Size-dependent vibration behavior of functionally graded CNT-Reinforced polymer microcantilevers: Modeling and optimization

• Concept of axially FGMs is applied to MWCNT-reinforced polymer microcantilevers.
• Their highest natural frequencies are analytically obtained for a given amount of MWCNTs.
• A two-fold improvement in the relative change of natural frequencies is achieved by adopting the proposed optimum CNT dispersion pattern.

Based on the modified couple stress theory, the free vibration behavior of micro scale Bernoulli–Euler nanocomposite cantilever beams is analytically investigated by introducing a material length scale parameter. The mechanical properties of polymer composite micro-beams reinforced by multi-walled carbon nanotubes (MWCNTs) are assumed to vary continuously in the longitudinal direction of the beam. A new exponential distribution of the volume fraction of the constituents is proposed to achieve the beam's highest fundamental natural frequency given a weight percent (wt.%) of MWCNTs. The effect of the material length scale parameter on the fundamental natural frequency of the ensuing axially functionally graded (FG) composite micro-beam is investigated for various CNT gradient indices. The difference between the frequencies, predicted by the modified couple stress theory and the classical continuum mechanics theory is considerable when the ratio of the beam thickness to the internal material length scale is approximately less than two. It is also observed that with a 1.0 wt.% addition of MWCNTs to the polymer-based microcantilevers, almost a two-fold improvement in the relative change of the fundamental natural frequency is achieved by adopting the proposed optimum CNT dispersion pattern rather than the commonly used uniform CNT distribution pattern.