Three-dimensional isogeometric model for nonlinear vibration analysis of graded inhomogeneous nanocomposite plates with inconstant thickness

Abstract

The current investigation intends, for the first time, to devise a three-dimensional plate model incorporating nonlinear Green-Lagrange strain tensor to analyze geometrical nonlinear oscillations of large-deflected functionally graded carbon nanotube (FG-CNT)-reinforced nanocomposite plates with dissimilar geometries and inconstant thickness. With the aid of isogeometric method and using desired polynomial type of B-spline basis functions, geometrical description in conjunction with large lateral deflection was accurately taken into consideration. Four different patterns of CNT reinforcement decorations were exploited, and their effectual mechanical characteristics were extracted using an extensive form of mixture rule. Additionally, it was assumed that plate thickness varied based on three different ventures including linear, convex, and concave ones. It was observed that by changing thickness variability venture from convex to concave, the role of CNT volume fraction on the nonlinear three-dimensional free oscillation feedback of FG-CNT-reinforced nanocomposite plates became more significant. This anticipation was duplicated for both types of plate boundary supports. Furthermore, it was shown that by changing thickness variability venture from linear to convex, the value of three-dimensional nonlinear frequency was reduced. However, by changing thickness variability venture from linear to concave, the three-dimensional nonlinear frequency of the system was increased.