Free vibration analysis of triangular CNT-reinforced composite plates subjected to in-plane stresses using FSDT element-free method

This study conducts the first-known vibration analysis of carbon nanotube (CNT) reinforced functionally graded composite triangular plates subjected to in-plane stresses. The first-order shear deformation theory is applied to study the effect of the transverse shear deformation of the plates and the element-free IMLS-Ritz method is used for numerical computation. Numerical experiments are carried out to examine the convergence and accuracy of the element-free IMLS-Ritz method in its application to the vibration of CNT-reinforced functionally graded composite plates subjected to in-plane stresses. In this study, sets of vibration frequency parameters and mode shapes for various CNT-reinforced functionally graded composite triangular plates are illustrated. The influences of CNT volume fraction, plate thickness-to-width ratio, CNT distribution type, isosceles triangular angle, in-plane stress ratio and boundary conditions on the plate’s vibration behaviors are investigated in detail. These results may serve as a benchmark for future studies.