Free vibration and modal stress analysis of FG-CNTRC beams under hygrothermal conditions using zigzag theory

Abstract

The present study aims to carry out free vibration analysis of functionally graded single-walled carbon nanotube-reinforced composite (FG-CNTRC) beams under hygro-thermal conditions. The study is carried out using the recently proposed C-0 finite element-based higher-order zigzag theory. The study is carried out on five different CNTRC graded beams. Temperature and moisture-dependent material properties are used. Constant temperature or moisture distribution across the thickness of the beam is taken. Hamilton's principle has been used for defining the governing differential equations. Modal stresses are also studied for the first six mode shapes. Stresses at the higher mode of vibration are found to be more affected by temperature or moisture concentration as compared to the stresses observed for the fundamental mode of vibration. It is observed that the nature of stress distribution across the beam is widely affected by the gradation law along with moisture or temperature values to which the beam is subjected. FG-O beam is found to be least sensitive under thermal conditions whereas FG-X beam is found to be the most.