Free vibration analysis of FGP complex shells with variable thickness

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Document Type : Research Article

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Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

Free vibrations of the cylindrical-hemispherical shell made of functionally graded porous materials with variable thickness are investigated in the cylindrical coordinate system. In this study, two boundary conditions is examined. The first B.C is assumed free-free and second B.C is considered clamped-free in cylindrical and hemispherical, respectively. The present analysis is based on three-dimensional elasticity relations and the Ritz method, using orthogonal polynomials such as Legendre as admissible functions. Convergence of results for natural frequencies is shown. The results were compared with the previous results of the finite element method and analytical studies. After confirming the accuracy of the results by adding the porosity effect, its effect on the frequency of the hemispherical-cylindrical shell was investigated. The results show that the shell frequency decreased with an increase in the porosity coefficient. Natural frequencies were obtained with different geometric parameters. Finally, the results show that the porosity coefficient and geometric parameters have a significant effect on the natural frequency of the porous complex shells. The results show that torsional modes (n=0^T) and axisymmetric modes (n=0^A) play a more important role in clamped-free B.C compared to free-free B.C. Decreasing the thickness generally decreases the frequencies in all modes. Also, it can be seen that with the increase of the porosity coefficient in the cylindrical-hemispherical shell due to the decrease in stiffness, the frequencies decrease in all modes.

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AUT Journal of Mechanical Engineering

Articles in Press, Accepted Manuscript
Available Online from 11 January 2025

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