Nonlinear vibration analysis of FG porous shear deformable cylindrical shells covered by CNTs-reinforced nanocomposite layers considering neutral surface exact position

This paper presents nonlinear vibration analysis of a composite cylindrical shell. The core of the shell is made of functionally graded (FG) porous materials and layers is fabricated of carbon nanotubes (CNTs) reinforced nanocomposites. To increase the accuracy of results, neutral surface position is considered. First-order shear deformation theory is used as displacement field to derive the basic relations of equation motions. In addition, von-Karman nonlinear strains are employed to account geometric nonlinearity and to enhance the results' precision, the exact position of the neutral surface is considered. To governing the partial equations of motion, the Hamilton's principle is used. To reduce the equation motions into a nonlinear motion equation, the Galerkin's approach is employed. After that the nonlinear motion equation is solved by multiple scales method. Effect of various parameters such as volume fraction and distribution of CNTs along the thickness directions, different patterns and efficiency coefficients of porous materials, geometric characteristics and initial conditions on nonlinear to linear ratio of frequency is investigated.