Similarity conditions for predicting the effect of carbon nano-tubes on the non-linear frequency of laminated doubly curved shells

Abstract

This paper presents a study of the relationship, based on structural similitude, for predicting the effect of the Carbon Nano-Tubes (CNTs) on the non-linear frequency of cross-ply laminated doubly curved shells. The frequency equation is used directly, to establish the similarity conditions between the two similar systems. The applicability of the small-scale model has recently been demonstrated for predicting the vibration and buckling responses of laminated composite shells and panels. In this study, limitations of previous studies were omitted. Unlike previous researches, it is not necessary to change all geometric dimensions proportionally with each other. The results show that, the scaling law is introduced can predict the results for prototypes with excellent accuracy. The effects of distorted models with relaxations in the CNTs weight percentage, large deflection and the stacking sequence are investigated. According to the results are obtained the models with different CNTs weight percentage, aspect ratio and stacking sequences than the prototypes can be used to predict the non-linear frequency of the prototypes accurately.