Novel Numerical Approach for Free Vibration of Nanocomposite Joined Conical-Cylindrical-Conical Shells

The free vibration of conical-cylindrical shells made of carbon nanotube (CNT) reinforced to polymer is investigated by a semi-analytical method based on the theory of Donnell type with a moderately large deformation. The uniform and functionally graded CNTs are used to reinforce through the thickness of the shells. An exact power series solution using the regression formulas (TRF) is chosen to solve the equations of motion, and then boundary and continuity conditions is utilized to obtain the algebraic equations; therefore the fundamental frequencies are found. The accuracy of the method depends on the number of terms of the solution and the error of the computer. The codes of Wolfram Mathematica and MATLAB software are built to give the optimization of the results of the problem. The obtained results are compared with the previous results for the models including cylindrical shells, conical shells, and conical-cylindrical shells. Furthermore, the obtained results have good agreement with the experimental and Finite Element Analysis (FEA) results. The effects of geometrical parameters and material characteristics are carefully taken into account in the present study. The obtained results can be used as benchmark solutions for serving in further research and have the valuable applications in submarine shell, UAV, shells in the aerospace and civil engineering.

Automated summary

The free vibration of conical-cylindrical shells reinforced with carbon nanotube-polymer composites is studied using a semi-analytical method. An exact power series solution and regression formulas are used to determine the fundamental frequencies. The accuracy and reliability of the method are validated by comparing results with previous studies.