Uncertain frequency responses of CNT – reinforced polymeric graded structure using fuzzified elastic properties – fuzzy finite element approach

A novel fuzzy finite element computational model is prepared to predict the frequency responses of the functionally graded carbon nanotube (FG-CNT) reinforced composite panel structure. The nanotube distributions in the matrix have an affinity towards the agglomeration and affect final properties. The model incurred the fuzzification of elastic properties (E11, E22, G12, and υ12) considering a ±20% as the degree of uncertainty via Mamdani’s fuzzy inference system (FIS). The extended rule of the mixture has been adopted to count the CNT properties for different grading patterns to achieve the realistic one in the framework of the higher-order polynomial model. Further, a set of fuzzy rules have been adopted to count the uncertainty in elastic properties with the help of the design of the experiment (Taguchi-L25 orthogonal array). The equation of motion is derived for the CNT-reinforced composite in association with Hamilton’s principle for the computation of natural frequency. An in-house computer code is derived in MATLAB with the help of a higher-order fuzzified finite element model (FFEM) for the computation. The suitability of the proposed model has been tested by solving a series of numerical examples and the output is discussed in detail.