavior of CNTs embedded in a Pasternak-type elastic medium with uncertain material properties. Different from probabilistic analysis approach, the material properties of CNTs are considered as uncertain-but-bounded variables, which can overcome the massive information required to set up the probabilistic distribution function. Based on the nonlocal Timoshenko beam theory, the wave-dispersion relationship of the embedded CNTs is derived. The upper and lower bounds of the wave frequencies are predicted under different elastic foundation and size scale parameters. It is demonstrated that the uncertain material properties have considerable effect on the wave-dispersion behavior of CNTs, and the size scale and elastic medium will also affect the wave-dispersion response of CNTs significantly. The Monte Carlo simulation is also presented to validate the proposed interval analysis method. The numerical results presented in this paper provide useful guidelines for employing CNTs as reinforced fibers to enhance the conventional composite materials.