Deterministic and stochastic free vibration analysis of CNT reinforced functionally graded cantilever plates

This paper presents both deterministic and stochastic free vibration analyses of carbon nanotube (CNT)-reinforced multi-layered functionally graded material (FGM) cantilever plates. The reinforcement varies linearly following a power-law distribution. The governing equation is derived using the first-order shear deformation theory (FSDT), while the rule of mixtures is applied to determine the effective elastic modulus, mass density, and Poisson's ratio of the CNT-reinforced FGM plate. A finite element-based Monte Carlo simulation (MCS) is employed for the stochastic analysis. The study begins with a validation of the finite element model by comparing the obtained results with existing literature. Subsequently, a parametric investigation is conducted, examining the effects of stochasticity percentage, power law index, plate thickness, volume fraction, temperature, and CNT size. Additionally, mode shapes for the first three vibration modes are plotted. The findings reveal that all these parameters significantly influence the first three natural frequencies.