Transient analysis and free vibration of functionally graded truncated conical shells subjected to moving pressure

In this paper an efficient and accurate solution method is developed for transient analysis and free vibration of functionally graded truncated conical shell, subjected to symmetric internal or external moving pressure. The material properties of the shell are graded continuously in the radial direction according to a Mori-Tanaka and volume fraction power-law distribution. A hybrid solution method composed of the layerwise theory, differential quadrature method, and Fourier series expansion is employed to investigate the aforementioned problem. A Fourier series expansion is used for the displacement components and dynamic pressure in the axial direction. Then the layerwise theory across the thickness direction in conjunction with the Hamilton’s principle is employed to obtain equations of motion and boundary conditions. Eventually, the differential quadrature method is implemented to discretize the governing equations in the time domain. This research shows some interesting results that can be helpful for design of functionally graded shells subjected to moving pressure. The developed results are successfully compared with the available results in the literature. The convergence study demonstrate the fast convergence rate with relatively low computational cost. The results reveal that a free vibration with significant amplitude is generated due to excitation from transition of the moving pressure. Also increasing the area of moving pressure in the case of constant load magnitude leads to reducing in the magnitudes of displacements and stresses components.