Free vibration analysis of smart laminated carbon nanotube-reinforced composite cylindrical shells with various boundary conditions in hygrothermal environments

Free vibration analysis is carried out for piezoelectric coupled carbon nanotube (CNT)-reinforced composite cylindrical shells with the influences of various boundary conditions and hygrothermal environmental conditions for the first time. A simple and effective non-iterative mathematical method is used to calculate the natural frequencies. The equilibrium equations of motion are obtained based on the first-order shear deformation shell theory with the coupling effects of piezoelectricity, temperature, and moisture, respectively based on the Maxwell equation, the Fourier heat conduction equation, and the Fickian moisture diffusion equation. The MoriTanaka micromechanics model is used to estimate the resulting material properties for a composite shell reinforced with CNTs. Presented methodology and attained results are validated with the existing results in the literature. The effects of the boundary conditions, lamination stacking sequence, volume fraction and orientation of CNTs, piezoelectricity, and geometry of the shell on the natural frequencies of the shell are investigated. A moderate effect of temperature/moisture variation on the natural frequencies is also observed. It is found that the influence of structural boundary conditions is more significant at higher CNT volume fractions and for thicker and shorter shells, and the piezoelectricity effect is more obvious at higher circumferential mode. The model and results presented in this study can be utilized to determine vibration characteristics of smart CNT-reinforced composites subjected to hygrothermal loading as well as mechanical loading.